version 1.8, 2011/11/21 20:43:15
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version 1.18, 2020/05/21 21:46:07
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*> \brief \b ZLANGB |
*> \brief \b ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. |
* |
* |
* =========== 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 ZLANGB + dependencies |
*> Download ZLANGB + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, |
* DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, |
* WORK ) |
* WORK ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER NORM |
* CHARACTER NORM |
* INTEGER KL, KU, LDAB, N |
* INTEGER KL, KU, LDAB, N |
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* DOUBLE PRECISION WORK( * ) |
* DOUBLE PRECISION WORK( * ) |
* COMPLEX*16 AB( LDAB, * ) |
* COMPLEX*16 AB( LDAB, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \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 November 2011 |
*> \date December 2016 |
* |
* |
*> \ingroup complex16GBauxiliary |
*> \ingroup complex16GBauxiliary |
* |
* |
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DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, |
DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, |
$ WORK ) |
$ WORK ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- 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 2011 |
* December 2016 |
* |
* |
|
IMPLICIT NONE |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM |
CHARACTER NORM |
INTEGER KL, KU, LDAB, N |
INTEGER KL, KU, LDAB, N |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER I, J, K, L |
INTEGER I, J, K, L |
DOUBLE PRECISION SCALE, SUM, VALUE |
DOUBLE PRECISION SUM, VALUE, TEMP |
|
* .. |
|
* .. Local Arrays .. |
|
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, MAX, MIN, SQRT |
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VALUE = ZERO |
VALUE = ZERO |
DO 20 J = 1, N |
DO 20 J = 1, N |
DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 ) |
DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 ) |
VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) |
TEMP = ABS( AB( 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 = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 ) |
DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 ) |
SUM = SUM + ABS( AB( I, J ) ) |
SUM = SUM + ABS( AB( 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, N |
DO 80 I = 1, N |
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 |
L = MAX( 1, J-KU ) |
L = MAX( 1, J-KU ) |
K = KU + 1 - J + L |
K = KU + 1 - J + L |
CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM ) |
COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, |
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$ 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 |
* |
* |
ZLANGB = VALUE |
ZLANGB = VALUE |