NAME

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

SYNOPSIS

  SUBROUTINE STPSV( UPLO, TRANSA, DIAG, N, A, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER N, INCY
  REAL A(*), Y(*)

  SUBROUTINE STPSV_64( UPLO, TRANSA, DIAG, N, A, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER*8 N, INCY
  REAL A(*), Y(*)

F95 INTERFACE

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

  SUBROUTINE TPSV_64( UPLO, [TRANSA], DIAG, [N], A, Y, [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  INTEGER(8) :: N, INCY
  REAL, DIMENSION(:) :: A, Y

C INTERFACE

#include <sunperf.h>

void stpsv(char uplo, char transa, char diag, int n, float *a, float *y, int incy);

void stpsv_64(char uplo, char transa, char diag, long n, float *a, float *y, long incy);

PURPOSE

stpsv 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, supplied in packed form.

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)
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array A must contain the upper triangular matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array A must contain the lower triangular matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. 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.