TESTING/LIN/ctrt03.f(3)    Library Functions Manual    TESTING/LIN/ctrt03.f(3)

NAME
       TESTING/LIN/ctrt03.f

SYNOPSIS
   Functions/Subroutines
       subroutine ctrt03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
           tscal, x, ldx, b, ldb, work, resid)
           CTRT03

Function/Subroutine Documentation
   subroutine ctrt03 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( lda, * ) a, integer lda, real
       scale, real, dimension( * ) cnorm, real tscal, complex, dimension( ldx,
       * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb,
       complex, dimension( * ) work, real resid)
       CTRT03

       Purpose:


            CTRT03 computes the residual for the solution to a scaled triangular
            system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.
            Here A is a triangular matrix, A**T denotes the transpose of A, A**H
            denotes the conjugate transpose of A, s is a scalar, and x and b are
            N by NRHS matrices.  The test ratio is the maximum over the number of
            right hand sides of
               norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
            where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the matrix A is upper or lower triangular.
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           TRANS

                     TRANS is CHARACTER*1
                     Specifies the operation applied to A.
                     = 'N':  A *x = s*b     (No transpose)
                     = 'T':  A**T *x = s*b  (Transpose)
                     = 'C':  A**H *x = s*b  (Conjugate transpose)

           DIAG

                     DIAG is CHARACTER*1
                     Specifies whether or not the matrix A is unit triangular.
                     = 'N':  Non-unit triangular
                     = 'U':  Unit triangular

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           NRHS

                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrices X and B.  NRHS >= 0.

           A

                     A is COMPLEX array, dimension (LDA,N)
                     The triangular matrix A.  If UPLO = 'U', the leading n by n
                     upper triangular part of the array A contains the upper
                     triangular matrix, and the strictly lower triangular part of
                     A is not referenced.  If UPLO = 'L', the leading n by n lower
                     triangular part of the array A contains the lower triangular
                     matrix, and the strictly upper triangular part of A is not
                     referenced.  If DIAG = 'U', the diagonal elements of A are
                     also not referenced and are assumed to be 1.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           SCALE

                     SCALE is REAL
                     The scaling factor s used in solving the triangular system.

           CNORM

                     CNORM is REAL array, dimension (N)
                     The 1-norms of the columns of A, not counting the diagonal.

           TSCAL

                     TSCAL is REAL
                     The scaling factor used in computing the 1-norms in CNORM.
                     CNORM actually contains the column norms of TSCAL*A.

           X

                     X is COMPLEX array, dimension (LDX,NRHS)
                     The computed solution vectors for the system of linear
                     equations.

           LDX

                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           B

                     B is COMPLEX array, dimension (LDB,NRHS)
                     The right hand side vectors for the system of linear
                     equations.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           WORK

                     WORK is COMPLEX array, dimension (N)

           RESID

                     RESID is REAL
                     The maximum over the number of right hand sides of
                     norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 169 of file ctrt03.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/LIN/ctrt03.f(3)