275 lines
8.0 KiB
Fortran
275 lines
8.0 KiB
Fortran
*> \brief \b CTRT03
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
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* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, TRANS, UPLO
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* INTEGER LDA, LDB, LDX, N, NRHS
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* REAL RESID, SCALE, TSCAL
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* ..
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* .. Array Arguments ..
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* REAL CNORM( * )
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* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
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* $ X( LDX, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CTRT03 computes the residual for the solution to a scaled triangular
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*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b.
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*> Here A is a triangular matrix, A**T denotes the transpose of A, A**H
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*> denotes the conjugate transpose of A, s is a scalar, and x and b are
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*> N by NRHS matrices. The test ratio is the maximum over the number of
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*> right hand sides of
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*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
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*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the matrix A is upper or lower triangular.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the operation applied to A.
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*> = 'N': A *x = s*b (No transpose)
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*> = 'T': A**T *x = s*b (Transpose)
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*> = 'C': A**H *x = s*b (Conjugate transpose)
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the matrix A is unit triangular.
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*> = 'N': Non-unit triangular
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*> = 'U': Unit triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrices X and B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,N)
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*> The triangular matrix A. If UPLO = 'U', the leading n by n
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*> upper triangular part of the array A contains the upper
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*> triangular matrix, and the strictly lower triangular part of
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*> A is not referenced. If UPLO = 'L', the leading n by n lower
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*> triangular part of the array A contains the lower triangular
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*> matrix, and the strictly upper triangular part of A is not
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*> referenced. If DIAG = 'U', the diagonal elements of A are
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*> also not referenced and are assumed to be 1.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] SCALE
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*> \verbatim
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*> SCALE is REAL
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*> The scaling factor s used in solving the triangular system.
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*> \endverbatim
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*>
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*> \param[in] CNORM
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*> \verbatim
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*> CNORM is REAL array, dimension (N)
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*> The 1-norms of the columns of A, not counting the diagonal.
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*> \endverbatim
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*>
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*> \param[in] TSCAL
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*> \verbatim
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*> TSCAL is REAL
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*> The scaling factor used in computing the 1-norms in CNORM.
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*> CNORM actually contains the column norms of TSCAL*A.
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is COMPLEX array, dimension (LDX,NRHS)
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*> The computed solution vectors for the system of linear
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*> equations.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is COMPLEX array, dimension (LDB,NRHS)
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*> The right hand side vectors for the system of linear
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*> equations.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is REAL
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*> The maximum over the number of right hand sides of
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*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
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$ CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, TRANS, UPLO
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INTEGER LDA, LDB, LDX, N, NRHS
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REAL RESID, SCALE, TSCAL
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* ..
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* .. Array Arguments ..
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REAL CNORM( * )
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COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
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$ X( LDX, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER IX, J
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REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ICAMAX
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REAL SLAMCH
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EXTERNAL LSAME, ICAMAX, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CAXPY, CCOPY, CSSCAL, CTRMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, CMPLX, MAX, REAL
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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EPS = SLAMCH( 'Epsilon' )
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SMLNUM = SLAMCH( 'Safe minimum' )
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*
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* Compute the norm of the triangular matrix A using the column
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* norms already computed by CLATRS.
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*
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TNORM = ZERO
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IF( LSAME( DIAG, 'N' ) ) THEN
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DO 10 J = 1, N
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TNORM = MAX( TNORM, TSCAL*ABS( A( J, J ) )+CNORM( J ) )
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10 CONTINUE
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ELSE
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DO 20 J = 1, N
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TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
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20 CONTINUE
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END IF
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*
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* Compute the maximum over the number of right hand sides of
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* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
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*
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RESID = ZERO
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DO 30 J = 1, NRHS
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CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
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IX = ICAMAX( N, WORK, 1 )
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XNORM = MAX( ONE, ABS( X( IX, J ) ) )
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XSCAL = ( ONE / XNORM ) / REAL( N )
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CALL CSSCAL( N, XSCAL, WORK, 1 )
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CALL CTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 )
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CALL CAXPY( N, CMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
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IX = ICAMAX( N, WORK, 1 )
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ERR = TSCAL*ABS( WORK( IX ) )
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IX = ICAMAX( N, X( 1, J ), 1 )
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XNORM = ABS( X( IX, J ) )
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IF( ERR*SMLNUM.LE.XNORM ) THEN
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IF( XNORM.GT.ZERO )
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$ ERR = ERR / XNORM
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ELSE
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IF( ERR.GT.ZERO )
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$ ERR = ONE / EPS
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END IF
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IF( ERR*SMLNUM.LE.TNORM ) THEN
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IF( TNORM.GT.ZERO )
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$ ERR = ERR / TNORM
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ELSE
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IF( ERR.GT.ZERO )
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$ ERR = ONE / EPS
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END IF
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RESID = MAX( RESID, ERR )
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30 CONTINUE
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*
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RETURN
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*
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* End of CTRT03
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*
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END
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