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version 1.18, 2020/05/21 21:46:07
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*> \brief \b ZLANGE 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 ZLANGE + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlange.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/zlange.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/zlange.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 ZLANGE( 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 WORK( * ) |
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* COMPLEX*16 A( LDA, * ) |
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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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*> ZLANGE 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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*> complex matrix A. |
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*> \endverbatim |
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*> |
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*> \return ZLANGE |
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*> \verbatim |
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*> |
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*> ZLANGE = ( 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 ZLANGE 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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*> ZLANGE 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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*> ZLANGE 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 COMPLEX*16 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 December 2016 |
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* |
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*> \ingroup complex16GEauxiliary |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK ) |
DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
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IMPLICIT NONE |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM |
CHARACTER NORM |
INTEGER LDA, M, N |
INTEGER LDA, M, N |
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COMPLEX*16 A( LDA, * ) |
COMPLEX*16 A( LDA, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLANGE 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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* complex matrix A. |
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* |
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* Description |
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* =========== |
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* |
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* ZLANGE returns the value |
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* |
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* ZLANGE = ( 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 ZLANGE 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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* ZLANGE 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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* ZLANGE is set to zero. |
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* |
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* A (input) COMPLEX*16 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER I, J |
INTEGER I, J |
DOUBLE PRECISION SCALE, SUM, VALUE |
DOUBLE PRECISION SUM, VALUE, TEMP |
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* .. |
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* .. Local Arrays .. |
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DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZLASSQ |
EXTERNAL ZLASSQ, DCOMBSSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, MAX, MIN, SQRT |
INTRINSIC ABS, MIN, SQRT |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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VALUE = ZERO |
VALUE = ZERO |
DO 20 J = 1, N |
DO 20 J = 1, N |
DO 10 I = 1, M |
DO 10 I = 1, M |
VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
TEMP = ABS( A( I, J ) ) |
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP |
10 CONTINUE |
10 CONTINUE |
20 CONTINUE |
20 CONTINUE |
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
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DO 30 I = 1, M |
DO 30 I = 1, M |
SUM = SUM + ABS( A( I, J ) ) |
SUM = SUM + ABS( A( I, J ) ) |
30 CONTINUE |
30 CONTINUE |
VALUE = MAX( VALUE, SUM ) |
IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
40 CONTINUE |
40 CONTINUE |
ELSE IF( LSAME( NORM, 'I' ) ) THEN |
ELSE IF( LSAME( NORM, 'I' ) ) THEN |
* |
* |
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70 CONTINUE |
70 CONTINUE |
VALUE = ZERO |
VALUE = ZERO |
DO 80 I = 1, M |
DO 80 I = 1, M |
VALUE = MAX( VALUE, WORK( I ) ) |
TEMP = WORK( I ) |
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP |
80 CONTINUE |
80 CONTINUE |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
* |
* |
* Find normF(A). |
* Find normF(A). |
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* SSQ(1) is scale |
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* SSQ(2) is sum-of-squares |
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* For better accuracy, sum each column separately. |
* |
* |
SCALE = ZERO |
SSQ( 1 ) = ZERO |
SUM = ONE |
SSQ( 2 ) = ONE |
DO 90 J = 1, N |
DO 90 J = 1, N |
CALL ZLASSQ( M, A( 1, J ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( M, A( 1, J ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
90 CONTINUE |
90 CONTINUE |
VALUE = SCALE*SQRT( SUM ) |
VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) |
END IF |
END IF |
* |
* |
ZLANGE = VALUE |
ZLANGE = VALUE |