C Library Functions - stpsv (3)

NAME

stpsv(3f) - [BLAS:SINGLE_BLAS_LEVEL2] SX:=INVERSE(A)*SX, A a packed symmetric matrix.

Synopsis
Definition
Options
X
Authors
Further Details
See Also

SYNOPSIS

subroutine stpsv(uplo,trans,diag,n,ap,x,incx)

      .. Scalar Arguments ..
      integer,intent(in)   :: incx,n
      character,intent(in) :: diag,trans,uplo
      ..
      .. Array Arguments ..
      real,intent(in)      :: ap(*)
      real,intent(inout)   :: x(*)
      ..

DEFINITION

STPSV solves one of the systems of equations
    A*x = b,   or   A**T*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.

OPTIONS

UPLO

UPLO is CHARACTER*1 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.

TRANS

TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows:

              TRANS = ’N’ or ’n’   A*x = b.

              TRANS = ’T’ or ’t’   A**T*x = b.

              TRANS = ’C’ or ’c’   A**T*x = b.

DIAG

DIAG is CHARACTER*1 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.

N

N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.

AP

AP is REAL array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = ’U’ or ’u’, the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = ’L’ or ’l’, the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 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.

X

X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.

INCX

INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

AUTHORS

o Univ. of Tennessee

o Univ. of California Berkeley

o Univ. of Colorado Denver

o NAG Ltd.
 date:December 2016

FURTHER DETAILS

Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.