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sjplimp
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*> \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
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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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*> \htmlonly
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*> Download DLANGE + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlange.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlange.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlange.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER NORM
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* INTEGER LDA, M, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), WORK( * )
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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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*> DLANGE returns the value of the one norm, or the Frobenius norm, or
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*> the infinity norm, or the element of largest absolute value of a
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*> real matrix A.
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*> \endverbatim
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*>
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*> \return DLANGE
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*> \verbatim
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*>
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*> DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
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*> (
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*> ( norm1(A), NORM = '1', 'O' or 'o'
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*> (
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*> ( normI(A), NORM = 'I' or 'i'
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*> (
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*> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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*>
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*> where norm1 denotes the one norm of a matrix (maximum column sum),
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*> normI denotes the infinity norm of a matrix (maximum row sum) and
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*> normF denotes the Frobenius norm of a matrix (square root of sum of
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*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
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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] NORM
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*> \verbatim
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*> NORM is CHARACTER*1
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*> Specifies the value to be returned in DLANGE as described
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*> above.
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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. When M = 0,
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*> DLANGE is set to zero.
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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. When N = 0,
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*> DLANGE is set to zero.
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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 DOUBLE PRECISION array, dimension (LDA,N)
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*> The m by 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(M,1).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
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*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
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*> referenced.
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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 September 2012
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*
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*> \ingroup doubleGEauxiliary
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*
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* =====================================================================
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DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
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*
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* -- LAPACK auxiliary routine (version 3.2) --
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* -- LAPACK auxiliary routine (version 3.4.2) --
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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 2006
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* September 2012
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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@ -13,56 +127,6 @@
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DOUBLE PRECISION A( LDA, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLANGE returns the value of the one norm, or the Frobenius norm, or
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* the infinity norm, or the element of largest absolute value of a
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* real matrix A.
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*
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* Description
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* ===========
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*
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* DLANGE returns the value
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*
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* DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
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* (
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* ( norm1(A), NORM = '1', 'O' or 'o'
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* (
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* ( normI(A), NORM = 'I' or 'i'
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* (
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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*
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* where norm1 denotes the one norm of a matrix (maximum column sum),
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* normI denotes the infinity norm of a matrix (maximum row sum) and
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* normF denotes the Frobenius norm of a matrix (square root of sum of
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies the value to be returned in DLANGE as described
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* above.
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0. When M = 0,
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* DLANGE is set to zero.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= 0. When N = 0,
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* DLANGE is set to zero.
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*
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* A (input) DOUBLE PRECISION array, dimension (LDA,N)
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* The m by n matrix A.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(M,1).
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
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* where LWORK >= M when NORM = 'I'; otherwise, WORK is not
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* referenced.
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*
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* =====================================================================
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*
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* .. Parameters ..
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@ -71,17 +135,17 @@
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION SCALE, SUM, VALUE
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DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASSQ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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LOGICAL LSAME, DISNAN
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EXTERNAL LSAME, DISNAN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, SQRT
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INTRINSIC ABS, MIN, SQRT
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* ..
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* .. Executable Statements ..
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*
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VALUE = ZERO
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DO 20 J = 1, N
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DO 10 I = 1, M
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VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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TEMP = ABS( A( I, J ) )
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
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10 CONTINUE
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20 CONTINUE
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ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
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@ -107,7 +172,7 @@
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DO 30 I = 1, M
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SUM = SUM + ABS( A( I, J ) )
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30 CONTINUE
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VALUE = MAX( VALUE, SUM )
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IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
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40 CONTINUE
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ELSE IF( LSAME( NORM, 'I' ) ) THEN
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*
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70 CONTINUE
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VALUE = ZERO
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DO 80 I = 1, M
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VALUE = MAX( VALUE, WORK( I ) )
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TEMP = WORK( I )
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
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80 CONTINUE
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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*
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