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cla_gercond_x.f
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*> \brief \b CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLA_GERCOND_X + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gercond_x.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gercond_x.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gercond_x.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION CLA_GERCOND_X( TRANS, N, A, LDA, AF, LDAF, IPIV, X,
* INFO, WORK, RWORK )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER N, LDA, LDAF, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
* REAL RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*>
*> CLA_GERCOND_X computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations:
*> = 'N': A * X = B (No transpose)
*> = 'T': A**T * X = B (Transpose)
*> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the N-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is COMPLEX array, dimension (LDAF,N)
*> The factors L and U from the factorization
*> A = P*L*U as computed by CGETRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from the factorization A = P*L*U
*> as computed by CGETRF; row i of the matrix was interchanged
*> with row IPIV(i).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is COMPLEX array, dimension (N)
*> The vector X in the formula op(A) * diag(X).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: Successful exit.
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexGEcomputational
*
* =====================================================================
REAL FUNCTION CLA_GERCOND_X( TRANS, N, A, LDA, AF, LDAF, IPIV, X,
$ INFO, WORK, RWORK )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER N, LDA, LDAF, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
REAL RWORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL NOTRANS
INTEGER KASE
REAL AINVNM, ANORM, TMP
INTEGER I, J
COMPLEX ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACN2, CGETRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, REAL, AIMAG
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
CLA_GERCOND_X = 0.0E+0
*
INFO = 0
NOTRANS = LSAME( TRANS, 'N' )
IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLA_GERCOND_X', -INFO )
RETURN
END IF
*
* Compute norm of op(A)*op2(C).
*
ANORM = 0.0
IF ( NOTRANS ) THEN
DO I = 1, N
TMP = 0.0E+0
DO J = 1, N
TMP = TMP + CABS1( A( I, J ) * X( J ) )
END DO
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
ELSE
DO I = 1, N
TMP = 0.0E+0
DO J = 1, N
TMP = TMP + CABS1( A( J, I ) * X( J ) )
END DO
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 ) THEN
CLA_GERCOND_X = 1.0E+0
RETURN
ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
RETURN
END IF
*
* Estimate the norm of inv(op(A)).
*
AINVNM = 0.0E+0
*
KASE = 0
10 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
* Multiply by R.
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
*
IF ( NOTRANS ) THEN
CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ELSE
CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ENDIF
*
* Multiply by inv(X).
*
DO I = 1, N
WORK( I ) = WORK( I ) / X( I )
END DO
ELSE
*
* Multiply by inv(X**H).
*
DO I = 1, N
WORK( I ) = WORK( I ) / X( I )
END DO
*
IF ( NOTRANS ) THEN
CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ELSE
CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
END IF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0E+0 )
$ CLA_GERCOND_X = 1.0E+0 / AINVNM
*
RETURN
*
END