| saxpy, daxpy, zaxpy, caxpy | Vector plus the product of a scalar and a vector |
| sconv_nonperiodic, dconv_nonperiodic, zconv_nonperiodic, cconv_nonperiodic | Nonperiodic convolution |
| sconv_nonperiodic_ext, dconv_nonperiodic_ext, zconv_nonperiodic_ext, cconv_nonperiodic_ext | Extended nonperiodic convolution |
| sconv_periodic, dconv_periodic, zconv_periodic, cconv_periodic | Periodic concolution |
| sconv_periodic_ext, dconv_periodic_ext, zconv_periodic_ext, cconv_periodic_ext | Extended periodic convolution |
| scopy, dcopy, zcopy, ccopy | Copy of a vector |
| ccorr_nonperiodic | |
| ccorr_nonperiodic_ext | |
| ccorr_periodic | |
| scorr_periodic_ext, dcorr_periodic_ext, zcorr_periodic_ext, ccorr_periodic_ext | Extended periodic correlation |
| sdot, ddot, dsdot, zdotc, cdotu, zdotu, cdotc | INNER PRODUCT OF TWO VECTORS |
| sdot, ddot, dsdot, cdotc, zdotc, zdotu, cdotu | INNER PRODUCT OF TWO VECTORS |
| sfft, dfft, zfft, cfft | Fast fourier transform in one dimension |
| sfft_2d, dfft_2d, zfft_2d, cfft_2d | Fast fourier transform in two dimensions |
| sfft_3d, dfft_3d, zfft_3d, cfft_3d | Fast fourier transform in three dimensions |
| sfft_apply, dfft_apply, zfft_apply, cfft_apply | Application step for fast fourier transform in one dimension |
| cfft_apply_2d | |
| sfft_apply_3d, dfft_apply_3d, zfft_apply_3d, cfft_apply_3d | Application step for fast fourier transform in three dimensions |
| sfft_apply_grp, dfft_apply_grp, zfft_apply_grp, cfft_apply_grp | Application step for group fast fourier transform in one dimension |
| sfft_exit, dfft_exit, zfft_exit, cfft_exit | Final step for fast fourier transform in one dimension |
| sfft_exit_2d, dfft_exit_2d, zfft_exit_2d, cfft_exit_2d | Final step for fast fourier transform in two dimensions |
| sfft_exit_3d, dfft_exit_3d, zfft_exit_3d, cfft_exit_3d | Final step for fast fourier transfrom in three dimension |
| sfft_exit_grp, dfft_exit_grp, zfft_exit_grp, cfft_exit_grp | Exit step for group fast fourier transform in one dimension |
| sfft_grp, dfft_grp, zfft_grp, cfft_grp | Group fast fourier transform in one dimension |
| sfft_init, dfft_init, zfft_init, cfft_init | Initialization step for fast fourier transform in one dimension |
| sfft_init_2d, dfft_init_2d, zfft_init_2d, cfft_init_2d | Initialization step for fast fourier transform in two dimensions |
| sfft_init_3d, dfft_init_3d, zfft_init_3d, cfft_init_3d | Initialization step for fast fourier transform in three dimension |
| sfft_init_grp, dfft_init_grp, zfft_init_grp, cfft_init_grp | Initialization step for group fast fourier transform in one dimension |
| sgbmv, ddbmv, zgbmv, cgbmv | Matrix-vector product for a general band matrix |
| sgema, dgema, zgema, cgema | Matrix-matrix addition |
| sgemm, dgemm, zgemm, cgemm | Matrix-matrix product and addition |
| sgems, dgems, zgems, cgems | Matrix-matrix subtraction |
| sgemt, dgemt, zgemt, cgemt | Matrix-matrix copy |
| sgemv, dgemv, zgemv, cgemv | Matrix-vector product for a general matrix |
| sger, dger, zgerc, cgeru, zgeru, cgerc | Rank-one update of a general matrix |
| sger, dger, cgerc, zgerc, zgeru, cgeru | Rank-one update of a general matrix |
| ssbmv, dsbmv, zhbmv, chbmv | Matrix-vector product for a symmetric or hermitian band matrix |
| ssymm, dsymm, csymm, zsymm, zhemm, chemm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| ssymv, dsymv, zhemv, chemv | Matrix-vector product for a symmetric or hermitian matrix |
| ssyr, dsyr, zher, cher | Rank-one update of a symmetric or hermitian matrix |
| ssyr2, dsyr2, zher2, cher2 | Rank-two update of a symmetric or hermitian matrix |
| zher2k, cher2k | Rank-2k update of a complex hermitian matrix |
| zherk, cherk | Rank-k update of a complex hermitian matrix |
| sspmv, dspmv, zhpmv, chpmv | Matrix-vector product for a symmetric or hermitian matrix stored in packed form |
| sspr, dspr, zhpr, chpr | Rank-one update of a symmetric or hermitian matrix stored in packed form |
| sspr2, dspr2, zhpr2, chpr2 | Rank-two update of a symmetric or hermitian matrix stored in packed form |
| srot, drot, zrot, csrot, zdrot, crot | Apply givens plane rotation |
| crotg | |
| sscal, dscal, zscal, csscal, zdscal, cscal | Product of a scalar and a vector |
| sset, dset, zset, cset | Set all elements of a vector to a scalar |
| srot, drot, crot, zrot, zdrot, csrot | Apply givens plane rotation |
| sscal, dscal, cscal, zscal, zdscal, csscal | Product of a scalar and a vector |
| ssum, dsum, zsum, csum | Sum of the values of the elements of a vector |
| svcal, dvcal, cvcal, zvcal, zdvcal, csvcal | Product of a scalar and a vector |
| sswap, dswap, zswap, cswap | Exchange the elements of two vectors |
| ssymm, dsymm, zsymm, chemm, zhemm, csymm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| ssyr2k, dsyr2k, zsyr2k, csyr2k | Rank-2k update of a symmetric matrix |
| ssyrk, dsyrk, zsyrk, csyrk | Rank-k update of a symmetric matrix |
| stbmv, dtbmv, ztbmv, ctbmv | Matrix-vector product for a triangular band matrix |
| stbsv, dtbsv, ztbsv, ctbsv | Solver of a system of linear equations with a triangular band matrix |
| stpmv, dtpmv, ztpmv, ctpmv | Matrix-vector product for a triangular matrix in packed form |
| stpsv, dtpsv, ztpsv, ctpsv | Solve a system of linear equations with a triangular matrix in packed form |
| strmm, dtrmm, ztrmm, ctrmm | Matrix-matrix product for triangular matrix |
| strmv, dtrmv, ztrmv, ctrmv | Marix-vector product for a triangular matrix |
| strsm, dtrsm, ztrsm, ctrsm | Solve a triangular system of equations with a triangular coefficient matrix |
| strsv, dtrsv, ztrsv, ctrsv | Solver of a system of linear equations with a triangular matrix |
| svcal, dvcal, zvcal, csvcal, zdvcal, cvcal | Product of a scalar and a vector |
| szaxpy, dzaxpy, zzaxpy, czaxpy | Vector plus the product of a scalar and a vector |
| samax, scamax, dzamax, damax | Maximum absolute value |
| damin | |
| sasum, scasum, dzasum, dasum | Sum of the absolute value |
| saxpy, caxpy, zaxpy, daxpy | Vector plus the product of a scalar and a vector |
| sconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic, dconv_nonperiodic | Nonperiodic convolution |
| sconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext, dconv_nonperiodic_ext | Extended nonperiodic convolution |
| sconv_periodic, cconv_periodic, zconv_periodic, dconv_periodic | Periodic concolution |
| sconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext, dconv_periodic_ext | Extended periodic convolution |
| scopy, ccopy, zcopy, dcopy | Copy of a vector |
| dcorr_nonperiodic | |
| dcorr_nonperiodic_ext | |
| dcorr_periodic | |
| scorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext, dcorr_periodic_ext | Extended periodic correlation |
| sdot, dsdot, cdotc, zdotc, cdotu, zdotu, ddot | INNER PRODUCT OF TWO VECTORS |
| sfct, dfct | Fast cosine transform in one dimension |
| sfct_apply, dfct_apply | Application step for fast cosine transform in one dimension |
| sfct_exit, dfct_exit | Final step for fast cosine transform in one dimension |
| sfct_init, dfct_init | Initialization step for fast cosine transform in one dimension |
| sfft, cfft, zfft, dfft | Fast fourier transform in one dimension |
| sfft_2d, cfft_2d, zfft_2d, dfft_2d | Fast fourier transform in two dimensions |
| sfft_3d, cfft_3d, zfft_3d, dfft_3d | Fast fourier transform in three dimensions |
| sfft_apply, cfft_apply, zfft_apply, dfft_apply | Application step for fast fourier transform in one dimension |
| dfft_apply_2d | |
| sfft_apply_3d, cfft_apply_3d, zfft_apply_3d, dfft_apply_3d | Application step for fast fourier transform in three dimensions |
| sfft_apply_grp, cfft_apply_grp, zfft_apply_grp, dfft_apply_grp | Application step for group fast fourier transform in one dimension |
| sfft_exit, cfft_exit, zfft_exit, dfft_exit | Final step for fast fourier transform in one dimension |
| sfft_exit_2d, cfft_exit_2d, zfft_exit_2d, dfft_exit_2d | Final step for fast fourier transform in two dimensions |
| sfft_exit_3d, cfft_exit_3d, zfft_exit_3d, dfft_exit_3d | Final step for fast fourier transfrom in three dimension |
| sfft_exit_grp, cfft_exit_grp, zfft_exit_grp, dfft_exit_grp | Exit step for group fast fourier transform in one dimension |
| sfft_grp, cfft_grp, zfft_grp, dfft_grp | Group fast fourier transform in one dimension |
| sfft_init, cfft_init, zfft_init, dfft_init | Initialization step for fast fourier transform in one dimension |
| sfft_init_2d, cfft_init_2d, zfft_init_2d, dfft_init_2d | Initialization step for fast fourier transform in two dimensions |
| sfft_init_3d, cfft_init_3d, zfft_init_3d, dfft_init_3d | Initialization step for fast fourier transform in three dimension |
| sfft_init_grp, cfft_init_grp, zfft_init_grp, dfft_init_grp | Initialization step for group fast fourier transform in one dimension |
| sfst, dfst | Fast sine transform in one dimension |
| sfst_apply, dfst_apply | Application step for fast sine transform in one dimension |
| sfst_exit, dfst_exit | Final step for fast sine transform in one dimension |
| sfst_init, dfst_init | Initialization step for fast sine transform in one dimension |
| sgbmv, ddbmv, cgbmv, zgbmv, dgbmv | Matrix-vector product for a general band matrix |
| sgema, cgema, zgema, dgema | Matrix-matrix addition |
| sgemm, cgemm, zgemm, dgemm | Matrix-matrix product and addition |
| sgems, cgems, zgems, dgems | Matrix-matrix subtraction |
| sgemt, cgemt, zgemt, dgemt | Matrix-matrix copy |
| sgemv, cgemv, zgemv, dgemv | Matrix-vector product for a general matrix |
| sger, cgerc, zgerc, cgeru, zgeru, dger | Rank-one update of a general matrix |
| smax, dmax | Largest element in a real vector |
| smin, dmin | Minimum value of the elements of a real vector |
| snorm2, scnorm2, dznorm2, dnorm2 | Square root of sum of the squares of the elements of a vector |
| snrm2, scnrm2, dznrm2, dnrm2 | Square root of sum of the squares of the elements of a vector |
| snrsq, scnrsq, dznrsq, dnrsq | Sum of the squares of the elements of a vector |
| srot, crot, zrot, csrot, zdrot, drot | Apply givens plane rotation |
| drotg | |
| srotm, drotm | Apply modified givens transformation |
| srotmg, drotmg | Generate elements for a modified Givens transform |
| ssbmv, chbmv, zhbmv, dsbmv | Matrix-vector product for a symmetric or hermitian band matrix |
| sscal, cscal, zscal, csscal, zdscal, dscal | Product of a scalar and a vector |
| sdot, ddot, cdotc, zdotc, cdotu, zdotu, dsdot | INNER PRODUCT OF TWO VECTORS |
| sset, cset, zset, dset | Set all elements of a vector to a scalar |
| isortq, ssortq, dsortq | Sort the elements of a vector |
| isortqx, ssortqx, dsortqx | Performs an indexed sort of a vector |
| sspmv, chpmv, zhpmv, dspmv | Matrix-vector product for a symmetric or hermitian matrix stored in packed form |
| sspr, chpr, zhpr, dspr | Rank-one update of a symmetric or hermitian matrix stored in packed form |
| sspr2, chpr2, zhpr2, dspr2 | Rank-two update of a symmetric or hermitian matrix stored in packed form |
| ssum, csum, zsum, dsum | Sum of the values of the elements of a vector |
| sswap, cswap, zswap, dswap | Exchange the elements of two vectors |
| ssymm, csymm, zsymm, chemm, zhemm, dsymm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| ssymv, chemv, zhemv, dsymv | Matrix-vector product for a symmetric or hermitian matrix |
| ssyr, cher, zher, dsyr | Rank-one update of a symmetric or hermitian matrix |
| ssyr2, cher2, zher2, dsyr2 | Rank-two update of a symmetric or hermitian matrix |
| ssyr2k, csyr2k, zsyr2k, dsyr2k | Rank-2k update of a symmetric matrix |
| ssyrk, csyrk, zsyrk, dsyrk | Rank-k update of a symmetric matrix |
| stbmv, ctbmv, ztbmv, dtbmv | Matrix-vector product for a triangular band matrix |
| stbsv, ctbsv, ztbsv, dtbsv | Solver of a system of linear equations with a triangular band matrix |
| stpmv, ctpmv, ztpmv, dtpmv | Matrix-vector product for a triangular matrix in packed form |
| stpsv, ctpsv, ztpsv, dtpsv | Solve a system of linear equations with a triangular matrix in packed form |
| strmm, ctrmm, ztrmm, dtrmm | Matrix-matrix product for triangular matrix |
| strmv, ctrmv, ztrmv, dtrmv | Marix-vector product for a triangular matrix |
| strsm, ctrsm, ztrsm, dtrsm | Solve a triangular system of equations with a triangular coefficient matrix |
| strsv, ctrsv, ztrsv, dtrsv | Solver of a system of linear equations with a triangular matrix |
| svcal, cvcal, zvcal, csvcal, zdvcal, dvcal | Product of a scalar and a vector |
| dxml | A library of linear algebra and signal processing routines |
| samax, damax, scamax, dzamax | Maximum absolute value |
| dzamin | |
| sasum, dasum, scasum, dzasum | Sum of the absolute value |
| szaxpy, czaxpy, zzaxpy, dzaxpy | Vector plus the product of a scalar and a vector |
| snorm2, dnorm2, scnorm2, dznorm2 | Square root of sum of the squares of the elements of a vector |
| snrm2, dnrm2, scnrm2, dznrm2 | Square root of sum of the squares of the elements of a vector |
| snrsq, dnrsq, scnrsq, dznrsq | Sum of the squares of the elements of a vector |
| gen_sort | Sort the elements of a vector |
| gen_sortx | Sort the elements of an indexed vector |
| isamax, idamax, izamax, icamax | Index of the element of a vector with maximum absolute value |
| icamin | |
| isamax, icamax, izamax, idamax | Index of the element of a vector with maximum absolute value |
| idamin | |
| ismax, idmax | Index of the real vector element with maximum value |
| ismin, idmin | Index of the real vector element with minimum value |
| idamax, icamax, izamax, isamax | Index of the element of a vector with maximum absolute value |
| isamin | |
| idmax, ismax | Index of the real vector element with maximum value |
| idmin, ismin | Index of the real vector element with minimum value |
| ssortq, dsortq, isortq | Sort the elements of a vector |
| ssortqx, dsortqx, isortqx | Performs an indexed sort of a vector |
| isamax, idamax, icamax, izamax | Index of the element of a vector with maximum absolute value |
| izamin | |
| ran16807 | Routine to generate single precision random numbers using a=16807 and m=2∗∗31-1 |
| ran69069 | Routine to generate single precision random numbers using a=69069 and m=2∗∗32 |
| ranl | Random number generator based on L’Ecuyer method |
| ranl_normal | Routine to generate normally distributed random numbers using summation of uniformly distributed random numbers |
| ranl_skip2 | Routine to skip forward 2∗∗d seeds for the RANL and RANL_NORMAL random number generators |
| ranl_skip64 | Routine to skip forward a given number, d, of seeds for the RANL and RANL_NORMAL random number generators |
| damax, scamax, dzamax, samax | Maximum absolute value |
| samin | |
| dasum, scasum, dzasum, sasum | Sum of the absolute value |
| daxpy, caxpy, zaxpy, saxpy | Vector plus the product of a scalar and a vector |
| samax, damax, dzamax, scamax | Maximum absolute value |
| scamin | |
| sasum, dasum, dzasum, scasum | Sum of the absolute value |
| snorm2, dnorm2, dznorm2, scnorm2 | Square root of sum of the squares of the elements of a vector |
| snrm2, dnrm2, dznrm2, scnrm2 | Square root of sum of the squares of the elements of a vector |
| snrsq, dnrsq, dznrsq, scnrsq | Sum of the squares of the elements of a vector |
| dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic, sconv_nonperiodic | Nonperiodic convolution |
| dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext, sconv_nonperiodic_ext | Extended nonperiodic convolution |
| dconv_periodic, cconv_periodic, zconv_periodic, sconv_periodic | Periodic concolution |
| dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext, sconv_periodic_ext | Extended periodic convolution |
| dcopy, ccopy, zcopy, scopy | Copy of a vector |
| scorr_nonperiodic | |
| scorr_nonperiodic_ext | |
| scorr_periodic | |
| dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext, scorr_periodic_ext | Extended periodic correlation |
| ddot, dsdot, cdotc, zdotc, cdotu, zdotu, sdot | INNER PRODUCT OF TWO VECTORS |
| sdsdot | Product of scaled vector and vector |
| dfct, sfct | Fast cosine transform in one dimension |
| dfct_apply, sfct_apply | Application step for fast cosine transform in one dimension |
| dfct_exit, sfct_exit | Final step for fast cosine transform in one dimension |
| dfct_init, sfct_init | Initialization step for fast cosine transform in one dimension |
| dfft, cfft, zfft, sfft | Fast fourier transform in one dimension |
| dfft_2d, cfft_2d, zfft_2d, sfft_2d | Fast fourier transform in two dimensions |
| dfft_3d, cfft_3d, zfft_3d, sfft_3d | Fast fourier transform in three dimensions |
| dfft_apply, cfft_apply, zfft_apply, sfft_apply | Application step for fast fourier transform in one dimension |
| sfft_apply_2d | |
| dfft_apply_3d, cfft_apply_3d, zfft_apply_3d, sfft_apply_3d | Application step for fast fourier transform in three dimensions |
| dfft_apply_grp, cfft_apply_grp, zfft_apply_grp, sfft_apply_grp | Application step for group fast fourier transform in one dimension |
| dfft_exit, cfft_exit, zfft_exit, sfft_exit | Final step for fast fourier transform in one dimension |
| dfft_exit_2d, cfft_exit_2d, zfft_exit_2d, sfft_exit_2d | Final step for fast fourier transform in two dimensions |
| dfft_exit_3d, cfft_exit_3d, zfft_exit_3d, sfft_exit_3d | Final step for fast fourier transfrom in three dimension |
| dfft_exit_grp, cfft_exit_grp, zfft_exit_grp, sfft_exit_grp | Exit step for group fast fourier transform in one dimension |
| dfft_grp, cfft_grp, zfft_grp, sfft_grp | Group fast fourier transform in one dimension |
| dfft_init, cfft_init, zfft_init, sfft_init | Initialization step for fast fourier transform in one dimension |
| dfft_init_2d, cfft_init_2d, zfft_init_2d, sfft_init_2d | Initialization step for fast fourier transform in two dimensions |
| dfft_init_3d, cfft_init_3d, zfft_init_3d, sfft_init_3d | Initialization step for fast fourier transform in three dimension |
| dfft_init_grp, cfft_init_grp, zfft_init_grp, sfft_init_grp | Initialization step for group fast fourier transform in one dimension |
| sfilter_apply_nonrec | Performs filtering in lowpass, highpass, bandpass, or bandstop (notch) mode by using the working array that was computed by SFILTER_INIT_NONREC. |
| sfilter_init_nonrec | Computes a working array that is used by sfilter_apply_nonrec routine. |
| sfilter_nonrec | Performs filtering in lowpass, highpass, bandpass, or bandstop (notch) mode. |
| dfst, sfst | Fast sine transform in one dimension |
| dfst_apply, sfst_apply | Application step for fast sine transform in one dimension |
| dfst_exit, sfst_exit | Final step for fast sine transform in one dimension |
| dfst_init, sfst_init | Initialization step for fast sine transform in one dimension |
| ddbmv, cgbmv, zgbmv, sgbmv | Matrix-vector product for a general band matrix |
| dgema, cgema, zgema, sgema | Matrix-matrix addition |
| dgemm, cgemm, zgemm, sgemm | Matrix-matrix product and addition |
| dgems, cgems, zgems, sgems | Matrix-matrix subtraction |
| dgemt, cgemt, zgemt, sgemt | Matrix-matrix copy |
| dgemv, cgemv, zgemv, sgemv | Matrix-vector product for a general matrix |
| dger, cgerc, zgerc, cgeru, zgeru, sger | Rank-one update of a general matrix |
| dmax, smax | Largest element in a real vector |
| dmin, smin | Minimum value of the elements of a real vector |
| dnorm2, scnorm2, dznorm2, snorm2 | Square root of sum of the squares of the elements of a vector |
| dnrm2, scnrm2, dznrm2, snrm2 | Square root of sum of the squares of the elements of a vector |
| dnrsq, scnrsq, dznrsq, snrsq | Sum of the squares of the elements of a vector |
| sorts | A library of sort routines |
| drot, crot, zrot, csrot, zdrot, srot | Apply givens plane rotation |
| srotg | |
| drotm, srotm | Apply modified givens transformation |
| drotmg, srotmg | Generate elements for a modified Givens transform |
| dsbmv, chbmv, zhbmv, ssbmv | Matrix-vector product for a symmetric or hermitian band matrix |
| dscal, cscal, zscal, csscal, zdscal, sscal | Product of a scalar and a vector |
| dset, cset, zset, sset | Set all elements of a vector to a scalar |
| isortq, dsortq, ssortq | Sort the elements of a vector |
| isortqx, dsortqx, ssortqx | Performs an indexed sort of a vector |
| dspmv, chpmv, zhpmv, sspmv | Matrix-vector product for a symmetric or hermitian matrix stored in packed form |
| dspr, chpr, zhpr, sspr | Rank-one update of a symmetric or hermitian matrix stored in packed form |
| dspr2, chpr2, zhpr2, sspr2 | Rank-two update of a symmetric or hermitian matrix stored in packed form |
| dsum, csum, zsum, ssum | Sum of the values of the elements of a vector |
| dswap, cswap, zswap, sswap | Exchange the elements of two vectors |
| dsymm, csymm, zsymm, chemm, zhemm, ssymm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| dsymv, chemv, zhemv, ssymv | Matrix-vector product for a symmetric or hermitian matrix |
| dsyr, cher, zher, ssyr | Rank-one update of a symmetric or hermitian matrix |
| dsyr2, cher2, zher2, ssyr2 | Rank-two update of a symmetric or hermitian matrix |
| dsyr2k, csyr2k, zsyr2k, ssyr2k | Rank-2k update of a symmetric matrix |
| dsyrk, csyrk, zsyrk, ssyrk | Rank-k update of a symmetric matrix |
| dtbmv, ctbmv, ztbmv, stbmv | Matrix-vector product for a triangular band matrix |
| dtbsv, ctbsv, ztbsv, stbsv | Solver of a system of linear equations with a triangular band matrix |
| dtpmv, ctpmv, ztpmv, stpmv | Matrix-vector product for a triangular matrix in packed form |
| dtpsv, ctpsv, ztpsv, stpsv | Solve a system of linear equations with a triangular matrix in packed form |
| dtrmm, ctrmm, ztrmm, strmm | Matrix-matrix product for triangular matrix |
| dtrmv, ctrmv, ztrmv, strmv | Marix-vector product for a triangular matrix |
| dtrsm, ctrsm, ztrsm, strsm | Solve a triangular system of equations with a triangular coefficient matrix |
| dtrsv, ctrsv, ztrsv, strsv | Solver of a system of linear equations with a triangular matrix |
| dvcal, cvcal, zvcal, csvcal, zdvcal, svcal | Product of a scalar and a vector |
| dzaxpy, czaxpy, zzaxpy, szaxpy | Vector plus the product of a scalar and a vector |
| vxworks_dxml | Using DXML on VxWorks |
| saxpy, daxpy, caxpy, zaxpy | Vector plus the product of a scalar and a vector |
| sconv_nonperiodic, dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic | Nonperiodic convolution |
| sconv_nonperiodic_ext, dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext | Extended nonperiodic convolution |
| sconv_periodic, dconv_periodic, cconv_periodic, zconv_periodic | Periodic concolution |
| sconv_periodic_ext, dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext | Extended periodic convolution |
| scopy, dcopy, ccopy, zcopy | Copy of a vector |
| zcorr_nonperiodic | |
| zcorr_nonperiodic_ext | |
| zcorr_periodic | |
| scorr_periodic_ext, dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext | Extended periodic correlation |
| sdot, ddot, dsdot, cdotc, cdotu, zdotu, zdotc | INNER PRODUCT OF TWO VECTORS |
| sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu | INNER PRODUCT OF TWO VECTORS |
| srot, drot, crot, zrot, csrot, zdrot | Apply givens plane rotation |
| sscal, dscal, cscal, zscal, csscal, zdscal | Product of a scalar and a vector |
| svcal, dvcal, cvcal, zvcal, csvcal, zdvcal | Product of a scalar and a vector |
| sfft, dfft, cfft, zfft | Fast fourier transform in one dimension |
| sfft_2d, dfft_2d, cfft_2d, zfft_2d | Fast fourier transform in two dimensions |
| sfft_3d, dfft_3d, cfft_3d, zfft_3d | Fast fourier transform in three dimensions |
| sfft_apply, dfft_apply, cfft_apply, zfft_apply | Application step for fast fourier transform in one dimension |
| zfft_apply_2d | |
| sfft_apply_3d, dfft_apply_3d, cfft_apply_3d, zfft_apply_3d | Application step for fast fourier transform in three dimensions |
| sfft_apply_grp, dfft_apply_grp, cfft_apply_grp, zfft_apply_grp | Application step for group fast fourier transform in one dimension |
| sfft_exit, dfft_exit, cfft_exit, zfft_exit | Final step for fast fourier transform in one dimension |
| sfft_exit_2d, dfft_exit_2d, cfft_exit_2d, zfft_exit_2d | Final step for fast fourier transform in two dimensions |
| sfft_exit_3d, dfft_exit_3d, cfft_exit_3d, zfft_exit_3d | Final step for fast fourier transfrom in three dimension |
| sfft_exit_grp, dfft_exit_grp, cfft_exit_grp, zfft_exit_grp | Exit step for group fast fourier transform in one dimension |
| sfft_grp, dfft_grp, cfft_grp, zfft_grp | Group fast fourier transform in one dimension |
| sfft_init, dfft_init, cfft_init, zfft_init | Initialization step for fast fourier transform in one dimension |
| sfft_init_2d, dfft_init_2d, cfft_init_2d, zfft_init_2d | Initialization step for fast fourier transform in two dimensions |
| sfft_init_3d, dfft_init_3d, cfft_init_3d, zfft_init_3d | Initialization step for fast fourier transform in three dimension |
| sfft_init_grp, dfft_init_grp, cfft_init_grp, zfft_init_grp | Initialization step for group fast fourier transform in one dimension |
| sgbmv, ddbmv, cgbmv, zgbmv | Matrix-vector product for a general band matrix |
| sgema, dgema, cgema, zgema | Matrix-matrix addition |
| sgemm, dgemm, cgemm, zgemm | Matrix-matrix product and addition |
| sgems, dgems, cgems, zgems | Matrix-matrix subtraction |
| sgemt, dgemt, cgemt, zgemt | Matrix-matrix copy |
| sgemv, dgemv, cgemv, zgemv | Matrix-vector product for a general matrix |
| sger, dger, cgerc, cgeru, zgeru, zgerc | Rank-one update of a general matrix |
| sger, dger, cgerc, zgerc, cgeru, zgeru | Rank-one update of a general matrix |
| ssbmv, dsbmv, chbmv, zhbmv | Matrix-vector product for a symmetric or hermitian band matrix |
| ssymm, dsymm, csymm, zsymm, chemm, zhemm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| ssymv, dsymv, chemv, zhemv | Matrix-vector product for a symmetric or hermitian matrix |
| ssyr, dsyr, cher, zher | Rank-one update of a symmetric or hermitian matrix |
| ssyr2, dsyr2, cher2, zher2 | Rank-two update of a symmetric or hermitian matrix |
| cher2k, zher2k | Rank-2k update of a complex hermitian matrix |
| cherk, zherk | Rank-k update of a complex hermitian matrix |
| sspmv, dspmv, chpmv, zhpmv | Matrix-vector product for a symmetric or hermitian matrix stored in packed form |
| sspr, dspr, chpr, zhpr | Rank-one update of a symmetric or hermitian matrix stored in packed form |
| sspr2, dspr2, chpr2, zhpr2 | Rank-two update of a symmetric or hermitian matrix stored in packed form |
| srot, drot, crot, csrot, zdrot, zrot | Apply givens plane rotation |
| zrotg | |
| sscal, dscal, cscal, csscal, zdscal, zscal | Product of a scalar and a vector |
| sset, dset, cset, zset | Set all elements of a vector to a scalar |
| ssum, dsum, csum, zsum | Sum of the values of the elements of a vector |
| sswap, dswap, cswap, zswap | Exchange the elements of two vectors |
| ssymm, dsymm, csymm, chemm, zhemm, zsymm | Matrix-matrix product and addition for a symmetric or hermitian matrix |
| ssyr2k, dsyr2k, csyr2k, zsyr2k | Rank-2k update of a symmetric matrix |
| ssyrk, dsyrk, csyrk, zsyrk | Rank-k update of a symmetric matrix |
| stbmv, dtbmv, ctbmv, ztbmv | Matrix-vector product for a triangular band matrix |
| stbsv, dtbsv, ctbsv, ztbsv | Solver of a system of linear equations with a triangular band matrix |
| stpmv, dtpmv, ctpmv, ztpmv | Matrix-vector product for a triangular matrix in packed form |
| stpsv, dtpsv, ctpsv, ztpsv | Solve a system of linear equations with a triangular matrix in packed form |
| strmm, dtrmm, ctrmm, ztrmm | Matrix-matrix product for triangular matrix |
| strmv, dtrmv, ctrmv, ztrmv | Marix-vector product for a triangular matrix |
| strsm, dtrsm, ctrsm, ztrsm | Solve a triangular system of equations with a triangular coefficient matrix |
| strsv, dtrsv, ctrsv, ztrsv | Solver of a system of linear equations with a triangular matrix |
| svcal, dvcal, cvcal, csvcal, zdvcal, zvcal | Product of a scalar and a vector |
| szaxpy, dzaxpy, czaxpy, zzaxpy | Vector plus the product of a scalar and a vector |
| CBDSQR, cbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| CGBBRD, cgbbrd | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation |
| CGBCON, cgbcon | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, |
| CGBEQU, cgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| CGBRFS, cgbrfs | 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 |
| CGBSV, cgbsv | 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 | 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 | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| CGBTRF, cgbtrf | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| CGBTRS, cgbtrs | 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 | 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 | balance a general complex matrix A |
| CGEBD2, cgebd2 | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation |
| CGEBRD, cgebrd | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation |
| CGECON, cgecon | 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 |
| CGEEQU, cgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| CGEES, cgees | 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 | 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 | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| CGEEVX, cgeevx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| CGEGS, cgegs | compute for a pair of N-by-N complex nonsymmetric matrices A, |
| CGEGV, cgegv | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, |
| CGEHD2, cgehd2 | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| CGEHRD, cgehrd | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| CGELQ2, cgelq2 | compute an LQ factorization of a complex m by n matrix A |
| CGELQF, cgelqf | compute an LQ factorization of a complex M-by-N matrix A |
| CGELS, cgels | 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 | compute the minimum norm solution to a complex linear least squares problem |
| CGELSX, cgelsx | compute the minimum-norm solution to a complex linear least squares problem |
| CGEQL2, cgeql2 | compute a QL factorization of a complex m by n matrix A |
| CGEQLF, cgeqlf | compute a QL factorization of a complex M-by-N matrix A |
| CGEQPF, cgeqpf | compute a QR factorization with column pivoting of a complex M-by-N matrix A |
| CGEQR2, cgeqr2 | compute a QR factorization of a complex m by n matrix A |
| CGEQRF, cgeqrf | compute a QR factorization of a complex M-by-N matrix A |
| CGERFS, cgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| CGERQ2, cgerq2 | compute an RQ factorization of a complex m by n matrix A |
| CGERQF, cgerqf | compute an RQ factorization of a complex M-by-N matrix A |
| CGESV, cgesv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CGESVD, cgesvd | 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 | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| CGETF2, cgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| CGETRF, cgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| CGETRI, cgetri | compute the inverse of a matrix using the LU factorization computed by CGETRF |
| CGETRS, cgetrs | 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 | 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 | balance a pair of general complex matrices (A,B) |
| CGGGLM, cggglm | solve a general Gauss-Markov linear model (GLM) problem |
| CGGHRD, cgghrd | 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 | solve the linear equality-constrained least squares (LSE) problem |
| CGGQRF, cggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| CGGRQF, cggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| CGGSVD, cggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B |
| CGGSVP, cggsvp | 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 | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF |
| CGTRFS, cgtrfs | 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 |
| CGTSV, cgtsv | solve the equation A∗X = B, |
| CGTSVX, cgtsvx | 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 | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| CGTTRS, cgttrs | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| CHBEV, chbev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| CHBEVD, chbevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| CHBEVX, chbevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| CHBGST, chbgst | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| CHBGV, chbgv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| CHBTRD, chbtrd | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| CHECON, checon | 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 | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| CHEEVD, cheevd | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| CHEEVX, cheevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| CHEGS2, chegs2 | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| CHEGST, chegst | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| CHEGV, chegv | 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 |
| CHERFS, cherfs | 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 |
| CHESV, chesv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CHESVX, chesvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| CHETD2, chetd2 | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| CHETF2, chetf2 | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| CHETRD, chetrd | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| CHETRF, chetrf | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| CHETRI, chetri | 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 | 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 | 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 |
| CHPCON, chpcon | 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 |
| CHPEV, chpev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage |
| CHPEVD, chpevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| CHPEVX, chpevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| CHPGST, chpgst | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage |
| CHPGV, chpgv | 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 |
| CHPRFS, chprfs | 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 |
| CHPSV, chpsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CHPSVX, chpsvx | 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 | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation |
| CHPTRF, chptrf | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method |
| CHPTRI, chptri | 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 | 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 | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H |
| CHSEQR, chseqr | 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 | 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 | conjugate a complex vector of length N |
| CLACON, clacon | estimate the 1-norm of a square, complex matrix A |
| CLACPY, clacpy | copie all or part of a two-dimensional matrix A to another matrix B |
| CLACRM, clacrm | perform a very simple matrix-matrix multiplication |
| CLACRT, clacrt | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex |
| CLADIV, cladiv | := X / Y, where X and Y are complex |
| CLAED0, claed0 | 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 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| CLAED8, claed8 | merge the two sets of eigenvalues together into a single sorted set |
| CLAEIN, claein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H |
| CLAESY, claesy | 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 | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] |
| clags2 | |
| CLAGTM, clagtm | 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 | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| CLAHQR, clahqr | 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 | 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 | applie one step of incremental condition estimation in its simplest version |
| CLANGB, clangb | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | two column vectors X and Y, let A = ( X Y ) |
| CLAPMT, clapmt | 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 | 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 | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| CLAQHB, claqhb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| CLAQHE, claqhe | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| CLAQHP, claqhp | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| CLAQSB, claqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| CLAQSP, claqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| CLAQSY, claqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| CLAR2V, clar2v | 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 | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right |
| CLARFB, clarfb | 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 | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| CLARFT, clarft | 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 | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right |
| CLARGV, clargv | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y |
| CLARNV, clarnv | return a vector of n random complex numbers from a uniform or normal distribution |
| CLARTG, clartg | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] |
| CLARTV, clartv | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y |
| CLASCL, clascl | multiplie the M by N complex matrix A by the real scalar CTO/CFROM |
| CLASET, claset | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| CLASR, clasr | 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 | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| CLASWP, claswp | perform a series of row interchanges on the matrix A |
| CLASYF, clasyf | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| CLATBS, clatbs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| CLATPS, clatps | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| CLATRD, clatrd | 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 | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| CLATZM, clatzm | applie a Householder matrix generated by CTZRQF to a matrix |
| CLAUU2, clauu2 | 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 | 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 |
| CLAZRO, clazro | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| CPBCON, cpbcon | 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 |
| CPBEQU, cpbequ | 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) |
| CPBRFS, cpbrfs | 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 |
| CPBSTF, cpbstf | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A |
| CPBSV, cpbsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CPBSVX, cpbsvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| CPBTRF, cpbtrf | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| CPBTRS, cpbtrs | 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 |
| CPOCON, cpocon | 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 |
| CPOEQU, cpoequ | 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) |
| CPORFS, cporfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, |
| CPOSV, cposv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CPOSVX, cposvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| CPOTRF, cpotrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| CPOTRI, cpotri | 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 | 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 |
| CPPCON, cppcon | 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 |
| CPPEQU, cppequ | 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) |
| CPPRFS, cpprfs | 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 |
| CPPSV, cppsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CPPSVX, cppsvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format |
| CPPTRI, cpptri | 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 | 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 | 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 | 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 | 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 |
| CPTSV, cptsv | 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 | 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 | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A |
| CPTTRS, cpttrs | 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 |
| CROT, crot | applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex |
| CSPCON, cspcon | 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 |
| CSPMV, cspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| CSPR, cspr | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, |
| CSPRFS, csprfs | 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 |
| CSPSV, cspsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CSPSVX, cspsvx | 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 | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| CSPTRI, csptri | 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 | 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 |
| CSRSCL, csrscl | multiplie an n-element complex vector x by the real scalar 1/a |
| CSTEDC, cstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| CSTEIN, cstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| CSTEQR, csteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| CSYCON, csycon | 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 |
| CSYMV, csymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| CSYR, csyr | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, |
| CSYRFS, csyrfs | 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 |
| CSYSV, csysv | compute the solution to a complex system of linear equations A ∗ X = B, |
| CSYSVX, csysvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| CSYTF2, csytf2 | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| CSYTRF, csytrf | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| CSYTRI, csytri | 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 | 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 | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| CTBRFS, ctbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| CTBTRS, ctbtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| CTGEVC, ctgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) |
| CTGSJA, ctgsja | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B |
| CTPCON, ctpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| CTPRFS, ctprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| CTPTRI, ctptri | compute the inverse of a complex upper or lower triangular matrix A stored in packed format |
| CTPTRS, ctptrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| CTRCON, ctrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| CTREVC, ctrevc | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T |
| CTREXC, ctrexc | 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 |
| CTRRFS, ctrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| CTRSEN, ctrsen | 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 |
| CTRSNA, ctrsna | 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) |
| CTRSYL, ctrsyl | solve the complex Sylvester matrix equation |
| CTRTI2, ctrti2 | compute the inverse of a complex upper or lower triangular matrix |
| CTRTRI, ctrtri | compute the inverse of a complex upper or lower triangular matrix A |
| CTRTRS, ctrtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| CTZRQF, ctzrqf | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations |
| CUNG2L, cung2l | generate an m by n complex matrix Q with orthonormal columns, |
| CUNG2R, cung2r | generate an m by n complex matrix Q with orthonormal columns, |
| CUNGBR, cungbr | 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 | 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 | generate an m-by-n complex matrix Q with orthonormal rows, |
| CUNGLQ, cunglq | generate an M-by-N complex matrix Q with orthonormal rows, |
| CUNGQL, cungql | generate an M-by-N complex matrix Q with orthonormal columns, |
| CUNGQR, cungqr | generate an M-by-N complex matrix Q with orthonormal columns, |
| CUNGR2, cungr2 | generate an m by n complex matrix Q with orthonormal rows, |
| CUNGRQ, cungrq | generate an M-by-N complex matrix Q with orthonormal rows, |
| CUNGTR, cungtr | 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 | 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 | 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 | VECT = ’Q’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNMHR, cunmhr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNML2, cunml2 | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNMQL, cunmql | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNMQR, cunmqr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNMR2, cunmr2 | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUNMTR, cunmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| CUPGTR, cupgtr | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DBDSQR, dbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| DDISNA, ddisna | 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 |
| DGBBRD, dgbbrd | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation |
| DGBCON, dgbcon | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, |
| DGBEQU, dgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| DGBRFS, dgbrfs | 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 |
| DGBSV, dgbsv | 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 | 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 | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| DGBTRF, dgbtrf | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| DGBTRS, dgbtrs | 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 | 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 | balance a general real matrix A |
| DGEBD2, dgebd2 | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| DGEBRD, dgebrd | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| DGECON, dgecon | 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 |
| DGEEQU, dgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| DGEES, dgees | 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 | 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 | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| DGEEVX, dgeevx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| DGEGS, dgegs | compute for a pair of N-by-N real nonsymmetric matrices A, B |
| DGEGV, dgegv | 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 | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| DGEHRD, dgehrd | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| DGELQ2, dgelq2 | compute an LQ factorization of a real m by n matrix A |
| DGELQF, dgelqf | compute an LQ factorization of a real M-by-N matrix A |
| DGELS, dgels | 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 | compute the minimum norm solution to a real linear least squares problem |
| DGELSX, dgelsx | compute the minimum-norm solution to a real linear least squares problem |
| DGEQL2, dgeql2 | compute a QL factorization of a real m by n matrix A |
| DGEQLF, dgeqlf | compute a QL factorization of a real M-by-N matrix A |
| DGEQPF, dgeqpf | compute a QR factorization with column pivoting of a real M-by-N matrix A |
| DGEQR2, dgeqr2 | compute a QR factorization of a real m by n matrix A |
| DGEQRF, dgeqrf | compute a QR factorization of a real M-by-N matrix A |
| DGERFS, dgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| DGERQ2, dgerq2 | compute an RQ factorization of a real m by n matrix A |
| DGERQF, dgerqf | compute an RQ factorization of a real M-by-N matrix A |
| DGESV, dgesv | compute the solution to a real system of linear equations A ∗ X = B, |
| DGESVD, dgesvd | 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 | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| DGETF2, dgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| DGETRF, dgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| DGETRI, dgetri | compute the inverse of a matrix using the LU factorization computed by DGETRF |
| DGETRS, dgetrs | 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 | 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 | balance a pair of general real matrices (A,B) |
| DGGGLM, dggglm | solve a general Gauss-Markov linear model (GLM) problem |
| DGGHRD, dgghrd | 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 | solve the linear equality-constrained least squares (LSE) problem |
| DGGQRF, dggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| DGGRQF, dggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| DGGSVD, dggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B |
| DGGSVP, dggsvp | 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 | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF |
| DGTRFS, dgtrfs | 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 |
| DGTSV, dgtsv | solve the equation A∗X = B, |
| DGTSVX, dgtsvx | 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 | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| DGTTRS, dgttrs | solve one of the systems of equations A∗X = B or A’∗X = B, |
| DHGEQZ, dhgeqz | 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 | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H |
| DHSEQR, dhseqr | 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 | 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 | 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 | estimate the 1-norm of a square, real matrix A |
| DLACPY, dlacpy | copie all or part of a two-dimensional matrix A to another matrix B |
| DLADIV, dladiv | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L |
| DLAE2, dlae2 | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| DLAEBZ, dlaebz | 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 | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| DLAED1, dlaed1 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| DLAED2, dlaed2 | merge the two sets of eigenvalues together into a single sorted set |
| DLAED3, dlaed3 | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP |
| DLAED4, dlaed4 | 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 | 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 | 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 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| DLAED8, dlaed8 | merge the two sets of eigenvalues together into a single sorted set |
| DLAED9, dlaed9 | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP |
| DLAEDA, dlaeda | 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 | 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 | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| DLAEXC, dlaexc | 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 | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow |
| DLAGTF, dlagtf | 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 | 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 | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, |
| DLAHQR, dlahqr | 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 | 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 | applie one step of incremental condition estimation in its simplest version |
| DLALN2, dlaln2 | 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 | determine double precision machine parameters |
| DLAMRG, dlamrg | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form |
| DLAPLL, dlapll | two column vectors X and Y, let A = ( X Y ) |
| DLAPMT, dlapmt | 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 | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow |
| DLAPY3, dlapy3 | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow |
| DLAQGB, dlaqgb | 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 | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| DLAQSB, dlaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| DLAQSP, dlaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| DLAQSY, dlaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| DLAQTR, dlaqtr | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE |
| DLAR2V, dlar2v | 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 | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| DLARFB, dlarfb | 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 | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| DLARFT, dlarft | 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 | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| DLARGV, dlargv | generate a vector of real plane rotations, determined by elements of the real vectors x and y |
| DLARNV, dlarnv | return a vector of n random real numbers from a uniform or normal distribution |
| DLARTG, dlartg | generate a plane rotation so that [ CS SN ] |
| DLARTV, dlartv | applie a vector of real plane rotations to elements of the real vectors x and y |
| DLARUV, dlaruv | return a vector of n random real numbers from a uniform (0,1) |
| DLAS2, dlas2 | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] |
| DLASCL, dlascl | multiplie the M by N real matrix A by the real scalar CTO/CFROM |
| DLASET, dlaset | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals |
| DLASQ1, dlasq1 | DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E |
| DLASQ2, dlasq2 | 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 | DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm |
| DLASQ4, dlasq4 | DLASQ4 estimates TAU, the smallest eigenvalue of a matrix |
| DLASR, dlasr | 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 | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) |
| DLASSQ, dlassq | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| DLASV2, dlasv2 | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] |
| DLASWP, dlaswp | perform a series of row interchanges on the matrix A |
| DLASY2, dlasy2 | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, |
| DLASYF, dlasyf | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| DLATBS, dlatbs | 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 | 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 | 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 | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow |
| DLATZM, dlatzm | applie a Householder matrix generated by DTZRQF to a matrix |
| DLAUU2, dlauu2 | 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 | 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 |
| DLAZRO, dlazro | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| DOPGTR, dopgtr | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORG2L, dorg2l | generate an m by n real matrix Q with orthonormal columns, |
| DORG2R, dorg2r | generate an m by n real matrix Q with orthonormal columns, |
| DORGBR, dorgbr | 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 | 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 | generate an m by n real matrix Q with orthonormal rows, |
| DORGLQ, dorglq | generate an M-by-N real matrix Q with orthonormal rows, |
| DORGQL, dorgql | generate an M-by-N real matrix Q with orthonormal columns, |
| DORGQR, dorgqr | generate an M-by-N real matrix Q with orthonormal columns, |
| DORGR2, dorgr2 | generate an m by n real matrix Q with orthonormal rows, |
| DORGRQ, dorgrq | generate an M-by-N real matrix Q with orthonormal rows, |
| DORGTR, dorgtr | 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 | 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 | 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 | VECT = ’Q’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORMHR, dormhr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORML2, dorml2 | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORMQL, dormql | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORMQR, dormqr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORMR2, dormr2 | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DORMTR, dormtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| DPBCON, dpbcon | 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 |
| DPBEQU, dpbequ | 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) |
| DPBRFS, dpbrfs | 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 |
| DPBSTF, dpbstf | compute a split Cholesky factorization of a real symmetric positive definite band matrix A |
| DPBSV, dpbsv | compute the solution to a real system of linear equations A ∗ X = B, |
| DPBSVX, dpbsvx | 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 | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| DPBTRF, dpbtrf | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| DPBTRS, dpbtrs | 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 |
| DPOCON, dpocon | 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 |
| DPOEQU, dpoequ | 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) |
| DPORFS, dporfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, |
| DPOSV, dposv | compute the solution to a real system of linear equations A ∗ X = B, |
| DPOSVX, dposvx | 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 | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| DPOTRF, dpotrf | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| DPOTRI, dpotri | 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 | 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 |
| DPPCON, dppcon | 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 |
| DPPEQU, dppequ | 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) |
| DPPRFS, dpprfs | 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 |
| DPPSV, dppsv | compute the solution to a real system of linear equations A ∗ X = B, |
| DPPSVX, dppsvx | 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 | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format |
| DPPTRI, dpptri | 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 | 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 | 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 | 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 | 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 |
| DPTSV, dptsv | 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 | 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 | compute the factorization of a real symmetric positive definite tridiagonal matrix A |
| DPTTRS, dpttrs | 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 |
| DRSCL, drscl | multiplie an n-element real vector x by the real scalar 1/a |
| DSBEV, dsbev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| DSBEVD, dsbevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| DSBEVX, dsbevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| DSBGST, dsbgst | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| DSBGV, dsbgv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| DSBTRD, dsbtrd | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| DSECND, dsecnd | return the user time for a process in seconds |
| DSPCON, dspcon | 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 |
| DSPEV, dspev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| DSPEVD, dspevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| DSPEVX, dspevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| DSPGST, dspgst | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage |
| DSPGV, dspgv | 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 |
| DSPRFS, dsprfs | 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 |
| DSPSV, dspsv | compute the solution to a real system of linear equations A ∗ X = B, |
| DSPSVX, dspsvx | 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 | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation |
| DSPTRF, dsptrf | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| DSPTRI, dsptri | 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 | 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 | compute the eigenvalues of a symmetric tridiagonal matrix T |
| DSTEDC, dstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| DSTEIN, dstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| DSTEQR, dsteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| DSTERF, dsterf | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm |
| DSTEV, dstev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| DSTEVD, dstevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| DSTEVX, dstevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| DSYCON, dsycon | 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 | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| DSYEVD, dsyevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| DSYEVX, dsyevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| DSYGS2, dsygs2 | reduce a real symmetric-definite generalized eigenproblem to standard form |
| DSYGST, dsygst | reduce a real symmetric-definite generalized eigenproblem to standard form |
| DSYGV, dsygv | 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 |
| DSYRFS, dsyrfs | 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 |
| DSYSV, dsysv | compute the solution to a real system of linear equations A ∗ X = B, |
| DSYSVX, dsysvx | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| DSYTD2, dsytd2 | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| DSYTF2, dsytf2 | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| DSYTRD, dsytrd | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation |
| DSYTRF, dsytrf | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| DSYTRI, dsytri | 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 | 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 | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| DTBRFS, dtbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| DTBTRS, dtbtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| DTGEVC, dtgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) |
| DTGSJA, dtgsja | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B |
| DTPCON, dtpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| DTPRFS, dtprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| DTPTRI, dtptri | compute the inverse of a real upper or lower triangular matrix A stored in packed format |
| DTPTRS, dtptrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| DTRCON, dtrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| DTREVC, dtrevc | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T |
| DTREXC, dtrexc | 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 |
| DTRRFS, dtrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| DTRSEN, dtrsen | 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, |
| DTRSNA, dtrsna | 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) |
| DTRSYL, dtrsyl | solve the real Sylvester matrix equation |
| DTRTI2, dtrti2 | compute the inverse of a real upper or lower triangular matrix |
| DTRTRI, dtrtri | compute the inverse of a real upper or lower triangular matrix A |
| DTRTRS, dtrtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| DTZRQF, dtzrqf | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations |
| DZSUM1, dzsum1 | take the sum of the absolute values of a complex vector and returns a double precision result |
| ICMAX1, icmax1 | find the index of the element whose real part has maximum absolute value |
| ILAENV, ilaenv | i called from the LAPACK routines to choose problem-dependent parameters for the local environment |
| IZMAX1, izmax1 | find the index of the element whose real part has maximum absolute value |
| lapack | |
| LSAME, lsame | return .TRUE |
| LSAMEN, lsamen | test if the first N letters of CA are the same as the first N letters of CB, regardless of case |
| SBDSQR, sbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| SCSUM1, scsum1 | take the sum of the absolute values of a complex vector and returns a single precision result |
| SDISNA, sdisna | 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 |
| SECOND, second | return the user time for a process in seconds |
| SGBBRD, sgbbrd | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation |
| SGBCON, sgbcon | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, |
| SGBEQU, sgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| SGBRFS, sgbrfs | 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 |
| SGBSV, sgbsv | 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 | 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 | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| SGBTRF, sgbtrf | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges |
| SGBTRS, sgbtrs | 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 | 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 | balance a general real matrix A |
| SGEBD2, sgebd2 | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| SGEBRD, sgebrd | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation |
| SGECON, sgecon | 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 |
| SGEEQU, sgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| SGEES, sgees | 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 | 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 | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| SGEEVX, sgeevx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| SGEGS, sgegs | compute for a pair of N-by-N real nonsymmetric matrices A, B |
| SGEGV, sgegv | 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 | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| SGEHRD, sgehrd | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation |
| SGELQ2, sgelq2 | compute an LQ factorization of a real m by n matrix A |
| SGELQF, sgelqf | compute an LQ factorization of a real M-by-N matrix A |
| SGELS, sgels | 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 | compute the minimum norm solution to a real linear least squares problem |
| SGELSX, sgelsx | compute the minimum-norm solution to a real linear least squares problem |
| SGEQL2, sgeql2 | compute a QL factorization of a real m by n matrix A |
| SGEQLF, sgeqlf | compute a QL factorization of a real M-by-N matrix A |
| SGEQPF, sgeqpf | compute a QR factorization with column pivoting of a real M-by-N matrix A |
| SGEQR2, sgeqr2 | compute a QR factorization of a real m by n matrix A |
| SGEQRF, sgeqrf | compute a QR factorization of a real M-by-N matrix A |
| SGERFS, sgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| SGERQ2, sgerq2 | compute an RQ factorization of a real m by n matrix A |
| SGERQF, sgerqf | compute an RQ factorization of a real M-by-N matrix A |
| SGESV, sgesv | compute the solution to a real system of linear equations A ∗ X = B, |
| SGESVD, sgesvd | 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 | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| SGETF2, sgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| SGETRF, sgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| SGETRI, sgetri | compute the inverse of a matrix using the LU factorization computed by SGETRF |
| SGETRS, sgetrs | 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 | 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 | balance a pair of general real matrices (A,B) |
| SGGGLM, sggglm | solve a general Gauss-Markov linear model (GLM) problem |
| SGGHRD, sgghrd | 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 | solve the linear equality-constrained least squares (LSE) problem |
| SGGQRF, sggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| SGGRQF, sggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| SGGSVD, sggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B |
| SGGSVP, sggsvp | 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 | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF |
| SGTRFS, sgtrfs | 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 |
| SGTSV, sgtsv | solve the equation A∗X = B, |
| SGTSVX, sgtsvx | 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 | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| SGTTRS, sgttrs | solve one of the systems of equations A∗X = B or A’∗X = B, |
| SHGEQZ, shgeqz | 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 | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H |
| SHSEQR, shseqr | 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 |
| SLABAD, slabad | 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 | 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 | estimate the 1-norm of a square, real matrix A |
| SLACPY, slacpy | copie all or part of a two-dimensional matrix A to another matrix B |
| SLADIV, sladiv | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L |
| SLAE2, slae2 | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| SLAEBZ, slaebz | 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 | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| SLAED1, slaed1 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| SLAED2, slaed2 | merge the two sets of eigenvalues together into a single sorted set |
| SLAED3, slaed3 | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP |
| SLAED4, slaed4 | 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 | 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 | 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 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| SLAED8, slaed8 | merge the two sets of eigenvalues together into a single sorted set |
| SLAED9, slaed9 | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP |
| SLAEDA, slaeda | 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 | 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 | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] |
| SLAEXC, slaexc | 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 | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow |
| SLAGTF, slagtf | 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 | 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 | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, |
| SLAHQR, slahqr | 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 | 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 | applie one step of incremental condition estimation in its simplest version |
| SLALN2, slaln2 | 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 | determine single precision machine parameters |
| SLAMRG, slamrg | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form |
| SLAPLL, slapll | two column vectors X and Y, let A = ( X Y ) |
| SLAPMT, slapmt | 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 | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow |
| SLAPY3, slapy3 | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow |
| SLAQGB, slaqgb | 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 | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| SLAQSB, slaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| SLAQSP, slaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| SLAQSY, slaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| SLAQTR, slaqtr | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE |
| SLAR2V, slar2v | 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 | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| SLARFB, slarfb | 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 | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| SLARFT, slarft | 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 | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right |
| SLARGV, slargv | generate a vector of real plane rotations, determined by elements of the real vectors x and y |
| SLARNV, slarnv | return a vector of n random real numbers from a uniform or normal distribution |
| SLARTG, slartg | generate a plane rotation so that [ CS SN ] |
| SLARTV, slartv | applie a vector of real plane rotations to elements of the real vectors x and y |
| SLARUV, slaruv | return a vector of n random real numbers from a uniform (0,1) |
| SLAS2, slas2 | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] |
| SLASCL, slascl | multiplie the M by N real matrix A by the real scalar CTO/CFROM |
| SLASET, slaset | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals |
| SLASQ1, slasq1 | SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E |
| SLASQ2, slasq2 | 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 | SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm |
| SLASQ4, slasq4 | SLASQ4 estimates TAU, the smallest eigenvalue of a matrix |
| SLASR, slasr | 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 | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) |
| SLASSQ, slassq | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| SLASV2, slasv2 | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] |
| SLASWP, slaswp | perform a series of row interchanges on the matrix A |
| SLASY2, slasy2 | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, |
| SLASYF, slasyf | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| SLATBS, slatbs | 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 | 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 | 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 | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow |
| SLATZM, slatzm | applie a Householder matrix generated by STZRQF to a matrix |
| SLAUU2, slauu2 | 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 | 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 |
| SLAZRO, slazro | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| SOPGTR, sopgtr | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORG2L, sorg2l | generate an m by n real matrix Q with orthonormal columns, |
| SORG2R, sorg2r | generate an m by n real matrix Q with orthonormal columns, |
| SORGBR, sorgbr | 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 | 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 | generate an m by n real matrix Q with orthonormal rows, |
| SORGLQ, sorglq | generate an M-by-N real matrix Q with orthonormal rows, |
| SORGQL, sorgql | generate an M-by-N real matrix Q with orthonormal columns, |
| SORGQR, sorgqr | generate an M-by-N real matrix Q with orthonormal columns, |
| SORGR2, sorgr2 | generate an m by n real matrix Q with orthonormal rows, |
| SORGRQ, sorgrq | generate an M-by-N real matrix Q with orthonormal rows, |
| SORGTR, sorgtr | 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 | 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 | 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 | VECT = ’Q’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORMHR, sormhr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORML2, sorml2 | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORMQL, sormql | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORMQR, sormqr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORMR2, sormr2 | 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 | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SORMTR, sormtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| SPBCON, spbcon | 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 |
| SPBEQU, spbequ | 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) |
| SPBRFS, spbrfs | 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 |
| SPBSTF, spbstf | compute a split Cholesky factorization of a real symmetric positive definite band matrix A |
| SPBSV, spbsv | compute the solution to a real system of linear equations A ∗ X = B, |
| SPBSVX, spbsvx | 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 | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| SPBTRF, spbtrf | compute the Cholesky factorization of a real symmetric positive definite band matrix A |
| SPBTRS, spbtrs | 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 |
| SPOCON, spocon | 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 |
| SPOEQU, spoequ | 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) |
| SPORFS, sporfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, |
| SPOSV, sposv | compute the solution to a real system of linear equations A ∗ X = B, |
| SPOSVX, sposvx | 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 | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| SPOTRF, spotrf | compute the Cholesky factorization of a real symmetric positive definite matrix A |
| SPOTRI, spotri | 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 | 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 |
| SPPCON, sppcon | 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 |
| SPPEQU, sppequ | 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) |
| SPPRFS, spprfs | 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 |
| SPPSV, sppsv | compute the solution to a real system of linear equations A ∗ X = B, |
| SPPSVX, sppsvx | 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 | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format |
| SPPTRI, spptri | 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 | 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 | 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 | 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 | 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 |
| SPTSV, sptsv | 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 | 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 | compute the factorization of a real symmetric positive definite tridiagonal matrix A |
| SPTTRS, spttrs | 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 |
| SRSCL, srscl | multiplie an n-element real vector x by the real scalar 1/a |
| SSBEV, ssbev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| SSBEVD, ssbevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| SSBEVX, ssbevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A |
| SSBGST, ssbgst | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| SSBGV, ssbgv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| SSBTRD, ssbtrd | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| SSPCON, sspcon | 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 |
| SSPEV, sspev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| SSPEVD, sspevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| SSPEVX, sspevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage |
| SSPGST, sspgst | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage |
| SSPGV, sspgv | 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 |
| SSPRFS, ssprfs | 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 |
| SSPSV, sspsv | compute the solution to a real system of linear equations A ∗ X = B, |
| SSPSVX, sspsvx | 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 | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation |
| SSPTRF, ssptrf | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| SSPTRI, ssptri | 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 | 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 | compute the eigenvalues of a symmetric tridiagonal matrix T |
| SSTEDC, sstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| SSTEIN, sstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| SSTEQR, ssteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| SSTERF, ssterf | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm |
| SSTEV, sstev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| SSTEVD, sstevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| SSTEVX, sstevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A |
| SSYCON, ssycon | 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 | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| SSYEVD, ssyevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| SSYEVX, ssyevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A |
| SSYGS2, ssygs2 | reduce a real symmetric-definite generalized eigenproblem to standard form |
| SSYGST, ssygst | reduce a real symmetric-definite generalized eigenproblem to standard form |
| SSYGV, ssygv | 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 |
| SSYRFS, ssyrfs | 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 |
| SSYSV, ssysv | compute the solution to a real system of linear equations A ∗ X = B, |
| SSYSVX, ssysvx | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, |
| SSYTD2, ssytd2 | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation |
| SSYTF2, ssytf2 | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| SSYTRD, ssytrd | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation |
| SSYTRF, ssytrf | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| SSYTRI, ssytri | 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 | 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 | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| STBRFS, stbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| STBTRS, stbtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| STGEVC, stgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) |
| STGSJA, stgsja | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B |
| STPCON, stpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| STPRFS, stprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| STPTRI, stptri | compute the inverse of a real upper or lower triangular matrix A stored in packed format |
| STPTRS, stptrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| STRCON, strcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| STREVC, strevc | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T |
| STREXC, strexc | 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 |
| STRRFS, strrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| STRSEN, strsen | 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, |
| STRSNA, strsna | 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) |
| STRSYL, strsyl | solve the real Sylvester matrix equation |
| STRTI2, strti2 | compute the inverse of a real upper or lower triangular matrix |
| STRTRI, strtri | compute the inverse of a real upper or lower triangular matrix A |
| STRTRS, strtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, |
| STZRQF, stzrqf | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations |
| XERBLA, xerbla | i an error handler for the LAPACK routines |
| ZBDSQR, zbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B |
| ZDRSCL, zdrscl | multiplie an n-element complex vector x by the real scalar 1/a |
| ZGBBRD, zgbbrd | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation |
| ZGBCON, zgbcon | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, |
| ZGBEQU, zgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number |
| ZGBRFS, zgbrfs | 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 |
| ZGBSV, zgbsv | 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 | 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 | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| ZGBTRF, zgbtrf | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges |
| ZGBTRS, zgbtrs | 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 | 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 | balance a general complex matrix A |
| ZGEBD2, zgebd2 | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation |
| ZGEBRD, zgebrd | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation |
| ZGECON, zgecon | 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 |
| ZGEEQU, zgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number |
| ZGEES, zgees | 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 | 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 | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| ZGEEVX, zgeevx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors |
| ZGEGS, zgegs | compute for a pair of N-by-N complex nonsymmetric matrices A, |
| ZGEGV, zgegv | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, |
| ZGEHD2, zgehd2 | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| ZGEHRD, zgehrd | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation |
| ZGELQ2, zgelq2 | compute an LQ factorization of a complex m by n matrix A |
| ZGELQF, zgelqf | compute an LQ factorization of a complex M-by-N matrix A |
| ZGELS, zgels | 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 | compute the minimum norm solution to a complex linear least squares problem |
| ZGELSX, zgelsx | compute the minimum-norm solution to a complex linear least squares problem |
| ZGEQL2, zgeql2 | compute a QL factorization of a complex m by n matrix A |
| ZGEQLF, zgeqlf | compute a QL factorization of a complex M-by-N matrix A |
| ZGEQPF, zgeqpf | compute a QR factorization with column pivoting of a complex M-by-N matrix A |
| ZGEQR2, zgeqr2 | compute a QR factorization of a complex m by n matrix A |
| ZGEQRF, zgeqrf | compute a QR factorization of a complex M-by-N matrix A |
| ZGERFS, zgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution |
| ZGERQ2, zgerq2 | compute an RQ factorization of a complex m by n matrix A |
| ZGERQF, zgerqf | compute an RQ factorization of a complex M-by-N matrix A |
| ZGESV, zgesv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZGESVD, zgesvd | 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 | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| ZGETF2, zgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges |
| ZGETRF, zgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges |
| ZGETRI, zgetri | compute the inverse of a matrix using the LU factorization computed by ZGETRF |
| ZGETRS, zgetrs | 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 | 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 | balance a pair of general complex matrices (A,B) |
| ZGGGLM, zggglm | solve a general Gauss-Markov linear model (GLM) problem |
| ZGGHRD, zgghrd | 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 | solve the linear equality-constrained least squares (LSE) problem |
| ZGGQRF, zggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B |
| ZGGRQF, zggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B |
| ZGGSVD, zggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B |
| ZGGSVP, zggsvp | 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 | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF |
| ZGTRFS, zgtrfs | 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 |
| ZGTSV, zgtsv | solve the equation A∗X = B, |
| ZGTSVX, zgtsvx | 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 | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges |
| ZGTTRS, zgttrs | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ZHBEV, zhbev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| ZHBEVD, zhbevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| ZHBEVX, zhbevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A |
| ZHBGST, zhbgst | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, |
| ZHBGV, zhbgv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x |
| ZHBTRD, zhbtrd | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| ZHECON, zhecon | 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 | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| ZHEEVD, zheevd | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| ZHEEVX, zheevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A |
| ZHEGS2, zhegs2 | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| ZHEGST, zhegst | reduce a complex Hermitian-definite generalized eigenproblem to standard form |
| ZHEGV, zhegv | 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 |
| ZHERFS, zherfs | 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 |
| ZHESV, zhesv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZHESVX, zhesvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| ZHETD2, zhetd2 | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| ZHETF2, zhetf2 | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZHETRD, zhetrd | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation |
| ZHETRF, zhetrf | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZHETRI, zhetri | 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 | 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 | 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 |
| ZHPCON, zhpcon | 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 |
| ZHPEV, zhpev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage |
| ZHPEVD, zhpevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| ZHPEVX, zhpevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage |
| ZHPGST, zhpgst | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage |
| ZHPGV, zhpgv | 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 |
| ZHPRFS, zhprfs | 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 |
| ZHPSV, zhpsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZHPSVX, zhpsvx | 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 | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation |
| ZHPTRF, zhptrf | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZHPTRI, zhptri | 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 | 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 | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H |
| ZHSEQR, zhseqr | 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 | 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 | conjugate a complex vector of length N |
| ZLACON, zlacon | estimate the 1-norm of a square, complex matrix A |
| ZLACPY, zlacpy | copie all or part of a two-dimensional matrix A to another matrix B |
| ZLACRM, zlacrm | perform a very simple matrix-matrix multiplication |
| ZLACRT, zlacrt | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex |
| ZLADIV, zladiv | := X / Y, where X and Y are complex |
| ZLAED0, zlaed0 | 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 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix |
| ZLAED8, zlaed8 | merge the two sets of eigenvalues together into a single sorted set |
| ZLAEIN, zlaein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H |
| ZLAESY, zlaesy | 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 | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] |
| zlags2 | |
| ZLAGTM, zlagtm | 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 | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZLAHQR, zlahqr | 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 | 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 | applie one step of incremental condition estimation in its simplest version |
| ZLANGB, zlangb | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | two column vectors X and Y, let A = ( X Y ) |
| ZLAPMT, zlapmt | 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 | 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 | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C |
| ZLAQHB, zlaqhb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| ZLAQHE, zlaqhe | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| ZLAQHP, zlaqhp | equilibrate a Hermitian matrix A using the scaling factors in the vector S |
| ZLAQSB, zlaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S |
| ZLAQSP, zlaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| ZLAQSY, zlaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S |
| ZLAR2V, zlar2v | 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 | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right |
| ZLARFB, zlarfb | 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 | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I |
| ZLARFT, zlarft | 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 | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right |
| ZLARGV, zlargv | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y |
| ZLARNV, zlarnv | return a vector of n random complex numbers from a uniform or normal distribution |
| ZLARTG, zlartg | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] |
| ZLARTV, zlartv | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y |
| ZLASCL, zlascl | multiplie the M by N complex matrix A by the real scalar CTO/CFROM |
| ZLASET, zlaset | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| ZLASR, zlasr | 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 | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, |
| ZLASWP, zlaswp | perform a series of row interchanges on the matrix A |
| ZLASYF, zlasyf | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZLATBS, zlatbs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| ZLATPS, zlatps | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| ZLATRD, zlatrd | 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 | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, |
| ZLATZM, zlatzm | applie a Householder matrix generated by ZTZRQF to a matrix |
| ZLAUU2, zlauu2 | 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 | 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 |
| ZLAZRO, zlazro | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals |
| ZPBCON, zpbcon | 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 |
| ZPBEQU, zpbequ | 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) |
| ZPBRFS, zpbrfs | 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 |
| ZPBSTF, zpbstf | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A |
| ZPBSV, zpbsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZPBSVX, zpbsvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| ZPBTRF, zpbtrf | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A |
| ZPBTRS, zpbtrs | 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 |
| ZPOCON, zpocon | 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 |
| ZPOEQU, zpoequ | 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) |
| ZPORFS, zporfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, |
| ZPOSV, zposv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZPOSVX, zposvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| ZPOTRF, zpotrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A |
| ZPOTRI, zpotri | 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 | 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 |
| ZPPCON, zppcon | 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 |
| ZPPEQU, zppequ | 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) |
| ZPPRFS, zpprfs | 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 |
| ZPPSV, zppsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZPPSVX, zppsvx | 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 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format |
| ZPPTRI, zpptri | 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 | 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 | 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 | 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 | 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 |
| ZPTSV, zptsv | 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 | 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 | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A |
| ZPTTRS, zpttrs | 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 |
| ZROT, zrot | applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex |
| ZSPCON, zspcon | 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 |
| ZSPMV, zspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| ZSPR, zspr | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, |
| ZSPRFS, zsprfs | 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 |
| ZSPSV, zspsv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZSPSVX, zspsvx | 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 | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method |
| ZSPTRI, zsptri | 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 | 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 |
| ZSRSCL, zsrscl | multiplie an n-element complex vector x by the real scalar 1/a |
| ZSTEDC, zstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method |
| ZSTEIN, zstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration |
| ZSTEQR, zsteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method |
| ZSYCON, zsycon | 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 |
| ZSYMV, zsymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, |
| ZSYR, zsyr | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, |
| ZSYRFS, zsyrfs | 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 |
| ZSYSV, zsysv | compute the solution to a complex system of linear equations A ∗ X = B, |
| ZSYSVX, zsysvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, |
| ZSYTF2, zsytf2 | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZSYTRF, zsytrf | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method |
| ZSYTRI, zsytri | 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 | 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 | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm |
| ZTBRFS, ztbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix |
| ZTBTRS, ztbtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ZTGEVC, ztgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) |
| ZTGSJA, ztgsja | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B |
| ZTPCON, ztpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm |
| ZTPRFS, ztprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix |
| ZTPTRI, ztptri | compute the inverse of a complex upper or lower triangular matrix A stored in packed format |
| ZTPTRS, ztptrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ZTRCON, ztrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm |
| ZTREVC, ztrevc | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T |
| ZTREXC, ztrexc | 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 |
| ZTRRFS, ztrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix |
| ZTRSEN, ztrsen | 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 |
| ZTRSNA, ztrsna | 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) |
| ZTRSYL, ztrsyl | solve the complex Sylvester matrix equation |
| ZTRTI2, ztrti2 | compute the inverse of a complex upper or lower triangular matrix |
| ZTRTRI, ztrtri | compute the inverse of a complex upper or lower triangular matrix A |
| ZTRTRS, ztrtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, |
| ZTZRQF, ztzrqf | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations |
| ZUNG2L, zung2l | generate an m by n complex matrix Q with orthonormal columns, |
| ZUNG2R, zung2r | generate an m by n complex matrix Q with orthonormal columns, |
| ZUNGBR, zungbr | 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 | 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 | generate an m-by-n complex matrix Q with orthonormal rows, |
| ZUNGLQ, zunglq | generate an M-by-N complex matrix Q with orthonormal rows, |
| ZUNGQL, zungql | generate an M-by-N complex matrix Q with orthonormal columns, |
| ZUNGQR, zungqr | generate an M-by-N complex matrix Q with orthonormal columns, |
| ZUNGR2, zungr2 | generate an m by n complex matrix Q with orthonormal rows, |
| ZUNGRQ, zungrq | generate an M-by-N complex matrix Q with orthonormal rows, |
| ZUNGTR, zungtr | 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 | 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 | 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 | VECT = ’Q’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNMHR, zunmhr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNML2, zunml2 | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNMQL, zunmql | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNMQR, zunmqr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNMR2, zunmr2 | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUNMTR, zunmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |
| ZUPGTR, zupgtr | 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 | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ |