NAME

DTPTRS - solve a triangular system of the form   A ∗ X = B or A∗∗T ∗ X = B,

SYNOPSIS

SUBROUTINE DTPTRS(
UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )

CHARACTER DIAG, TRANS, UPLO

INTEGER INFO, LDB, N, NRHS

DOUBLE PRECISION AP( ∗ ), B( LDB, ∗ )

PURPOSE

DTPTRS solves a triangular system of the form
 
where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.  A check is made to verify that A is nonsingular.
 

ARGUMENTS

UPLO    (input) CHARACTER∗1
= ’U’:  A is upper triangular;
= ’L’:  A is lower triangular.

TRANS   (input) CHARACTER∗1
Specifies the form of the system of equations:
= ’N’:  A ∗ X = B  (No transpose)
= ’T’:  A∗∗T ∗ X = B  (Transpose)
= ’C’:  A∗∗H ∗ X = B  (Conjugate transpose = Transpose)

DIAG    (input) CHARACTER∗1
= ’N’:  A is non-unit triangular;
= ’U’:  A is unit triangular.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS >= 0.

AP      (input) DOUBLE PRECISION array, dimension (N∗(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the array AP as follows: if UPLO = ’U’, AP(i + (j-1)∗j/2) = A(i,j) for 1<=i<=j; if UPLO = ’L’, AP(i + (j-1)∗(2∗n-j)/2) = A(i,j) for j<=i<=n.

B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed.

  —  LAPACK version 2.0  —  08 October 1994