220 lines
5.8 KiB
Fortran
220 lines
5.8 KiB
Fortran
*> \brief \b SQRT16
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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 SQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
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* RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER LDA, LDB, LDX, M, N, NRHS
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
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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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*> SQRT16 computes the residual for a solution of a system of linear
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*> equations A*x = b or A'*x = b:
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*> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
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*> where 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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the form of the system of equations:
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*> = 'N': A *x = b
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*> = 'T': A'*x = b, where A' is the transpose of A
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*> = 'C': A'*x = b, where A' is the transpose of A
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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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 number of columns 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 columns of B, the matrix of right hand sides.
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*> 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 REAL array, dimension (LDA,N)
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*> The original M x N matrix A.
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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,M).
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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 REAL 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. If TRANS = 'N',
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*> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors for the system of
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*> linear equations.
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*> On exit, B is overwritten with the difference B - A*X.
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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. IF TRANS = 'N',
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*> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (M)
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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(B - A*X) / ( max(m,n) * norm(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 single_lin
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*
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* =====================================================================
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SUBROUTINE SQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
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$ RWORK, 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 TRANS
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INTEGER LDA, LDB, LDX, M, N, NRHS
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
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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 ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER J, N1, N2
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REAL ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SASUM, SLAMCH, SLANGE
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EXTERNAL LSAME, SASUM, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if M = 0 or N = 0 or NRHS = 0
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*
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IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
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ANORM = SLANGE( 'I', M, N, A, LDA, RWORK )
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N1 = N
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N2 = M
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ELSE
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ANORM = SLANGE( '1', M, N, A, LDA, RWORK )
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N1 = M
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N2 = N
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END IF
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*
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EPS = SLAMCH( 'Epsilon' )
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*
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* Compute B - A*X (or B - A'*X ) and store in B.
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*
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CALL SGEMM( TRANS, 'No transpose', N1, NRHS, N2, -ONE, A, LDA, X,
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$ LDX, ONE, B, LDB )
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*
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* Compute the maximum over the number of right hand sides of
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* norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) .
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*
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RESID = ZERO
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DO 10 J = 1, NRHS
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BNORM = SASUM( N1, B( 1, J ), 1 )
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XNORM = SASUM( N2, X( 1, J ), 1 )
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IF( ANORM.EQ.ZERO .AND. BNORM.EQ.ZERO ) THEN
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RESID = ZERO
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ELSE IF( ANORM.LE.ZERO .OR. XNORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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ELSE
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RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) /
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$ ( MAX( M, N )*EPS ) )
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END IF
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10 CONTINUE
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*
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RETURN
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*
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* End of SQRT16
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*
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END
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