dtpsv

NAME

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

SYNOPSIS 

  SUBROUTINE DTPSV( UPLO, TRANSA, DIAG, N, A, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER N, INCY
  DOUBLE PRECISION A(*), Y(*)
 
  SUBROUTINE DTPSV_64( UPLO, TRANSA, DIAG, N, A, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER*8 N, INCY
  DOUBLE PRECISION A(*), Y(*)

F95 INTERFACE 

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

C INTERFACE

#include <sunperf.h>

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

void dtpsv_64(char uplo, char transa, char diag, long n, double *a, double *y, long incy);

PURPOSE

dtpsv 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.