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cla_gbrcond_x.f
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*> \brief \b CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLA_GBRCOND_X + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gbrcond_x.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gbrcond_x.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gbrcond_x.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION CLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB,
* LDAFB, IPIV, X, INFO, WORK, RWORK )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
* $ X( * )
* REAL RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLA_GBRCOND_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] KL
*> \verbatim
*> KL is INTEGER
*> The number of subdiagonals within the band of A. KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The number of superdiagonals within the band of A. KU >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is COMPLEX array, dimension (LDAB,N)
*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
*> The j-th column of A is stored in the j-th column of the
*> array AB as follows:
*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KL+KU+1.
*> \endverbatim
*>
*> \param[in] AFB
*> \verbatim
*> AFB is COMPLEX array, dimension (LDAFB,N)
*> Details of the LU factorization of the band matrix A, as
*> computed by CGBTRF. U is stored as an upper triangular
*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
*> and the multipliers used during the factorization are stored
*> in rows KL+KU+2 to 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDAFB
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from the factorization A = P*L*U
*> as computed by CGBTRF; 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[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N).
*> Workspace.
*> \endverbatim
*>
*> \param[out] 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 complexGBcomputational
*
* =====================================================================
REAL FUNCTION CLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB,
$ LDAFB, 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, KL, KU, KD, KE, LDAB, LDAFB, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
$ X( * )
REAL RWORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL NOTRANS
INTEGER KASE, I, J
REAL AINVNM, ANORM, TMP
COMPLEX ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACN2, CGBTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
CLA_GBRCOND_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( KL.LT.0 .OR. KL.GT.N-1 ) THEN
INFO = -3
ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KL+KU+1 ) THEN
INFO = -6
ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLA_GBRCOND_X', -INFO )
RETURN
END IF
*
* Compute norm of op(A)*op2(C).
*
KD = KU + 1
KE = KL + 1
ANORM = 0.0
IF ( NOTRANS ) THEN
DO I = 1, N
TMP = 0.0E+0
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KD+I-J, 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 = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KE-I+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_GBRCOND_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 CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, 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 CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ 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_GBRCOND_X = 1.0E+0 / AINVNM
*
RETURN
*
END