*> \brief \b CGECON

*

* =========== DOCUMENTATION ===========

*

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* http://www.netlib.org/lapack/explore-html/

*

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*

* Definition:

* ===========

*

* SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,

* INFO )

*

* .. Scalar Arguments ..

* CHARACTER NORM

* INTEGER INFO, LDA, N

* REAL ANORM, RCOND

* ..

* .. Array Arguments ..

* REAL RWORK( * )

* COMPLEX A( LDA, * ), WORK( * )

* ..

*

*

*> \par Purpose:

* =============

*>

*> \verbatim

*>

*> CGECON estimates the reciprocal of the condition number of a general

*> complex matrix A, in either the 1-norm or the infinity-norm, using

*> the LU factorization computed by CGETRF.

*>

*> An estimate is obtained for norm(inv(A)), and the reciprocal of the

*> condition number is computed as

*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).

*> \endverbatim

*

* Arguments:

* ==========

*

*> \param[in] NORM

*> \verbatim

*> NORM is CHARACTER*1

*> Specifies whether the 1-norm condition number or the

*> infinity-norm condition number is required:

*> = '1' or 'O': 1-norm;

*> = 'I': Infinity-norm.

*> \endverbatim

*>

*> \param[in] N

*> \verbatim

*> N is INTEGER

*> The order of the matrix A. N >= 0.

*> \endverbatim

*>

*> \param[in] A

*> \verbatim

*> A is COMPLEX array, dimension (LDA,N)

*> The factors L and U from the factorization A = P*L*U

*> as computed by CGETRF.

*> \endverbatim

*>

*> \param[in] LDA

*> \verbatim

*> LDA is INTEGER

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

*> \endverbatim

*>

*> \param[in] ANORM

*> \verbatim

*> ANORM is REAL

*> If NORM = '1' or 'O', the 1-norm of the original matrix A.

*> If NORM = 'I', the infinity-norm of the original matrix A.

*> \endverbatim

*>

*> \param[out] RCOND

*> \verbatim

*> RCOND is REAL

*> The reciprocal of the condition number of the matrix A,

*> computed as RCOND = 1/(norm(A) * norm(inv(A))).

*> \endverbatim

*>

*> \param[out] WORK

*> \verbatim

*> WORK is COMPLEX array, dimension (2*N)

*> \endverbatim

*>

*> \param[out] RWORK

*> \verbatim

*> RWORK is REAL array, dimension (2*N)

*> \endverbatim

*>

*> \param[out] INFO

*> \verbatim

*> INFO is INTEGER

*> = 0: successful exit

*> < 0: if INFO = -i, the i-th argument had an illegal value

*> \endverbatim

*

* Authors:

* ========

*

*> \author Univ. of Tennessee

*> \author Univ. of California Berkeley

*> \author Univ. of Colorado Denver

*> \author NAG Ltd.

*

*> \ingroup complexGEcomputational

*

* =====================================================================

SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,

$ INFO )

*

* -- LAPACK computational routine --

* -- LAPACK is a software package provided by Univ. of Tennessee, --

* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--

*

* .. Scalar Arguments ..

CHARACTER NORM

INTEGER INFO, LDA, N

REAL ANORM, RCOND

* ..

* .. Array Arguments ..

REAL RWORK( * )

COMPLEX A( LDA, * ), WORK( * )

* ..

*

* =====================================================================

*

* .. Parameters ..

REAL ONE, ZERO

PARAMETER ( ONE = 1.0E 0, ZERO = 0.0E 0 )

* ..

* .. Local Scalars ..

LOGICAL ONENRM

CHARACTER NORMIN

INTEGER IX, KASE, KASE1

REAL AINVNM, SCALE, SL, SMLNUM, SU

COMPLEX ZDUM

* ..

* .. Local Arrays ..

INTEGER ISAVE( 3 )

* ..

* .. External Functions ..

LOGICAL LSAME

INTEGER ICAMAX

REAL SLAMCH

EXTERNAL LSAME, ICAMAX, SLAMCH

* ..

* .. External Subroutines ..

EXTERNAL CLACN2, CLATRS, CSRSCL, XERBLA

* ..

* .. Intrinsic Functions ..

INTRINSIC ABS, AIMAG, MAX, REAL

* ..

* .. Statement Functions ..

REAL CABS1

* ..

* .. Statement Function definitions ..

CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) ABS( AIMAG( ZDUM ) )

* ..

* .. Executable Statements ..

*

* Test the input parameters.

*

INFO = 0

ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )

IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN

INFO = -1

ELSE IF( N.LT.0 ) THEN

INFO = -2

ELSE IF( LDA.LT.MAX( 1, N ) ) THEN

INFO = -4

ELSE IF( ANORM.LT.ZERO ) THEN

INFO = -5

END IF

IF( INFO.NE.0 ) THEN

CALL XERBLA( 'CGECON', -INFO )

RETURN

END IF

*

* Quick return if possible

*

RCOND = ZERO

IF( N.EQ.0 ) THEN

RCOND = ONE

RETURN

ELSE IF( ANORM.EQ.ZERO ) THEN

RETURN

END IF

*

SMLNUM = SLAMCH( 'Safe minimum' )

*

* Estimate the norm of inv(A).

*

AINVNM = ZERO

NORMIN = 'N'

IF( ONENRM ) THEN

KASE1 = 1

ELSE

KASE1 = 2

END IF

KASE = 0

10 CONTINUE

CALL CLACN2( N, WORK( N 1 ), WORK, AINVNM, KASE, ISAVE )

IF( KASE.NE.0 ) THEN

IF( KASE.EQ.KASE1 ) THEN

*

* Multiply by inv(L).

*

CALL CLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A,

$ LDA, WORK, SL, RWORK, INFO )

*

* Multiply by inv(U).

*

CALL CLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,

$ A, LDA, WORK, SU, RWORK( N 1 ), INFO )

ELSE

*

* Multiply by inv(U**H).

*

CALL CLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',

$ NORMIN, N, A, LDA, WORK, SU, RWORK( N 1 ),

$ INFO )

*

* Multiply by inv(L**H).

*

CALL CLATRS( 'Lower', 'Conjugate transpose', 'Unit', NORMIN,

$ N, A, LDA, WORK, SL, RWORK, INFO )

END IF

*

* Divide X by 1/(SL*SU) if doing so will not cause overflow.

*

SCALE = SL*SU

NORMIN = 'Y'

IF( SCALE.NE.ONE ) THEN

IX = ICAMAX( N, WORK, 1 )

IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )

$ GO TO 20

CALL CSRSCL( N, SCALE, WORK, 1 )

END IF

GO TO 10

END IF

*

* Compute the estimate of the reciprocal condition number.

*

IF( AINVNM.NE.ZERO )

$ RCOND = ( ONE / AINVNM ) / ANORM

*

20 CONTINUE

RETURN

*

* End of CGECON

*

END