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lapack/SRC/checon.f
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Hans Johnson 9dafba6d41 STYLE: Remove trailing whitespace in Fortran files 
This is mostly a long term maintenance improvement.

Many coding styles require elimination of trailing whitespace, and
many editors and source code management configurations automatically
gobble up whitespace. When these tools gobble up whitespace, it
complicates reviewing the meaningful code changes.

By removing whitespace on one patch, it makes future
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if which tempfile &>/dev/null; then
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elif which mktemp &>/dev/null; then
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fi

MYTEMP=$($TEMPMAKER)
trap 'rm -f $MYTEMP' SIGINT SIGTERM

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}

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=================================================
2016-07-09 11:19:34 -05:00

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*> \brief \b CHECON
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CHECON + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/checon.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/checon.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/checon.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* REAL ANORM, RCOND
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHECON estimates the reciprocal of the condition number of a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by CHETRF.
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the details of the factorization are stored
*> as an upper or lower triangular matrix.
*> = 'U': Upper triangular, form is A = U*D*U**H;
*> = 'L': Lower triangular, form is A = L*D*L**H.
*> \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 block diagonal matrix D and the multipliers used to
*> obtain the factor U or L as computed by CHETRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D
*> as determined by CHETRF.
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*> ANORM is REAL
*> The 1-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/(ANORM * AINVNM), where AINVNM is an
*> estimate of the 1-norm of inv(A) computed in this routine.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX 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.
*
*> \date November 2011
*
*> \ingroup complexHEcomputational
*
* =====================================================================
SUBROUTINE CHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
REAL ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, KASE
REAL AINVNM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CHETRS, CLACN2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) 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 = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHECON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.LE.ZERO ) THEN
RETURN
END IF
*
* Check that the diagonal matrix D is nonsingular.
*
IF( UPPER ) THEN
*
* Upper triangular storage: examine D from bottom to top
*
DO 10 I = N, 1, -1
IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
DO 20 I = 1, N
IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
$ RETURN
20 CONTINUE
END IF
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
30 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
*
* Multiply by inv(L*D*L**H) or inv(U*D*U**H).
*
CALL CHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
GO TO 30
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / AINVNM ) / ANORM
*
RETURN
*
* End of CHECON
*
END
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