• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dtrsv - solve one of the systems of equations A*x = b, or A'*x = b

SYNOPSIS

  SUBROUTINE DTRSV( UPLO, TRANSA, DIAG, N, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER N, LDA, INCY
  DOUBLE PRECISION A(LDA,*), Y(*)

  SUBROUTINE DTRSV_64( UPLO, TRANSA, DIAG, N, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER*8 N, LDA, INCY
  DOUBLE PRECISION A(LDA,*), Y(*)

F95 INTERFACE

  SUBROUTINE TRSV( UPLO, [TRANSA], DIAG, [N], A, [LDA], Y, [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  INTEGER :: N, LDA, INCY
  REAL(8), DIMENSION(:) :: Y
  REAL(8), DIMENSION(:,:) :: A

  SUBROUTINE TRSV_64( UPLO, [TRANSA], DIAG, [N], A, [LDA], Y, [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  INTEGER(8) :: N, LDA, INCY
  REAL(8), DIMENSION(:) :: Y
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void dtrsv(char uplo, char transa, char diag, int n, double *a, int lda, double *y, int incy);

void dtrsv_64(char uplo, char transa, char diag, long n, double *a, long lda, double *y, long incy);

PURPOSE

dtrsv solves one of the systems of equations A*x = b, or A'*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

ARGUMENTS

• UPLO (input)
  On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

  UPLO = 'U' or 'u' A is an upper triangular matrix.

  UPLO = 'L' or 'l' A is a lower triangular matrix.

  Unchanged on exit.

• TRANSA (input)
  On entry, TRANSA specifies the equations to be solved as follows:

  TRANSA = 'N' or 'n' A*x = b.

  TRANSA = 'T' or 't' A'*x = b.

  TRANSA = 'C' or 'c' A'*x = b.

  Unchanged on exit.

• DIAG (input)
  On entry, DIAG specifies whether or not A is unit triangular as follows:

  DIAG = 'U' or 'u' A is assumed to be unit triangular.

  DIAG = 'N' or 'n' A is not assumed to be unit triangular.

  Unchanged on exit.

• N (input)
  On entry, N specifies the order of the matrix A. N > = 0. Unchanged on exit.

• A (input)
  Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit.

• LDA (input)
  On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA > = max( 1, n ). Unchanged on exit.

• Y (input/output)
  ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element right-hand side vector b. On exit, Y is overwritten with the solution vector x.

• INCY (input)
  On entry, INCY specifies the increment for the elements of Y. INCY < > 0. Unchanged on exit.