C Library Functions - ctrsv (3)

NAME

ctrsv(3f) - [BLAS:COMPLEX_BLAS_LEVEL2] CX := INVERSE(A)*CX, where A is a triangular matrix.

Synopsis
Definition
Options
X
Authors
Further Details
See Also

SYNOPSIS

subroutine ctrsv(uplo,trans,diag,n,a,lda,x,incx)

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

DEFINITION

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

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**H*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.

A

A is COMPLEX array, dimension ( LDA, N ) 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.

LDA

LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).

X

X is COMPLEX 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.