version 1.11, 2012/12/14 12:30:31
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version 1.18, 2020/05/21 21:46:07
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* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZLANHE + dependencies |
*> Download ZLANHE + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhe.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhe.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhe.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhe.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhe.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhe.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) |
* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER NORM, UPLO |
* CHARACTER NORM, UPLO |
* INTEGER LDA, N |
* INTEGER LDA, N |
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* DOUBLE PRECISION WORK( * ) |
* DOUBLE PRECISION WORK( * ) |
* COMPLEX*16 A( LDA, * ) |
* COMPLEX*16 A( LDA, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date September 2012 |
*> \date December 2016 |
* |
* |
*> \ingroup complex16HEauxiliary |
*> \ingroup complex16HEauxiliary |
* |
* |
* ===================================================================== |
* ===================================================================== |
DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) |
DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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..-- |
* September 2012 |
* December 2016 |
* |
* |
|
IMPLICIT NONE |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM, UPLO |
CHARACTER NORM, UPLO |
INTEGER LDA, N |
INTEGER LDA, N |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER I, J |
INTEGER I, J |
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
DOUBLE PRECISION ABSA, SUM, VALUE |
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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, DISNAN |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME, DISNAN |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZLASSQ |
EXTERNAL ZLASSQ, DCOMBSSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, SQRT |
INTRINSIC ABS, DBLE, SQRT |
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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. |
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* |
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SSQ( 1 ) = ZERO |
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SSQ( 2 ) = ONE |
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* |
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* Sum off-diagonals |
* |
* |
SCALE = ZERO |
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SUM = ONE |
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IF( LSAME( UPLO, 'U' ) ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
DO 110 J = 2, N |
DO 110 J = 2, N |
CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( J-1, A( 1, J ), 1, |
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$ COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
110 CONTINUE |
110 CONTINUE |
ELSE |
ELSE |
DO 120 J = 1, N - 1 |
DO 120 J = 1, N - 1 |
CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( N-J, A( J+1, J ), 1, |
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$ COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
120 CONTINUE |
120 CONTINUE |
END IF |
END IF |
SUM = 2*SUM |
SSQ( 2 ) = 2*SSQ( 2 ) |
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* |
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* Sum diagonal |
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* |
DO 130 I = 1, N |
DO 130 I = 1, N |
IF( DBLE( A( I, I ) ).NE.ZERO ) THEN |
IF( DBLE( A( I, I ) ).NE.ZERO ) THEN |
ABSA = ABS( DBLE( A( I, I ) ) ) |
ABSA = ABS( DBLE( A( I, I ) ) ) |
IF( SCALE.LT.ABSA ) THEN |
IF( SSQ( 1 ).LT.ABSA ) THEN |
SUM = ONE + SUM*( SCALE / ABSA )**2 |
SSQ( 2 ) = ONE + SSQ( 2 )*( SSQ( 1 ) / ABSA )**2 |
SCALE = ABSA |
SSQ( 1 ) = ABSA |
ELSE |
ELSE |
SUM = SUM + ( ABSA / SCALE )**2 |
SSQ( 2 ) = SSQ( 2 ) + ( ABSA / SSQ( 1 ) )**2 |
END IF |
END IF |
END IF |
END IF |
130 CONTINUE |
130 CONTINUE |
VALUE = SCALE*SQRT( SUM ) |
VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) |
END IF |
END IF |
* |
* |
ZLANHE = VALUE |
ZLANHE = VALUE |