| intro, Intro | introduction to mathematical library functions and constants |
| sin, cos, tan, asin, atan, atan2, acos | trigonometric functions |
| sincos, sind, cosd, tand, asind, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, acosd | more trigonometric functions |
| sinh, cosh, tanh, asinh, atanh, acosh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, acosp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, atanpi, atan2pi, sincospi, acospi | more trigonometric functions |
| addrans | additive pseudo-random number generators |
| anint, irint, nint, aint | round to integral value in floating-point or integer format |
| aint, irint, nint, anint | round to integral value in floating-point or integer format |
| exp2, exp10, log2, compound, annuity | exponential, logarithm, financial |
| sin, cos, tan, acos, atan, atan2, asin | trigonometric functions |
| sincos, sind, cosd, tand, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, asind | more trigonometric functions |
| sinh, cosh, tanh, acosh, atanh, asinh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, asinp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, acospi, atanpi, atan2pi, sincospi, asinpi | more trigonometric functions |
| sin, cos, tan, asin, acos, atan2, atan | trigonometric functions |
| sin, cos, tan, asin, acos, atan, atan2 | trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, atan2d | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, sincospi, atan2pi | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, atand | more trigonometric functions |
| sinh, cosh, tanh, asinh, acosh, atanh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, atanp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atan2pi, sincospi, atanpi | more trigonometric functions |
| j0, j1, jn, y0, y1, yn, bessel | Bessel functions |
| hypot, cabs | Euclidean distance |
| sqrt, cbrt | square root, cube root |
| floor, rint, ceil | round to integral value in floating-point format |
| fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, class | miscellaneous functions for IEEE arithmetic |
| exp2, exp10, log2, annuity, compound | exponential, logarithm, financial |
| convert_external | convert external binary data formats |
| ilogb, isnan, fabs, finite, fmod, nextafter, remainder, scalbn, copysign | appendix and related miscellaneous functions for IEEE arithmetic |
| sin, tan, asin, acos, atan, atan2, cos | trigonometric functions |
| sincos, sind, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, cosd | more trigonometric functions |
| sinh, tanh, asinh, acosh, atanh, cosh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, cosp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, cospi | more trigonometric functions |
| erfc, erf | error functions |
| erf, erfc | error functions |
| expm1, log, log1p, log10, pow, exp | exponential, logarithm, power |
| exp2, log2, compound, annuity, exp10 | exponential, logarithm, financial |
| exp10, log2, compound, annuity, exp2 | exponential, logarithm, financial |
| exp, log, log1p, log10, pow, expm1 | exponential, logarithm, power |
| ilogb, isnan, copysign, finite, fmod, nextafter, remainder, scalbn, fabs | appendix and related miscellaneous functions for IEEE arithmetic |
| ilogb, isnan, copysign, fabs, fmod, nextafter, remainder, scalbn, finite | appendix and related miscellaneous functions for IEEE arithmetic |
| ceil, rint, floor | round to integral value in floating-point format |
| ilogb, isnan, copysign, fabs, finite, nextafter, remainder, scalbn, fmod | appendix and related miscellaneous functions for IEEE arithmetic |
| isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, fp_class | miscellaneous functions for IEEE arithmetic |
| lgamma, gamma | log gamma function |
| lgamma, gamma, gamma_r | log gamma function |
| sinh, cosh, tanh, asinh, acosh, atanh, hyperbolic | hyperbolic functions |
| hypot | Euclidean distance |
| ieee_flags | mode and status function for IEEE standard arithmetic |
| ilogb, isnan, copysign, fabs, finite, fmod, nextafter, remainder, scalbn, ieee_functions | appendix and related miscellaneous functions for IEEE arithmetic |
| ieee_handler | IEEE exception trap handler function |
| fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective | miscellaneous functions for IEEE arithmetic |
| fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, ieee_sun | miscellaneous functions for IEEE arithmetic |
| logb, scalb, significand, ieee_test | IEEE test functions for verifying standard compliance |
| min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan, ieee_values | functions that return extreme values of IEEE arithmetic |
| isnan, copysign, fabs, finite, fmod, nextafter, remainder, scalbn, ilogb | appendix and related miscellaneous functions for IEEE arithmetic |
| ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, quiet_nan, signaling_nan, infinity | functions that return extreme values of IEEE arithmetic |
| intro | introduction to mathematical library functions and constants |
| aint, anint, nint, irint | round to integral value in floating-point or integer format |
| fp_class, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, isinf | miscellaneous functions for IEEE arithmetic |
| ilogb, copysign, fabs, finite, fmod, nextafter, remainder, scalbn, isnan | appendix and related miscellaneous functions for IEEE arithmetic |
| fp_class, isinf, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, isnormal | miscellaneous functions for IEEE arithmetic |
| fp_class, isinf, isnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, issubnormal | miscellaneous functions for IEEE arithmetic |
| fp_class, isinf, isnormal, issubnormal, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, iszero | miscellaneous functions for IEEE arithmetic |
| j1, jn, y0, y1, yn, j0 | Bessel functions |
| j0, jn, y0, y1, yn, j1 | Bessel functions |
| j0, j1, y0, y1, yn, jn | Bessel functions |
| lcrans | linear congruential pseudo-random number generators |
| gamma, lgamma | log gamma function |
| lgamma, gamma, lgamma_r | log gamma function |
| exp, expm1, log1p, log10, pow, log | exponential, logarithm, power |
| exp, expm1, log, log1p, pow, log10 | exponential, logarithm, power |
| exp, expm1, log, log10, pow, log1p | exponential, logarithm, power |
| exp2, exp10, compound, annuity, log2 | exponential, logarithm, financial |
| scalb, significand, logb | IEEE test functions for verifying standard compliance |
| matherr | math library exception-handling function |
| ieee_values, min_subnormal, max_subnormal, min_normal, infinity, quiet_nan, signaling_nan, max_normal | functions that return extreme values of IEEE arithmetic |
| ieee_values, min_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan, max_subnormal | functions that return extreme values of IEEE arithmetic |
| ieee_values, min_subnormal, max_subnormal, max_normal, infinity, quiet_nan, signaling_nan, min_normal | functions that return extreme values of IEEE arithmetic |
| ieee_values, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan, min_subnormal | functions that return extreme values of IEEE arithmetic |
| ilogb, isnan, copysign, fabs, finite, fmod, remainder, scalbn, nextafter | appendix and related miscellaneous functions for IEEE arithmetic |
| aint, anint, irint, nint | round to integral value in floating-point or integer format |
| fp_class, isinf, isnormal, issubnormal, iszero, signbit, standard_arithmetic, ieee_retrospective, nonstandard_arithmetic | miscellaneous functions for IEEE arithmetic |
| exp, expm1, log, log1p, log10, pow | exponential, logarithm, power |
| quad_precision | Quadruple-precision access to libm and libsunmath functions |
| ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, signaling_nan, quiet_nan | functions that return extreme values of IEEE arithmetic |
| ilogb, isnan, copysign, fabs, finite, fmod, nextafter, scalbn, remainder | appendix and related miscellaneous functions for IEEE arithmetic |
| floor, ceil, rint | round to integral value in floating-point format |
| logb, significand, scalb | IEEE test functions for verifying standard compliance |
| ilogb, isnan, copysign, fabs, finite, fmod, nextafter, remainder, scalbn | appendix and related miscellaneous functions for IEEE arithmetic |
| shufrans | random number shufflers |
| ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan | functions that return extreme values of IEEE arithmetic |
| fp_class, isinf, isnormal, issubnormal, iszero, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective, signbit | miscellaneous functions for IEEE arithmetic |
| logb, scalb, significand | IEEE test functions for verifying standard compliance |
| cos, tan, asin, acos, atan, atan2, sin | trigonometric functions |
| sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sincos | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sincosd | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sincosp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi | more trigonometric functions |
| sincos, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sind | more trigonometric functions |
| single_precision | Single-precision access to libm and libsunmath functions |
| cosh, tanh, asinh, acosh, atanh, sinh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sinp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, sinpi | more trigonometric functions |
| cbrt, sqrt | square root, cube root |
| fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, ieee_retrospective, standard_arithmetic | miscellaneous functions for IEEE arithmetic |
| sin, cos, asin, acos, atan, atan2, tan | trigonometric functions |
| sincos, sind, cosd, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, tand | more trigonometric functions |
| sinh, cosh, asinh, acosh, atanh, tanh | hyperbolic functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, tanp | more trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, asinpi, acospi, atanpi, atan2pi, sincospi, tanpi | more trigonometric functions |
| sin, cos, tan, asin, acos, atan, atan2, trig | trigonometric functions |
| sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi, trig_sun | more trigonometric functions |
| j0, j1, jn, y1, yn, y0 | Bessel functions |
| j0, j1, jn, y0, yn, y1 | Bessel functions |
| j0, j1, jn, y0, y1, yn | Bessel functions |
| CAXPY, caxpy.l | Compute y := alpha ∗ x + y |
| cbdsqr, cbdsqr.l | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| cchdc, cchdc.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| cchdd, cchdd.l | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| cchex, cchex.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| cchud, cchud.l | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| CCOPY, ccopy.l | Copy x to y |
| CDOTU, cdotc.l | Compute the dot product of two vectors x and conjg(y). |
| CDOTU, cdotu.l | Compute the dot product of two vectors x and y. |
| cfftb, cfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| cfftf, cfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| cffti, cffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| cgbbrd, cgbbrd.l | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation |
| cgbco, cgbco.l | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| cgbcon, cgbcon.l | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, |
| cgbdi, cgbdi.l | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. |
| cgbequ, cgbequ.l | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| cgbfa, cgbfa.l | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| cgbmv, cgbmv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y |
| cgbrfs, cgbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution |
| cgbsl, cgbsl.l | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. |
| cgbsv, cgbsv.l | compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices |
| cgbsvx, cgbsvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| cgbtf2, cgbtf2.l | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| cgbtrf, cgbtrf.l | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| cgbtrs, cgbtrs.l | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by CGBTRF |
| cgebak, cgebak.l | form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL |
| cgebal, cgebal.l | balance a general complex matrix A |
| cgebd2, cgebd2.l | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation |
| cgebrd, cgebrd.l | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation |
| cgeco, cgeco.l | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. |
| cgecon, cgecon.l | estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF |
| cgedi, cgedi.l | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. |
| cgeequ, cgeequ.l | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| cgees, cgees.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z |
| cgeesx, cgeesx.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z |
| cgeev, cgeev.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| cgeevx, cgeevx.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| cgefa, cgefa.l | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. |
| cgegs, cgegs.l | compute for a pair of N-by-N complex nonsymmetric matrices A, |
| cgegv, cgegv.l | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, |
| cgehd2, cgehd2.l | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| cgehrd, cgehrd.l | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| cgelq2, cgelq2.l | compute an LQ factorization of a complex m by n matrix A |
| cgelqf, cgelqf.l | compute an LQ factorization of a complex M-by-N matrix A |
| cgels, cgels.l | solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A |
| cgelss, cgelss.l | compute the minimum norm solution to a complex linear least squares problem |
| cgelsx, cgelsx.l | compute the minimum-norm solution to a complex linear least squares problem |
| cgemm, cgemm.l | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C |
| cgemv, cgemv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y |
| cgeql2, cgeql2.l | compute a QL factorization of a complex m by n matrix A |
| cgeqlf, cgeqlf.l | compute a QL factorization of a complex M-by-N matrix A |
| cgeqpf, cgeqpf.l | compute a QR factorization with column pivoting of a complex M-by-N matrix A |
| cgeqr2, cgeqr2.l | compute a QR factorization of a complex m by n matrix A |
| cgeqrf, cgeqrf.l | compute a QR factorization of a complex M-by-N matrix A |
| cgerc, cgerc.l | perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A |
| cgerfs, cgerfs.l | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| cgerq2, cgerq2.l | compute an RQ factorization of a complex m by n matrix A |
| cgerqf, cgerqf.l | compute an RQ factorization of a complex M-by-N matrix A |
| cgeru, cgeru.l | perform the rank 1 operation A := alpha∗x∗y’ + A |
| cgesl, cgesl.l | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. |
| cgesv, cgesv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| cgesvd, cgesvd.l | compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors |
| cgesvx, cgesvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| cgetf2, cgetf2.l | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| cgetrf, cgetrf.l | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| cgetri, cgetri.l | compute the inverse of a matrix using the LU factorization computed by CGETRF |
| cgetrs, cgetrs.l | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF |
| cggbak, cggbak.l | form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL |
| cggbal, cggbal.l | balance a pair of general complex matrices (A,B) |
| cggglm, cggglm.l | solve a general Gauss-Markov linear model (GLM) problem |
| cgghrd, cgghrd.l | reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular |
| cgglse, cgglse.l | solve the linear equality-constrained least squares (LSE) problem |
| cggqrf, cggqrf.l | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| cggrqf, cggrqf.l | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| cggsvd, cggsvd.l | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B |
| cggsvp, cggsvp.l | compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 |
| cgtcon, cgtcon.l | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF |
| cgtrfs, cgtrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution |
| cgtsl, cgtsl.l | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. |
| cgtsv, cgtsv.l | solve the equation A∗X = B, |
| cgtsvx, cgtsvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| cgttrf, cgttrf.l | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| cgttrs, cgttrs.l | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| chbev, chbev.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| chbevd, chbevd.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| chbevx, chbevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| chbgst, chbgst.l | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| chbgv, chbgv.l | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| chbmv, chbmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| chbtrd, chbtrd.l | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| checon, checon.l | estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF |
| cheev, cheev.l | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| cheevd, cheevd.l | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| cheevx, cheevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| chegs2, chegs2.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| chegst, chegst.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| chegv, chegv.l | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| chemm, chemm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| chemv, chemv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| cher, cher.l | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A |
| cher2, cher2.l | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A |
| cher2k, cher2k.l | perform one of the Hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C |
| cherfs, cherfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution |
| cherk, cherk.l | perform one of the Hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C |
| chesv, chesv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| chesvx, chesvx.l | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| chetd2, chetd2.l | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| chetf2, chetf2.l | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| chetrd, chetrd.l | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| chetrf, chetrf.l | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| chetri, chetri.l | compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF |
| chetrs, chetrs.l | solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF |
| chgeqz, chgeqz.l | implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right |
| chico, chico.l | compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. |
| chidi, chidi.l | compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA. |
| chifa, chifa.l | compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. |
| chisl, chisl.l | solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x. |
| chpco, chpco.l | compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. |
| chpcon, chpcon.l | estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF |
| chpdi, chpdi.l | compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA. |
| chpev, chpev.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage |
| chpevd, chpevd.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| chpevx, chpevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| chpfa, chpfa.l | compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. |
| chpgst, chpgst.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage |
| chpgv, chpgv.l | compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| chpmv, chpmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| chpr, chpr.l | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A |
| chpr2, chpr2.l | perform the Hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A |
| chprfs, chprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution |
| chpsl, chpsl.l | solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x. |
| chpsv, chpsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| chpsvx, chpsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices |
| chptrd, chptrd.l | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation |
| chptrf, chptrf.l | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method |
| chptri, chptri.l | compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF |
| chptrs, chptrs.l | solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF |
| chsein, chsein.l | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H |
| chseqr, chseqr.l | compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors |
| clabrd, clabrd.l | reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A |
| clacgv, clacgv.l | conjugate a complex vector of length N |
| clacon, clacon.l | estimate the 1-norm of a square, complex matrix A |
| clacpy, clacpy.l | copie all or part of a two-dimensional matrix A to another matrix B |
| clacrm, clacrm.l | perform a very simple matrix-matrix multiplication |
| clacrt, clacrt.l | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex |
| cladiv, cladiv.l | := X / Y, where X and Y are complex |
| claed0, claed0.l | the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix |
| claed7, claed7.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| claed8, claed8.l | merge the two sets of eigenvalues together into a single sorted set |
| claein, claein.l | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H |
| claesy, claesy.l | compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value |
| claev2, claev2.l | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] |
| clags2, clags2.l | compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), |
| clagtm, clagtm.l | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 |
| clahef, clahef.l | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| clahqr, clahqr.l | i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI |
| clahrd, clahrd.l | reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero |
| claic1, claic1.l | applie one step of incremental condition estimation in its simplest version |
| clangb, clangb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals |
| clange, clange.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A |
| clangt, clangt.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A |
| clanhb, clanhb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals |
| clanhe, clanhe.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A |
| clanhp, clanhp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form |
| clanhs, clanhs.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A |
| clanht, clanht.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A |
| clansb, clansb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals |
| clansp, clansp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form |
| clansy, clansy.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A |
| clantb, clantb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals |
| clantp, clantp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form |
| clantr, clantr.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A |
| clapll, clapll.l | two column vectors X and Y, let A = ( X Y ) |
| clapmt, clapmt.l | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N |
| claqgb, claqgb.l | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C |
| claqge, claqge.l | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| claqhb, claqhb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| claqhe, claqhe.l | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| claqhp, claqhp.l | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| claqsb, claqsb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| claqsp, claqsp.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| claqsy, claqsy.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| clar2v, clar2v.l | applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, |
| clarf, clarf.l | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right |
| clarfb, clarfb.l | applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right |
| clarfg, clarfg.l | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| clarft, clarft.l | form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors |
| clarfx, clarfx.l | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right |
| clargv, clargv.l | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y |
| clarnv, clarnv.l | return a vector of n random complex numbers from a uniform or normal distribution |
| clartg, clartg.l | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] |
| clartv, clartv.l | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y |
| clascl, clascl.l | multiply the M by N complex matrix A by the real scalar CTO/CFROM |
| claset, claset.l | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| clasr, clasr.l | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, |
| classq, classq.l | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| claswp, claswp.l | perform a series of row interchanges on the matrix A |
| clasyf, clasyf.l | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| clatbs, clatbs.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| clatps, clatps.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| clatrd, clatrd.l | reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A |
| clatrs, clatrs.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| clatzm, clatzm.l | applie a Householder matrix generated by CTZRQF to a matrix |
| clauu2, clauu2.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| clauum, clauum.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| cosqb, cosqb.l | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| cosqf, cosqf.l | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| cosqi, cosqi.l | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. |
| cost, cost.l | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. |
| costi, costi.l | initialize the array xWSAVE, which is used in xCOST. |
| cpbco, cpbco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| cpbcon, cpbcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF |
| cpbdi, cpbdi.l | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. |
| cpbequ, cpbequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) |
| cpbfa, cpbfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| cpbrfs, cpbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution |
| cpbsl, cpbsl.l | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. |
| cpbstf, cpbstf.l | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A |
| cpbsv, cpbsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| cpbsvx, cpbsvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| cpbtf2, cpbtf2.l | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| cpbtrf, cpbtrf.l | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| cpbtrs, cpbtrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF |
| cpoco, cpoco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| cpocon, cpocon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF |
| cpodi, cpodi.l | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. |
| cpoequ, cpoequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) |
| cpofa, cpofa.l | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| cporfs, cporfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, |
| cposl, cposl.l | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. |
| cposv, cposv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| cposvx, cposvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| cpotf2, cpotf2.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| cpotrf, cpotrf.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| cpotri, cpotri.l | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF |
| cpotrs, cpotrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF |
| cppco, cppco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| cppcon, cppcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF |
| cppdi, cppdi.l | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. |
| cppequ, cppequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) |
| cppfa, cppfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| cpprfs, cpprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution |
| cppsl, cppsl.l | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. |
| cppsv, cppsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| cppsvx, cppsvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| cpptrf, cpptrf.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format |
| cpptri, cpptri.l | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF |
| cpptrs, cpptrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF |
| cptcon, cptcon.l | compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by CPTTRF |
| cpteqr, cpteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor |
| cptrfs, cptrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution |
| cptsl, cptsl.l | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. |
| cptsv, cptsv.l | compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices |
| cptsvx, cptsvx.l | use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices |
| cpttrf, cpttrf.l | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A |
| cpttrs, cpttrs.l | solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by CPTTRF |
| cqrdc, cqrdc.l | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. |
| cqrsl, cqrsl.l | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. |
| crot, crot.l | apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex |
| CROTG, crotg.l | Construct a Given’s plane rotation |
| CSCAL, cscal.l | Compute y := alpha ∗ y |
| csico, csico.l | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| csidi, csidi.l | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. |
| csifa, csifa.l | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| csisl, csisl.l | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. |
| cspco, cspco.l | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| cspcon, cspcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF |
| cspdi, cspdi.l | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. |
| cspfa, cspfa.l | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| cspmv, cspmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| cspr, cspr.l | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, |
| csprfs, csprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution |
| cspsl, cspsl.l | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. |
| cspsv, cspsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| cspsvx, cspsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices |
| csptrf, csptrf.l | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| csptri, csptri.l | compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF |
| csptrs, csptrs.l | solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF |
| SROT, csrot.l | Apply a Given’s rotation constructed by SROTG. |
| csrscl, csrscl.l | multiply an n-element complex vector x by the real scalar 1/a |
| csscal, csscal.l | Compute y := alpha ∗ y |
| cstedc, cstedc.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| cstein, cstein.l | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| csteqr, csteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| csvdc, csvdc.l | compute the singular value decomposition of a general matrix A. |
| CSWAP, cswap.l | Exchange vectors x and y. |
| csycon, csycon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF |
| csymm, csymm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| csymv, csymv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| csyr, csyr.l | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, |
| csyr2k, csyr2k.l | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C |
| csyrfs, csyrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution |
| csyrk, csyrk.l | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C |
| csysv, csysv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| csysvx, csysvx.l | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| csytf2, csytf2.l | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| csytrf, csytrf.l | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| csytri, csytri.l | compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF |
| csytrs, csytrs.l | solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF |
| ctbcon, ctbcon.l | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| ctbmv, ctbmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ctbrfs, ctbrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| ctbsv, ctbsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ctbtrs, ctbtrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ctgevc, ctgevc.l | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) |
| ctgsja, ctgsja.l | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B |
| ctpcon, ctpcon.l | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| ctpmv, ctpmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ctprfs, ctprfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| ctpsv, ctpsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ctptri, ctptri.l | compute the inverse of a complex upper or lower triangular matrix A stored in packed format |
| ctptrs, ctptrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ctrco, ctrco.l | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. |
| ctrcon, ctrcon.l | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| ctrdi, ctrdi.l | compute the determinant and inverse of a triangular matrix A. |
| ctrevc, ctrevc.l | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T |
| ctrexc, ctrexc.l | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST |
| ctrmm, ctrmm.l | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ ) |
| ctrmv, ctrmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ctrrfs, ctrrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| ctrsen, ctrsen.l | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace |
| ctrsl, ctrsl.l | solve the linear system Ax = b for a triangular matrix A and vectors b and x. |
| ctrsm, ctrsm.l | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B |
| ctrsna, ctrsna.l | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary) |
| ctrsv, ctrsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ctrsyl, ctrsyl.l | solve the complex Sylvester matrix equation |
| ctrti2, ctrti2.l | compute the inverse of a complex upper or lower triangular matrix |
| ctrtri, ctrtri.l | compute the inverse of a complex upper or lower triangular matrix A |
| ctrtrs, ctrtrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ctzrqf, ctzrqf.l | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations |
| cung2l, cung2l.l | generate an m by n complex matrix Q with orthonormal columns, |
| cung2r, cung2r.l | generate an m by n complex matrix Q with orthonormal columns, |
| cungbr, cungbr.l | generate one of the complex unitary matrices Q or P∗∗H determined by CGEBRD when reducing a complex matrix A to bidiagonal form |
| cunghr, cunghr.l | generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD |
| cungl2, cungl2.l | generate an m-by-n complex matrix Q with orthonormal rows, |
| cunglq, cunglq.l | generate an M-by-N complex matrix Q with orthonormal rows, |
| cungql, cungql.l | generate an M-by-N complex matrix Q with orthonormal columns, |
| cungqr, cungqr.l | generate an M-by-N complex matrix Q with orthonormal columns, |
| cungr2, cungr2.l | generate an m by n complex matrix Q with orthonormal rows, |
| cungrq, cungrq.l | generate an M-by-N complex matrix Q with orthonormal rows, |
| cungtr, cungtr.l | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD |
| cunm2l, cunm2l.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| cunm2r, cunm2r.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| cunmbr, cunmbr.l | VECT = ’Q’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunmhr, cunmhr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunml2, cunml2.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| cunmlq, cunmlq.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunmql, cunmql.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunmqr, cunmqr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunmr2, cunmr2.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| cunmrq, cunmrq.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cunmtr, cunmtr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| cupgtr, cupgtr.l | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage |
| cupmtr, cupmtr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DASUM, dasum.l | Return the sum of the absolute values of a vector x. |
| DAXPY, daxpy.l | Compute y := alpha ∗ x + y |
| dbdsqr, dbdsqr.l | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| dchdc, dchdc.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| dchdd, dchdd.l | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| dchex, dchex.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| dchud, dchud.l | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| DCOPY, dcopy.l | Copy x to y |
| dcosqb, dcosqb.l | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| dcosqf, dcosqf.l | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| dcosqi, dcosqi.l | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. |
| dcost, dcost.l | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. |
| dcosti, dcosti.l | initialize the array xWSAVE, which is used in xCOST. |
| ddisna, ddisna.l | compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix |
| DDOT, ddot.l | Compute the dot product of two vectors x and y. |
| dfftb, dfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| dfftf, dfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| dffti, dffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| dgbbrd, dgbbrd.l | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation |
| dgbco, dgbco.l | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| dgbcon, dgbcon.l | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, |
| dgbdi, dgbdi.l | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. |
| dgbequ, dgbequ.l | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| dgbfa, dgbfa.l | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| dgbmv, dgbmv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y |
| dgbrfs, dgbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution |
| dgbsl, dgbsl.l | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. |
| dgbsv, dgbsv.l | compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices |
| dgbsvx, dgbsvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| dgbtf2, dgbtf2.l | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| dgbtrf, dgbtrf.l | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| dgbtrs, dgbtrs.l | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by DGBTRF |
| dgebak, dgebak.l | form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL |
| dgebal, dgebal.l | balance a general real matrix A |
| dgebd2, dgebd2.l | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| dgebrd, dgebrd.l | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| dgeco, dgeco.l | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. |
| dgecon, dgecon.l | estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF |
| dgedi, dgedi.l | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. |
| dgeequ, dgeequ.l | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| dgees, dgees.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z |
| dgeesx, dgeesx.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z |
| dgeev, dgeev.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| dgeevx, dgeevx.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| dgefa, dgefa.l | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. |
| dgegs, dgegs.l | compute for a pair of N-by-N real nonsymmetric matrices A, B |
| dgegv, dgegv.l | compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) |
| dgehd2, dgehd2.l | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| dgehrd, dgehrd.l | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| dgelq2, dgelq2.l | compute an LQ factorization of a real m by n matrix A |
| dgelqf, dgelqf.l | compute an LQ factorization of a real M-by-N matrix A |
| dgels, dgels.l | solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A |
| dgelss, dgelss.l | compute the minimum norm solution to a real linear least squares problem |
| dgelsx, dgelsx.l | compute the minimum-norm solution to a real linear least squares problem |
| dgemm, dgemm.l | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C |
| dgemv, dgemv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y |
| dgeql2, dgeql2.l | compute a QL factorization of a real m by n matrix A |
| dgeqlf, dgeqlf.l | compute a QL factorization of a real M-by-N matrix A |
| dgeqpf, dgeqpf.l | compute a QR factorization with column pivoting of a real M-by-N matrix A |
| dgeqr2, dgeqr2.l | compute a QR factorization of a real m by n matrix A |
| dgeqrf, dgeqrf.l | compute a QR factorization of a real M-by-N matrix A |
| dger, dger.l | perform the rank 1 operation A := alpha∗x∗y’ + A |
| dgerfs, dgerfs.l | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| dgerq2, dgerq2.l | compute an RQ factorization of a real m by n matrix A |
| dgerqf, dgerqf.l | compute an RQ factorization of a real M-by-N matrix A |
| dgesl, dgesl.l | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. |
| dgesv, dgesv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dgesvd, dgesvd.l | compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors |
| dgesvx, dgesvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| dgetf2, dgetf2.l | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| dgetrf, dgetrf.l | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| dgetri, dgetri.l | compute the inverse of a matrix using the LU factorization computed by DGETRF |
| dgetrs, dgetrs.l | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF |
| dggbak, dggbak.l | form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL |
| dggbal, dggbal.l | balance a pair of general real matrices (A,B) |
| dggglm, dggglm.l | solve a general Gauss-Markov linear model (GLM) problem |
| dgghrd, dgghrd.l | reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular |
| dgglse, dgglse.l | solve the linear equality-constrained least squares (LSE) problem |
| dggqrf, dggqrf.l | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| dggrqf, dggrqf.l | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| dggsvd, dggsvd.l | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B |
| dggsvp, dggsvp.l | compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 |
| dgtcon, dgtcon.l | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF |
| dgtrfs, dgtrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution |
| dgtsl, dgtsl.l | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. |
| dgtsv, dgtsv.l | solve the equation A∗X = B, |
| dgtsvx, dgtsvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B, |
| dgttrf, dgttrf.l | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| dgttrs, dgttrs.l | solve one of the systems of equations A∗X = B or A’∗X = B, |
| dhgeqz, dhgeqz.l | implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form |
| dhsein, dhsein.l | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H |
| dhseqr, dhseqr.l | compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors |
| dlabad, dlabad.l | take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large |
| dlabrd, dlabrd.l | reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A |
| dlacon, dlacon.l | estimate the 1-norm of a square, real matrix A |
| dlacpy, dlacpy.l | copie all or part of a two-dimensional matrix A to another matrix B |
| dladiv, dladiv.l | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L |
| dlae2, dlae2.l | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| dlaebz, dlaebz.l | contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w |
| dlaed0, dlaed0.l | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| dlaed1, dlaed1.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| dlaed2, dlaed2.l | merge the two sets of eigenvalues together into a single sorted set |
| dlaed3, dlaed3.l | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP |
| dlaed4, dlaed4.l | subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 |
| dlaed5, dlaed5.l | subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j |
| dlaed6, dlaed6.l | compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true |
| dlaed7, dlaed7.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| dlaed8, dlaed8.l | merge the two sets of eigenvalues together into a single sorted set |
| dlaed9, dlaed9.l | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP |
| dlaeda, dlaeda.l | compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem |
| dlaein, dlaein.l | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H |
| dlaev2, dlaev2.l | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| dlaexc, dlaexc.l | swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation |
| dlag2, dlag2.l | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow |
| dlags2, dlags2.l | compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z’ denotes the transpose of Z |
| dlagtf, dlagtf.l | factorize the matrix (T - lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda∗I = PLU, |
| dlagtm, dlagtm.l | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 |
| dlagts, dlagts.l | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, |
| dlahqr, dlahqr.l | i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI |
| dlahrd, dlahrd.l | reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero |
| dlaic1, dlaic1.l | applie one step of incremental condition estimation in its simplest version |
| dlaln2, dlaln2.l | solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A |
| dlamch, dlamch.l | determine double precision machine parameters |
| dlamrg, dlamrg.l | will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order |
| dlangb, dlangb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals |
| dlange, dlange.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A |
| dlangt, dlangt.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A |
| dlanhs, dlanhs.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A |
| dlansb, dlansb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals |
| dlansp, dlansp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form |
| dlanst, dlanst.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A |
| dlansy, dlansy.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A |
| dlantb, dlantb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals |
| dlantp, dlantp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form |
| dlantr, dlantr.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A |
| dlanv2, dlanv2.l | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form |
| dlapll, dlapll.l | two column vectors X and Y, let A = ( X Y ) |
| dlapmt, dlapmt.l | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N |
| dlapy2, dlapy2.l | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow |
| dlapy3, dlapy3.l | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow |
| dlaqgb, dlaqgb.l | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C |
| dlaqge, dlaqge.l | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| dlaqsb, dlaqsb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| dlaqsp, dlaqsp.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| dlaqsy, dlaqsy.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| dlaqtr, dlaqtr.l | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE |
| dlar2v, dlar2v.l | applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z |
| dlarf, dlarf.l | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| dlarfb, dlarfb.l | applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right |
| dlarfg, dlarfg.l | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| dlarft, dlarft.l | form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors |
| dlarfx, dlarfx.l | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| dlargv, dlargv.l | generate a vector of real plane rotations, determined by elements of the real vectors x and y |
| dlarnv, dlarnv.l | return a vector of n random real numbers from a uniform or normal distribution |
| dlartg, dlartg.l | generate a plane rotation so that [ CS SN ] |
| dlartv, dlartv.l | applie a vector of real plane rotations to elements of the real vectors x and y |
| dlaruv, dlaruv.l | return a vector of n random real numbers from a uniform (0,1) |
| dlas2, dlas2.l | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] |
| dlascl, dlascl.l | multiply the M by N real matrix A by the real scalar CTO/CFROM |
| dlaset, dlaset.l | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals |
| dlasq1, dlasq1.l | DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E |
| dlasq2, dlasq2.l | DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E |
| dlasq3, dlasq3.l | DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm |
| dlasq4, dlasq4.l | DLASQ4 estimates TAU, the smallest eigenvalue of a matrix |
| dlasr, dlasr.l | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, |
| dlasrt, dlasrt.l | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) |
| dlassq, dlassq.l | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| dlasv2, dlasv2.l | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] |
| dlaswp, dlaswp.l | perform a series of row interchanges on the matrix A |
| dlasy2, dlasy2.l | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, |
| dlasyf, dlasyf.l | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| dlatbs, dlatbs.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix |
| dlatps, dlatps.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form |
| dlatrd, dlatrd.l | reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A |
| dlatrs, dlatrs.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow |
| dlatzm, dlatzm.l | applie a Householder matrix generated by DTZRQF to a matrix |
| dlauu2, dlauu2.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| dlauum, dlauum.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| DNRM2, dnrm2.l | Return the Euclidian norm of a vector. |
| dopgtr, dopgtr.l | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage |
| dopmtr, dopmtr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dorg2l, dorg2l.l | generate an m by n real matrix Q with orthonormal columns, |
| dorg2r, dorg2r.l | generate an m by n real matrix Q with orthonormal columns, |
| dorgbr, dorgbr.l | generate one of the real orthogonal matrices Q or P∗∗T determined by DGEBRD when reducing a real matrix A to bidiagonal form |
| dorghr, dorghr.l | generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD |
| dorgl2, dorgl2.l | generate an m by n real matrix Q with orthonormal rows, |
| dorglq, dorglq.l | generate an M-by-N real matrix Q with orthonormal rows, |
| dorgql, dorgql.l | generate an M-by-N real matrix Q with orthonormal columns, |
| dorgqr, dorgqr.l | generate an M-by-N real matrix Q with orthonormal columns, |
| dorgr2, dorgr2.l | generate an m by n real matrix Q with orthonormal rows, |
| dorgrq, dorgrq.l | generate an M-by-N real matrix Q with orthonormal rows, |
| dorgtr, dorgtr.l | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD |
| dorm2l, dorm2l.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| dorm2r, dorm2r.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| dormbr, dormbr.l | VECT = ’Q’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dormhr, dormhr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dorml2, dorml2.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| dormlq, dormlq.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dormql, dormql.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dormqr, dormqr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dormr2, dormr2.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| dormrq, dormrq.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dormtr, dormtr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| dpbco, dpbco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| dpbcon, dpbcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF |
| dpbdi, dpbdi.l | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. |
| dpbequ, dpbequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) |
| dpbfa, dpbfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| dpbrfs, dpbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution |
| dpbsl, dpbsl.l | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. |
| dpbstf, dpbstf.l | compute a split Cholesky factorization of a real symmetric positive definite band matrix A |
| dpbsv, dpbsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dpbsvx, dpbsvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| dpbtf2, dpbtf2.l | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| dpbtrf, dpbtrf.l | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| dpbtrs, dpbtrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF |
| dpoco, dpoco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| dpocon, dpocon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF |
| dpodi, dpodi.l | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. |
| dpoequ, dpoequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) |
| dpofa, dpofa.l | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| dporfs, dporfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, |
| dposl, dposl.l | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. |
| dposv, dposv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dposvx, dposvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| dpotf2, dpotf2.l | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| dpotrf, dpotrf.l | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| dpotri, dpotri.l | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF |
| dpotrs, dpotrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF |
| dppco, dppco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| dppcon, dppcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF |
| dppdi, dppdi.l | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. |
| dppequ, dppequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) |
| dppfa, dppfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| dpprfs, dpprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution |
| dppsl, dppsl.l | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. |
| dppsv, dppsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dppsvx, dppsvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| dpptrf, dpptrf.l | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format |
| dpptri, dpptri.l | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF |
| dpptrs, dpptrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF |
| dptcon, dptcon.l | compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF |
| dpteqr, dpteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor |
| dptrfs, dptrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution |
| dptsl, dptsl.l | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. |
| dptsv, dptsv.l | compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices |
| dptsvx, dptsvx.l | use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices |
| dpttrf, dpttrf.l | compute the factorization of a real symmetric positive definite tridiagonal matrix A |
| dpttrs, dpttrs.l | solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF |
| DQDOTA, dqdota.l | Compute a double precision constant plus an extended precision constant plus the extended precision dot product of two double precision vectors x and y. |
| DQDOTI, dqdoti.l | Compute a constant plus the extended precision dot product of two double precision vectors x and y. |
| dqrdc, dqrdc.l | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. |
| dqrsl, dqrsl.l | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. |
| DROT, drot.l | Apply a Given’s rotation constructed by DROTG. |
| DROTG, drotg.l | Construct a Given’s plane rotation |
| DROTM, drotm.l | Apply a Gentleman’s modified Given’s rotation constructed by DROTMG. |
| DROTMG, drotmg.l | Construct a Gentleman’s modified Given’s plane rotation |
| drscl, drscl.l | multiply an n-element real vector x by the real scalar 1/a |
| dsbev, dsbev.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| dsbevd, dsbevd.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| dsbevx, dsbevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| dsbgst, dsbgst.l | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| dsbgv, dsbgv.l | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| dsbmv, dsbmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| dsbtrd, dsbtrd.l | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| DSCAL, dscal.l | Compute y := alpha ∗ y |
| DSDOT, dsdot.l | Compute the double precision dot product of two single precision vectors x and y. |
| dsecnd, dsecnd.l | return the user time for a process in seconds |
| dsico, dsico.l | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| dsidi, dsidi.l | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. |
| dsifa, dsifa.l | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| dsinqb, dsinqb.l | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| dsinqf, dsinqf.l | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| dsinqi, dsinqi.l | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. |
| dsint, dsint.l | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. |
| dsinti, dsinti.l | initialize the array xWSAVE, which is used in subroutine xSINT. |
| dsisl, dsisl.l | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. |
| dspco, dspco.l | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| dspcon, dspcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF |
| dspdi, dspdi.l | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. |
| dspev, dspev.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| dspevd, dspevd.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| dspevx, dspevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| dspfa, dspfa.l | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| dspgst, dspgst.l | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage |
| dspgv, dspgv.l | compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| dspmv, dspmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| dspr, dspr.l | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A |
| dspr2, dspr2.l | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A |
| dsprfs, dsprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution |
| dspsl, dspsl.l | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. |
| dspsv, dspsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dspsvx, dspsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices |
| dsptrd, dsptrd.l | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation |
| dsptrf, dsptrf.l | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| dsptri, dsptri.l | compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF |
| dsptrs, dsptrs.l | solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF |
| dstebz, dstebz.l | compute the eigenvalues of a symmetric tridiagonal matrix T |
| dstedc, dstedc.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| dstein, dstein.l | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| dsteqr, dsteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| dsterf, dsterf.l | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm |
| dstev, dstev.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| dstevd, dstevd.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| dstevx, dstevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| dsvdc, dsvdc.l | compute the singular value decomposition of a general matrix A. |
| DSWAP, dswap.l | Exchange vectors x and y. |
| dsycon, dsycon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF |
| dsyev, dsyev.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| dsyevd, dsyevd.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| dsyevx, dsyevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| dsygs2, dsygs2.l | reduce a real symmetric-definite generalized eigenproblem to standard form |
| dsygst, dsygst.l | reduce a real symmetric-definite generalized eigenproblem to standard form |
| dsygv, dsygv.l | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| dsymm, dsymm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| dsymv, dsymv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| dsyr, dsyr.l | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A |
| dsyr2, dsyr2.l | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A |
| dsyr2k, dsyr2k.l | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C |
| dsyrfs, dsyrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution |
| dsyrk, dsyrk.l | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C |
| dsysv, dsysv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| dsysvx, dsysvx.l | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| dsytd2, dsytd2.l | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| dsytf2, dsytf2.l | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| dsytrd, dsytrd.l | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation |
| dsytrf, dsytrf.l | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| dsytri, dsytri.l | compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF |
| dsytrs, dsytrs.l | solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF |
| dtbcon, dtbcon.l | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| dtbmv, dtbmv.l | perform one of the matrix-vector operations x := A∗x or x := A’∗x |
| dtbrfs, dtbrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| dtbsv, dtbsv.l | solve one of the systems of equations A∗x = b or A’∗x = b |
| dtbtrs, dtbtrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| dtgevc, dtgevc.l | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) |
| dtgsja, dtgsja.l | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B |
| dtpcon, dtpcon.l | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| dtpmv, dtpmv.l | perform one of the matrix-vector operations x := A∗x or x := A’∗x |
| dtprfs, dtprfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| dtpsv, dtpsv.l | solve one of the systems of equations A∗x = b or A’∗x = b |
| dtptri, dtptri.l | compute the inverse of a real upper or lower triangular matrix A stored in packed format |
| dtptrs, dtptrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| dtrco, dtrco.l | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. |
| dtrcon, dtrcon.l | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| dtrdi, dtrdi.l | compute the determinant and inverse of a triangular matrix A. |
| dtrevc, dtrevc.l | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T |
| dtrexc, dtrexc.l | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST |
| dtrmm, dtrmm.l | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) |
| dtrmv, dtrmv.l | perform one of the matrix-vector operations x := A∗x or x := A’∗x |
| dtrrfs, dtrrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| dtrsen, dtrsen.l | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, |
| dtrsl, dtrsl.l | solve the linear system Ax = b for a triangular matrix A and vectors b and x. |
| dtrsm, dtrsm.l | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B |
| dtrsna, dtrsna.l | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal) |
| dtrsv, dtrsv.l | solve one of the systems of equations A∗x = b or A’∗x = b |
| dtrsyl, dtrsyl.l | solve the real Sylvester matrix equation |
| dtrti2, dtrti2.l | compute the inverse of a real upper or lower triangular matrix |
| dtrtri, dtrtri.l | compute the inverse of a real upper or lower triangular matrix A |
| dtrtrs, dtrtrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| dtzrqf, dtzrqf.l | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations |
| DZASUM, dzasum.l | Return the sum of the absolute values of a vector x. |
| DZNRM2, dznrm2.l | Return the Euclidian norm of a vector. |
| dzsum1, dzsum1.l | take the sum of the absolute values of a complex vector and returns a double precision result |
| ezfftb, ezfftb.l | computes a perodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB. |
| ezfftf, ezfftf.l | computes the Fourier coefficients of a perodic sequence. EZFFTF is a simplified but slower version of RFFTF. |
| ezffti, ezffti.l | initializes the array WSAVE, which is used in both EZFFTF and EZFFTB. |
| ICAMAX, icamax.l | Return the index of the element with largest absolute value. |
| icmax1, icmax1.l | find the index of the element whose real part has maximum absolute value |
| IDAMAX, idamax.l | Return the index of the element with largest absolute value. |
| ilaenv, ilaenv.l | choose problem-dependent parameters |
| ISAMAX, isamax.l | Return the index of the element with largest absolute value. |
| IZAMAX, izamax.l | Return the index of the element with largest absolute value. |
| izmax1, izmax1.l | find the index of the element whose real part has maximum absolute value |
| lapack.l | |
| lsame, lsame.l | case-insensitive comparison of two characters |
| lsamen, lsamen.l | test if the first N letters of CA are the same as the first N letters of CB, regardless of case |
| rfftb, rfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| rfftf, rfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| rffti, rffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| SASUM, sasum.l | Return the sum of the absolute values of a vector x. |
| SAXPY, saxpy.l | Compute y := alpha ∗ x + y |
| sbdsqr, sbdsqr.l | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| SCASUM, scasum.l | Return the sum of the absolute values of a vector x. |
| schdc, schdc.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| schdd, schdd.l | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| schex, schex.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| schud, schud.l | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| SCNRM2, scnrm2.l | Return the Euclidian norm of a vector. |
| SCOPY, scopy.l | Copy x to y |
| scsum1, scsum1.l | take the sum of the absolute values of a complex vector and returns a single precision result |
| sdisna, sdisna.l | compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix |
| SDOT, sdot.l | Compute the dot product of two vectors x and y. |
| SDSDOT, sdsdot.l | Compute a constant plus the double precision dot product of two single precision vectors x and y. |
| second, second.l | return the user time for a process in seconds |
| sgbbrd, sgbbrd.l | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation |
| sgbco, sgbco.l | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| sgbcon, sgbcon.l | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, |
| sgbdi, sgbdi.l | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. |
| sgbequ, sgbequ.l | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| sgbfa, sgbfa.l | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| sgbmv, sgbmv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y |
| sgbrfs, sgbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution |
| sgbsl, sgbsl.l | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. |
| sgbsv, sgbsv.l | compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices |
| sgbsvx, sgbsvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| sgbtf2, sgbtf2.l | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| sgbtrf, sgbtrf.l | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| sgbtrs, sgbtrs.l | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by SGBTRF |
| sgebak, sgebak.l | form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL |
| sgebal, sgebal.l | balance a general real matrix A |
| sgebd2, sgebd2.l | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| sgebrd, sgebrd.l | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| sgeco, sgeco.l | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. |
| sgecon, sgecon.l | estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF |
| sgedi, sgedi.l | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. |
| sgeequ, sgeequ.l | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| sgees, sgees.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z |
| sgeesx, sgeesx.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z |
| sgeev, sgeev.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| sgeevx, sgeevx.l | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| sgefa, sgefa.l | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. |
| sgegs, sgegs.l | compute for a pair of N-by-N real nonsymmetric matrices A, B |
| sgegv, sgegv.l | compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) |
| sgehd2, sgehd2.l | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| sgehrd, sgehrd.l | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| sgelq2, sgelq2.l | compute an LQ factorization of a real m by n matrix A |
| sgelqf, sgelqf.l | compute an LQ factorization of a real M-by-N matrix A |
| sgels, sgels.l | solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A |
| sgelss, sgelss.l | compute the minimum norm solution to a real linear least squares problem |
| sgelsx, sgelsx.l | compute the minimum-norm solution to a real linear least squares problem |
| sgemm, sgemm.l | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C |
| sgemv, sgemv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y |
| sgeql2, sgeql2.l | compute a QL factorization of a real m by n matrix A |
| sgeqlf, sgeqlf.l | compute a QL factorization of a real M-by-N matrix A |
| sgeqpf, sgeqpf.l | compute a QR factorization with column pivoting of a real M-by-N matrix A |
| sgeqr2, sgeqr2.l | compute a QR factorization of a real m by n matrix A |
| sgeqrf, sgeqrf.l | compute a QR factorization of a real M-by-N matrix A |
| sger, sger.l | perform the rank 1 operation A := alpha∗x∗y’ + A |
| sgerfs, sgerfs.l | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| sgerq2, sgerq2.l | compute an RQ factorization of a real m by n matrix A |
| sgerqf, sgerqf.l | compute an RQ factorization of a real M-by-N matrix A |
| sgesl, sgesl.l | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. |
| sgesv, sgesv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| sgesvd, sgesvd.l | compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors |
| sgesvx, sgesvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| sgetf2, sgetf2.l | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| sgetrf, sgetrf.l | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| sgetri, sgetri.l | compute the inverse of a matrix using the LU factorization computed by SGETRF |
| sgetrs, sgetrs.l | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF |
| sggbak, sggbak.l | form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL |
| sggbal, sggbal.l | balance a pair of general real matrices (A,B) |
| sggglm, sggglm.l | solve a general Gauss-Markov linear model (GLM) problem |
| sgghrd, sgghrd.l | reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular |
| sgglse, sgglse.l | solve the linear equality-constrained least squares (LSE) problem |
| sggqrf, sggqrf.l | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| sggrqf, sggrqf.l | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| sggsvd, sggsvd.l | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B |
| sggsvp, sggsvp.l | compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 |
| sgtcon, sgtcon.l | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF |
| sgtrfs, sgtrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution |
| sgtsl, sgtsl.l | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. |
| sgtsv, sgtsv.l | solve the equation A∗X = B, |
| sgtsvx, sgtsvx.l | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B, |
| sgttrf, sgttrf.l | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| sgttrs, sgttrs.l | solve one of the systems of equations A∗X = B or A’∗X = B, |
| shgeqz, shgeqz.l | implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form |
| shsein, shsein.l | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H |
| shseqr, shseqr.l | compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors |
| sinqb, sinqb.l | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| sinqf, sinqf.l | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| sinqi, sinqi.l | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. |
| sint, sint.l | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. |
| sinti, sinti.l | initialize the array xWSAVE, which is used in subroutine xSINT. |
| slabad, slabad.l | take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large |
| slabrd, slabrd.l | reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A |
| slacon, slacon.l | estimate the 1-norm of a square, real matrix A |
| slacpy, slacpy.l | copie all or part of a two-dimensional matrix A to another matrix B |
| sladiv, sladiv.l | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L |
| slae2, slae2.l | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| slaebz, slaebz.l | contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w |
| slaed0, slaed0.l | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| slaed1, slaed1.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| slaed2, slaed2.l | merge the two sets of eigenvalues together into a single sorted set |
| slaed3, slaed3.l | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP |
| slaed4, slaed4.l | subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 |
| slaed5, slaed5.l | subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j |
| slaed6, slaed6.l | compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true |
| slaed7, slaed7.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| slaed8, slaed8.l | merge the two sets of eigenvalues together into a single sorted set |
| slaed9, slaed9.l | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP |
| slaeda, slaeda.l | compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem |
| slaein, slaein.l | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H |
| slaev2, slaev2.l | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| slaexc, slaexc.l | swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation |
| slag2, slag2.l | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow |
| slags2, slags2.l | compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z’ denotes the transpose of Z |
| slagtf, slagtf.l | factorize the matrix (T - lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda∗I = PLU, |
| slagtm, slagtm.l | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 |
| slagts, slagts.l | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, |
| slahqr, slahqr.l | i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI |
| slahrd, slahrd.l | reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero |
| slaic1, slaic1.l | applie one step of incremental condition estimation in its simplest version |
| slaln2, slaln2.l | solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A |
| slamch, slamch.l | determine single precision machine parameters |
| slamrg, slamrg.l | will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order |
| slangb, slangb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals |
| slange, slange.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A |
| slangt, slangt.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A |
| slanhs, slanhs.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A |
| slansb, slansb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals |
| slansp, slansp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form |
| slanst, slanst.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A |
| slansy, slansy.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A |
| slantb, slantb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals |
| slantp, slantp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form |
| slantr, slantr.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A |
| slanv2, slanv2.l | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form |
| slapll, slapll.l | two column vectors X and Y, let A = ( X Y ) |
| slapmt, slapmt.l | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N |
| slapy2, slapy2.l | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow |
| slapy3, slapy3.l | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow |
| slaqgb, slaqgb.l | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C |
| slaqge, slaqge.l | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| slaqsb, slaqsb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| slaqsp, slaqsp.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| slaqsy, slaqsy.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| slaqtr, slaqtr.l | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE |
| slar2v, slar2v.l | applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z |
| slarf, slarf.l | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| slarfb, slarfb.l | applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right |
| slarfg, slarfg.l | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| slarft, slarft.l | form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors |
| slarfx, slarfx.l | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| slargv, slargv.l | generate a vector of real plane rotations, determined by elements of the real vectors x and y |
| slarnv, slarnv.l | return a vector of n random real numbers from a uniform or normal distribution |
| slartg, slartg.l | generate a plane rotation so that [ CS SN ] |
| slartv, slartv.l | applie a vector of real plane rotations to elements of the real vectors x and y |
| slaruv, slaruv.l | return a vector of n random real numbers from a uniform (0,1) |
| slas2, slas2.l | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] |
| slascl, slascl.l | multiply the M by N real matrix A by the real scalar CTO/CFROM |
| slaset, slaset.l | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals |
| slasq1, slasq1.l | SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E |
| slasq2, slasq2.l | SLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E |
| slasq3, slasq3.l | SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm |
| slasq4, slasq4.l | SLASQ4 estimates TAU, the smallest eigenvalue of a matrix |
| slasr, slasr.l | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, |
| slasrt, slasrt.l | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) |
| slassq, slassq.l | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| slasv2, slasv2.l | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] |
| slaswp, slaswp.l | perform a series of row interchanges on the matrix A |
| slasy2, slasy2.l | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, |
| slasyf, slasyf.l | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| slatbs, slatbs.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix |
| slatps, slatps.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form |
| slatrd, slatrd.l | reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A |
| slatrs, slatrs.l | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow |
| slatzm, slatzm.l | applie a Householder matrix generated by STZRQF to a matrix |
| slauu2, slauu2.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| slauum, slauum.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| SNRM2, snrm2.l | Return the Euclidian norm of a vector. |
| sopgtr, sopgtr.l | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage |
| sopmtr, sopmtr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sorg2l, sorg2l.l | generate an m by n real matrix Q with orthonormal columns, |
| sorg2r, sorg2r.l | generate an m by n real matrix Q with orthonormal columns, |
| sorgbr, sorgbr.l | generate one of the real orthogonal matrices Q or P∗∗T determined by SGEBRD when reducing a real matrix A to bidiagonal form |
| sorghr, sorghr.l | generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD |
| sorgl2, sorgl2.l | generate an m by n real matrix Q with orthonormal rows, |
| sorglq, sorglq.l | generate an M-by-N real matrix Q with orthonormal rows, |
| sorgql, sorgql.l | generate an M-by-N real matrix Q with orthonormal columns, |
| sorgqr, sorgqr.l | generate an M-by-N real matrix Q with orthonormal columns, |
| sorgr2, sorgr2.l | generate an m by n real matrix Q with orthonormal rows, |
| sorgrq, sorgrq.l | generate an M-by-N real matrix Q with orthonormal rows, |
| sorgtr, sorgtr.l | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD |
| sorm2l, sorm2l.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| sorm2r, sorm2r.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| sormbr, sormbr.l | VECT = ’Q’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sormhr, sormhr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sorml2, sorml2.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| sormlq, sormlq.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sormql, sormql.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sormqr, sormqr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sormr2, sormr2.l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, |
| sormrq, sormrq.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| sormtr, sormtr.l | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| spbco, spbco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| spbcon, spbcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF |
| spbdi, spbdi.l | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. |
| spbequ, spbequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) |
| spbfa, spbfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| spbrfs, spbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution |
| spbsl, spbsl.l | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. |
| spbstf, spbstf.l | compute a split Cholesky factorization of a real symmetric positive definite band matrix A |
| spbsv, spbsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| spbsvx, spbsvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| spbtf2, spbtf2.l | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| spbtrf, spbtrf.l | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| spbtrs, spbtrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF |
| spoco, spoco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| spocon, spocon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF |
| spodi, spodi.l | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. |
| spoequ, spoequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) |
| spofa, spofa.l | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| sporfs, sporfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, |
| sposl, sposl.l | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. |
| sposv, sposv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| sposvx, sposvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| spotf2, spotf2.l | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| spotrf, spotrf.l | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| spotri, spotri.l | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF |
| spotrs, spotrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF |
| sppco, sppco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| sppcon, sppcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF |
| sppdi, sppdi.l | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. |
| sppequ, sppequ.l | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) |
| sppfa, sppfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| spprfs, spprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution |
| sppsl, sppsl.l | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. |
| sppsv, sppsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| sppsvx, sppsvx.l | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, |
| spptrf, spptrf.l | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format |
| spptri, spptri.l | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF |
| spptrs, spptrs.l | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF |
| sptcon, sptcon.l | compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF |
| spteqr, spteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor |
| sptrfs, sptrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution |
| sptsl, sptsl.l | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. |
| sptsv, sptsv.l | compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices |
| sptsvx, sptsvx.l | use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices |
| spttrf, spttrf.l | compute the factorization of a real symmetric positive definite tridiagonal matrix A |
| spttrs, spttrs.l | solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF |
| sqrdc, sqrdc.l | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. |
| sqrsl, sqrsl.l | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. |
| SROT, srot.l | Apply a Given’s rotation constructed by SROTG. |
| SROTG, srotg.l | Construct a Given’s plane rotation |
| SROTM, srotm.l | Apply a Gentleman’s modified Given’s rotation constructed by SROTMG. |
| SROTMG, srotmg.l | Construct a Gentleman’s modified Given’s plane rotation |
| srscl, srscl.l | multiply an n-element real vector x by the real scalar 1/a |
| ssbev, ssbev.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| ssbevd, ssbevd.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| ssbevx, ssbevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| ssbgst, ssbgst.l | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| ssbgv, ssbgv.l | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| ssbmv, ssbmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| ssbtrd, ssbtrd.l | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| SSCAL, sscal.l | Compute y := alpha ∗ y |
| ssico, ssico.l | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| ssidi, ssidi.l | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. |
| ssifa, ssifa.l | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| ssisl, ssisl.l | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. |
| sspco, sspco.l | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| sspcon, sspcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF |
| sspdi, sspdi.l | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. |
| sspev, sspev.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| sspevd, sspevd.l | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| sspevx, sspevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| sspfa, sspfa.l | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| sspgst, sspgst.l | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage |
| sspgv, sspgv.l | compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| sspmv, sspmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| sspr, sspr.l | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A |
| sspr2, sspr2.l | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A |
| ssprfs, ssprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution |
| sspsl, sspsl.l | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. |
| sspsv, sspsv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| sspsvx, sspsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices |
| ssptrd, ssptrd.l | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation |
| ssptrf, ssptrf.l | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| ssptri, ssptri.l | compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF |
| ssptrs, ssptrs.l | solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF |
| sstebz, sstebz.l | compute the eigenvalues of a symmetric tridiagonal matrix T |
| sstedc, sstedc.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| sstein, sstein.l | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| ssteqr, ssteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| ssterf, ssterf.l | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm |
| sstev, sstev.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| sstevd, sstevd.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| sstevx, sstevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| ssvdc, ssvdc.l | compute the singular value decomposition of a general matrix A. |
| SSWAP, sswap.l | Exchange vectors x and y. |
| ssycon, ssycon.l | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF |
| ssyev, ssyev.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| ssyevd, ssyevd.l | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| ssyevx, ssyevx.l | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| ssygs2, ssygs2.l | reduce a real symmetric-definite generalized eigenproblem to standard form |
| ssygst, ssygst.l | reduce a real symmetric-definite generalized eigenproblem to standard form |
| ssygv, ssygv.l | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| ssymm, ssymm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| ssymv, ssymv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| ssyr, ssyr.l | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A |
| ssyr2, ssyr2.l | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A |
| ssyr2k, ssyr2k.l | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C |
| ssyrfs, ssyrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution |
| ssyrk, ssyrk.l | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C |
| ssysv, ssysv.l | compute the solution to a real system of linear equations A ∗ X = B, |
| ssysvx, ssysvx.l | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| ssytd2, ssytd2.l | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| ssytf2, ssytf2.l | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| ssytrd, ssytrd.l | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation |
| ssytrf, ssytrf.l | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| ssytri, ssytri.l | compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF |
| ssytrs, ssytrs.l | solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF |
| stbcon, stbcon.l | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| stbmv, stbmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x |
| stbrfs, stbrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| stbsv, stbsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b |
| stbtrs, stbtrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| stgevc, stgevc.l | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) |
| stgsja, stgsja.l | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B |
| stpcon, stpcon.l | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| stpmv, stpmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x |
| stprfs, stprfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| stpsv, stpsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b |
| stptri, stptri.l | compute the inverse of a real upper or lower triangular matrix A stored in packed format |
| stptrs, stptrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| strco, strco.l | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. |
| strcon, strcon.l | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| strdi, strdi.l | compute the determinant and inverse of a triangular matrix A. |
| strevc, strevc.l | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T |
| strexc, strexc.l | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST |
| strmm, strmm.l | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) |
| strmv, strmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x |
| strrfs, strrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| strsen, strsen.l | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, |
| strsl, strsl.l | solve the linear system Ax = b for a triangular matrix A and vectors b and x. |
| strsm, strsm.l | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B |
| strsna, strsna.l | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal) |
| strsv, strsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b |
| strsyl, strsyl.l | solve the real Sylvester matrix equation |
| strti2, strti2.l | compute the inverse of a real upper or lower triangular matrix |
| strtri, strtri.l | compute the inverse of a real upper or lower triangular matrix A |
| strtrs, strtrs.l | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| stzrqf, stzrqf.l | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations |
| vcosqb, vcosqb.l | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| vcosqf, vcosqf.l | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| vcosqi, vcosqi.l | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. |
| vcost, vcost.l | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. |
| vcosti, vcosti.l | initialize the array xWSAVE, which is used in xCOST. |
| vdcosqb, vdcosqb.l | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| vdcosqf, vdcosqf.l | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. |
| vdcosqi, vdcosqi.l | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. |
| vdcost, vdcost.l | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. |
| vdcosti, vdcosti.l | initialize the array xWSAVE, which is used in xCOST. |
| vdfftb, vdfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| vdfftf, vdfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| vdffti, vdffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| vdsinqb, vdsinqb.l | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| vdsinqf, vdsinqf.l | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| vdsinqi, vdsinqi.l | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. |
| vdsinti, vdsint.l | initialize the array xWSAVE, which is used in subroutine xSINT. |
| vdsinti, vdsinti.l | initialize the array xWSAVE, which is used in subroutine xSINT. |
| vrfftb, vrfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| vrfftf, vrfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| vrffti, vrffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| vsinqb, vsinqb.l | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| vsinqf, vsinqf.l | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. |
| vsinqi, vsinqi.l | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. |
| vsint, vsint.l | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. |
| vsinti, vsinti.l | initialize the array xWSAVE, which is used in subroutine xSINT. |
| xerbla, xerbla.l | error handler for the LAPACK routines |
| ZAXPY, zaxpy.l | Compute y := alpha ∗ x + y |
| zbdsqr, zbdsqr.l | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| zchdc, zchdc.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| zchdd, zchdd.l | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| zchex, zchex.l | compute the Cholesky decomposition of a symmetric positive definite matrix A. |
| zchud, zchud.l | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. |
| ZCOPY, zcopy.l | Copy x to y |
| ZDOTU, zdotc.l | Compute the dot product of two vectors x and conjg(y). |
| ZDOTU, zdotu.l | Compute the dot product of two vectors x and y. |
| zdrscl, zdrscl.l | multiply an n-element complex vector x by the real scalar 1/a |
| zdscal, zdscal.l | Compute y := alpha ∗ y |
| zfftb, zfftb.l | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| zfftf, zfftf.l | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. |
| zffti, zffti.l | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. |
| zgbbrd, zgbbrd.l | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation |
| zgbco, zgbco.l | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| zgbcon, zgbcon.l | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, |
| zgbdi, zgbdi.l | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. |
| zgbequ, zgbequ.l | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| zgbfa, zgbfa.l | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. |
| zgbmv, zgbmv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y |
| zgbrfs, zgbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution |
| zgbsl, zgbsl.l | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. |
| zgbsv, zgbsv.l | compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices |
| zgbsvx, zgbsvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| zgbtf2, zgbtf2.l | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| zgbtrf, zgbtrf.l | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| zgbtrs, zgbtrs.l | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by ZGBTRF |
| zgebak, zgebak.l | form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL |
| zgebal, zgebal.l | balance a general complex matrix A |
| zgebd2, zgebd2.l | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation |
| zgebrd, zgebrd.l | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation |
| zgeco, zgeco.l | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. |
| zgecon, zgecon.l | estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF |
| zgedi, zgedi.l | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. |
| zgeequ, zgeequ.l | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| zgees, zgees.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z |
| zgeesx, zgeesx.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z |
| zgeev, zgeev.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| zgeevx, zgeevx.l | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| zgefa, zgefa.l | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. |
| zgegs, zgegs.l | compute for a pair of N-by-N complex nonsymmetric matrices A, |
| zgegv, zgegv.l | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, |
| zgehd2, zgehd2.l | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| zgehrd, zgehrd.l | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| zgelq2, zgelq2.l | compute an LQ factorization of a complex m by n matrix A |
| zgelqf, zgelqf.l | compute an LQ factorization of a complex M-by-N matrix A |
| zgels, zgels.l | solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A |
| zgelss, zgelss.l | compute the minimum norm solution to a complex linear least squares problem |
| zgelsx, zgelsx.l | compute the minimum-norm solution to a complex linear least squares problem |
| zgemm, zgemm.l | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C |
| zgemv, zgemv.l | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y |
| zgeql2, zgeql2.l | compute a QL factorization of a complex m by n matrix A |
| zgeqlf, zgeqlf.l | compute a QL factorization of a complex M-by-N matrix A |
| zgeqpf, zgeqpf.l | compute a QR factorization with column pivoting of a complex M-by-N matrix A |
| zgeqr2, zgeqr2.l | compute a QR factorization of a complex m by n matrix A |
| zgeqrf, zgeqrf.l | compute a QR factorization of a complex M-by-N matrix A |
| zgerc, zgerc.l | perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A |
| zgerfs, zgerfs.l | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| zgerq2, zgerq2.l | compute an RQ factorization of a complex m by n matrix A |
| zgerqf, zgerqf.l | compute an RQ factorization of a complex M-by-N matrix A |
| zgeru, zgeru.l | perform the rank 1 operation A := alpha∗x∗y’ + A |
| zgesl, zgesl.l | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. |
| zgesv, zgesv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zgesvd, zgesvd.l | compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors |
| zgesvx, zgesvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| zgetf2, zgetf2.l | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| zgetrf, zgetrf.l | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| zgetri, zgetri.l | compute the inverse of a matrix using the LU factorization computed by ZGETRF |
| zgetrs, zgetrs.l | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF |
| zggbak, zggbak.l | form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL |
| zggbal, zggbal.l | balance a pair of general complex matrices (A,B) |
| zggglm, zggglm.l | solve a general Gauss-Markov linear model (GLM) problem |
| zgghrd, zgghrd.l | reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular |
| zgglse, zgglse.l | solve the linear equality-constrained least squares (LSE) problem |
| zggqrf, zggqrf.l | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| zggrqf, zggrqf.l | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| zggsvd, zggsvd.l | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B |
| zggsvp, zggsvp.l | compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 |
| zgtcon, zgtcon.l | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF |
| zgtrfs, zgtrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution |
| zgtsl, zgtsl.l | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. |
| zgtsv, zgtsv.l | solve the equation A∗X = B, |
| zgtsvx, zgtsvx.l | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| zgttrf, zgttrf.l | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| zgttrs, zgttrs.l | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| zhbev, zhbev.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| zhbevd, zhbevd.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| zhbevx, zhbevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| zhbgst, zhbgst.l | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| zhbgv, zhbgv.l | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| zhbmv, zhbmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| zhbtrd, zhbtrd.l | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| zhecon, zhecon.l | estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF |
| zheev, zheev.l | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| zheevd, zheevd.l | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| zheevx, zheevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| zhegs2, zhegs2.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| zhegst, zhegst.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| zhegv, zhegv.l | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| zhemm, zhemm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| zhemv, zhemv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| zher, zher.l | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A |
| zher2, zher2.l | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A |
| zher2k, zher2k.l | perform one of the hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C |
| zherfs, zherfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution |
| zherk, zherk.l | perform one of the hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C |
| zhesv, zhesv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zhesvx, zhesvx.l | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| zhetd2, zhetd2.l | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| zhetf2, zhetf2.l | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| zhetrd, zhetrd.l | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| zhetrf, zhetrf.l | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| zhetri, zhetri.l | compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF |
| zhetrs, zhetrs.l | solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF |
| zhgeqz, zhgeqz.l | implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right |
| zhico, zhico.l | compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. |
| zhidi, zhidi.l | compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA. |
| zhifa, zhifa.l | compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. |
| zhisl, zhisl.l | solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x. |
| zhpco, zhpco.l | compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. |
| zhpcon, zhpcon.l | estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF |
| zhpdi, zhpdi.l | compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA. |
| zhpev, zhpev.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage |
| zhpevd, zhpevd.l | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| zhpevx, zhpevx.l | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| zhpfa, zhpfa.l | compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. |
| zhpgst, zhpgst.l | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage |
| zhpgv, zhpgv.l | compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x |
| zhpmv, zhpmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y |
| zhpr, zhpr.l | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A |
| zhpr2, zhpr2.l | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A |
| zhprfs, zhprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution |
| zhpsl, zhpsl.l | solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x. |
| zhpsv, zhpsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zhpsvx, zhpsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices |
| zhptrd, zhptrd.l | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation |
| zhptrf, zhptrf.l | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method |
| zhptri, zhptri.l | compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF |
| zhptrs, zhptrs.l | solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF |
| zhsein, zhsein.l | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H |
| zhseqr, zhseqr.l | compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors |
| zlabrd, zlabrd.l | reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A |
| zlacgv, zlacgv.l | conjugate a complex vector of length N |
| zlacon, zlacon.l | estimate the 1-norm of a square, complex matrix A |
| zlacpy, zlacpy.l | copie all or part of a two-dimensional matrix A to another matrix B |
| zlacrm, zlacrm.l | perform a very simple matrix-matrix multiplication |
| zlacrt, zlacrt.l | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex |
| zladiv, zladiv.l | := X / Y, where X and Y are complex |
| zlaed0, zlaed0.l | the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix |
| zlaed7, zlaed7.l | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| zlaed8, zlaed8.l | merge the two sets of eigenvalues together into a single sorted set |
| zlaein, zlaein.l | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H |
| zlaesy, zlaesy.l | compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value |
| zlaev2, zlaev2.l | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] |
| zlags2, zlags2.l | compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), |
| zlagtm, zlagtm.l | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 |
| zlahef, zlahef.l | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| zlahqr, zlahqr.l | i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI |
| zlahrd, zlahrd.l | reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero |
| zlaic1, zlaic1.l | applie one step of incremental condition estimation in its simplest version |
| zlangb, zlangb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals |
| zlange, zlange.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A |
| zlangt, zlangt.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A |
| zlanhb, zlanhb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals |
| zlanhe, zlanhe.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A |
| zlanhp, zlanhp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form |
| zlanhs, zlanhs.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A |
| zlanht, zlanht.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A |
| zlansb, zlansb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals |
| zlansp, zlansp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form |
| zlansy, zlansy.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A |
| zlantb, zlantb.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals |
| zlantp, zlantp.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form |
| zlantr, zlantr.l | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A |
| zlapll, zlapll.l | two column vectors X and Y, let A = ( X Y ) |
| zlapmt, zlapmt.l | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N |
| zlaqgb, zlaqgb.l | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C |
| zlaqge, zlaqge.l | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| zlaqhb, zlaqhb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| zlaqhe, zlaqhe.l | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| zlaqhp, zlaqhp.l | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| zlaqsb, zlaqsb.l | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| zlaqsp, zlaqsp.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| zlaqsy, zlaqsy.l | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| zlar2v, zlar2v.l | applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, |
| zlarf, zlarf.l | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right |
| zlarfb, zlarfb.l | applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right |
| zlarfg, zlarfg.l | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| zlarft, zlarft.l | form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors |
| zlarfx, zlarfx.l | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right |
| zlargv, zlargv.l | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y |
| zlarnv, zlarnv.l | return a vector of n random complex numbers from a uniform or normal distribution |
| zlartg, zlartg.l | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] |
| zlartv, zlartv.l | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y |
| zlascl, zlascl.l | multiply the M by N complex matrix A by the real scalar CTO/CFROM |
| zlaset, zlaset.l | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| zlasr, zlasr.l | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, |
| zlassq, zlassq.l | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| zlaswp, zlaswp.l | perform a series of row interchanges on the matrix A |
| zlasyf, zlasyf.l | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| zlatbs, zlatbs.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| zlatps, zlatps.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| zlatrd, zlatrd.l | reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A |
| zlatrs, zlatrs.l | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| zlatzm, zlatzm.l | applie a Householder matrix generated by ZTZRQF to a matrix |
| zlauu2, zlauu2.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| zlauum, zlauum.l | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A |
| zpbco, zpbco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| zpbcon, zpbcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF |
| zpbdi, zpbdi.l | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. |
| zpbequ, zpbequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) |
| zpbfa, zpbfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. |
| zpbrfs, zpbrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution |
| zpbsl, zpbsl.l | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. |
| zpbstf, zpbstf.l | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A |
| zpbsv, zpbsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zpbsvx, zpbsvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| zpbtf2, zpbtf2.l | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| zpbtrf, zpbtrf.l | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| zpbtrs, zpbtrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF |
| zpoco, zpoco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| zpocon, zpocon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF |
| zpodi, zpodi.l | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. |
| zpoequ, zpoequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) |
| zpofa, zpofa.l | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. |
| zporfs, zporfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, |
| zposl, zposl.l | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. |
| zposv, zposv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zposvx, zposvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| zpotf2, zpotf2.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| zpotrf, zpotrf.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| zpotri, zpotri.l | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF |
| zpotrs, zpotrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF |
| zppco, zppco.l | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| zppcon, zppcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF |
| zppdi, zppdi.l | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. |
| zppequ, zppequ.l | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) |
| zppfa, zppfa.l | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. |
| zpprfs, zpprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution |
| zppsl, zppsl.l | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. |
| zppsv, zppsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zppsvx, zppsvx.l | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, |
| zpptrf, zpptrf.l | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format |
| zpptri, zpptri.l | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF |
| zpptrs, zpptrs.l | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF |
| zptcon, zptcon.l | compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by ZPTTRF |
| zpteqr, zpteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidiagonal factor |
| zptrfs, zptrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution |
| zptsl, zptsl.l | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. |
| zptsv, zptsv.l | compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices |
| zptsvx, zptsvx.l | use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices |
| zpttrf, zpttrf.l | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A |
| zpttrs, zpttrs.l | solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by ZPTTRF |
| zqrdc, zqrdc.l | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. |
| zqrsl, zqrsl.l | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. |
| zrot, zrot.l | apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex |
| ZROTG, zrotg.l | Construct a Given’s plane rotation |
| ZSCAL, zscal.l | Compute y := alpha ∗ y |
| zsico, zsico.l | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| zsidi, zsidi.l | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. |
| zsifa, zsifa.l | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. |
| zsisl, zsisl.l | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. |
| zspco, zspco.l | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| zspcon, zspcon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF |
| zspdi, zspdi.l | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. |
| zspfa, zspfa.l | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. |
| zspmv, zspmv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| zspr, zspr.l | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, |
| zsprfs, zsprfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution |
| zspsl, zspsl.l | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. |
| zspsv, zspsv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zspsvx, zspsvx.l | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices |
| zsptrf, zsptrf.l | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| zsptri, zsptri.l | compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF |
| zsptrs, zsptrs.l | solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF |
| zstedc, zstedc.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| zstein, zstein.l | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| zsteqr, zsteqr.l | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| zsvdc, zsvdc.l | compute the singular value decomposition of a general matrix A. |
| ZSWAP, zswap.l | Exchange vectors x and y. |
| zsycon, zsycon.l | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF |
| zsymm, zsymm.l | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C |
| zsymv, zsymv.l | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| zsyr, zsyr.l | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, |
| zsyr2k, zsyr2k.l | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C |
| zsyrfs, zsyrfs.l | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution |
| zsyrk, zsyrk.l | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C |
| zsysv, zsysv.l | compute the solution to a complex system of linear equations A ∗ X = B, |
| zsysvx, zsysvx.l | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| zsytf2, zsytf2.l | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| zsytrf, zsytrf.l | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| zsytri, zsytri.l | compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF |
| zsytrs, zsytrs.l | solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF |
| ztbcon, ztbcon.l | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| ztbmv, ztbmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ztbrfs, ztbrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| ztbsv, ztbsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ztbtrs, ztbtrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ztgevc, ztgevc.l | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) |
| ztgsja, ztgsja.l | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B |
| ztpcon, ztpcon.l | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| ztpmv, ztpmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ztprfs, ztprfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| ztpsv, ztpsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ztptri, ztptri.l | compute the inverse of a complex upper or lower triangular matrix A stored in packed format |
| ztptrs, ztptrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ztrco, ztrco.l | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. |
| ztrcon, ztrcon.l | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| ztrdi, ztrdi.l | compute the determinant and inverse of a triangular matrix A. |
| ztrevc, ztrevc.l | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T |
| ztrexc, ztrexc.l | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST |
| ztrmm, ztrmm.l | perform one of the matrix-matrix operations B := alpha∗op( A )∗B or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ ) |
| ztrmv, ztrmv.l | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x |
| ztrrfs, ztrrfs.l | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| ztrsen, ztrsen.l | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace |
| ztrsl, ztrsl.l | solve the linear system Ax = b for a triangular matrix A and vectors b and x. |
| ztrsm, ztrsm.l | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B |
| ztrsna, ztrsna.l | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary) |
| ztrsv, ztrsv.l | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b |
| ztrsyl, ztrsyl.l | solve the complex Sylvester matrix equation |
| ztrti2, ztrti2.l | compute the inverse of a complex upper or lower triangular matrix |
| ztrtri, ztrtri.l | compute the inverse of a complex upper or lower triangular matrix A |
| ztrtrs, ztrtrs.l | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ztzrqf, ztzrqf.l | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations |
| zung2l, zung2l.l | generate an m by n complex matrix Q with orthonormal columns, |
| zung2r, zung2r.l | generate an m by n complex matrix Q with orthonormal columns, |
| zungbr, zungbr.l | generate one of the complex unitary matrices Q or P∗∗H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form |
| zunghr, zunghr.l | generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD |
| zungl2, zungl2.l | generate an m-by-n complex matrix Q with orthonormal rows, |
| zunglq, zunglq.l | generate an M-by-N complex matrix Q with orthonormal rows, |
| zungql, zungql.l | generate an M-by-N complex matrix Q with orthonormal columns, |
| zungqr, zungqr.l | generate an M-by-N complex matrix Q with orthonormal columns, |
| zungr2, zungr2.l | generate an m by n complex matrix Q with orthonormal rows, |
| zungrq, zungrq.l | generate an M-by-N complex matrix Q with orthonormal rows, |
| zungtr, zungtr.l | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD |
| zunm2l, zunm2l.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| zunm2r, zunm2r.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| zunmbr, zunmbr.l | VECT = ’Q’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunmhr, zunmhr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunml2, zunml2.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| zunmlq, zunmlq.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunmql, zunmql.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunmqr, zunmqr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunmr2, zunmr2.l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, |
| zunmrq, zunmrq.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zunmtr, zunmtr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| zupgtr, zupgtr.l | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage |
| zupmtr, zupmtr.l | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |