version 1.8, 2011/11/21 20:42:56
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version 1.18, 2020/05/21 21:45:59
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*> \brief \b DLANSB |
*> \brief \b DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric 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 DLANSB + dependencies |
*> Download DLANSB + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansb.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansb.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansb.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB, |
* DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB, |
* WORK ) |
* WORK ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER NORM, UPLO |
* CHARACTER NORM, UPLO |
* INTEGER K, LDAB, N |
* INTEGER K, LDAB, N |
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* .. Array Arguments .. |
* .. Array Arguments .. |
* DOUBLE PRECISION AB( LDAB, * ), WORK( * ) |
* DOUBLE PRECISION AB( LDAB, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \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 doubleOTHERauxiliary |
*> \ingroup doubleOTHERauxiliary |
* |
* |
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DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB, |
DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, 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, UPLO |
CHARACTER NORM, UPLO |
INTEGER K, LDAB, N |
INTEGER K, LDAB, N |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER I, J, L |
INTEGER I, J, L |
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
DOUBLE PRECISION ABSA, SUM, VALUE |
* .. |
* .. |
* .. External Subroutines .. |
* .. Local Arrays .. |
EXTERNAL DLASSQ |
DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME |
EXTERNAL LSAME, DISNAN |
|
* .. |
|
* .. External Subroutines .. |
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EXTERNAL DLASSQ, DCOMBSSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, MAX, MIN, SQRT |
INTRINSIC ABS, MAX, MIN, SQRT |
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IF( LSAME( UPLO, 'U' ) ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
DO 20 J = 1, N |
DO 20 J = 1, N |
DO 10 I = MAX( K+2-J, 1 ), K + 1 |
DO 10 I = MAX( K+2-J, 1 ), K + 1 |
VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) |
SUM = ABS( AB( I, J ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
10 CONTINUE |
10 CONTINUE |
20 CONTINUE |
20 CONTINUE |
ELSE |
ELSE |
DO 40 J = 1, N |
DO 40 J = 1, N |
DO 30 I = 1, MIN( N+1-J, K+1 ) |
DO 30 I = 1, MIN( N+1-J, K+1 ) |
VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) |
SUM = ABS( AB( I, J ) ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
30 CONTINUE |
30 CONTINUE |
40 CONTINUE |
40 CONTINUE |
END IF |
END IF |
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WORK( J ) = SUM + ABS( AB( K+1, J ) ) |
WORK( J ) = SUM + ABS( AB( K+1, J ) ) |
60 CONTINUE |
60 CONTINUE |
DO 70 I = 1, N |
DO 70 I = 1, N |
VALUE = MAX( VALUE, WORK( I ) ) |
SUM = WORK( I ) |
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IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
70 CONTINUE |
70 CONTINUE |
ELSE |
ELSE |
DO 80 I = 1, N |
DO 80 I = 1, N |
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SUM = SUM + ABSA |
SUM = SUM + ABSA |
WORK( I ) = WORK( I ) + ABSA |
WORK( I ) = WORK( I ) + ABSA |
90 CONTINUE |
90 CONTINUE |
VALUE = MAX( VALUE, SUM ) |
IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM |
100 CONTINUE |
100 CONTINUE |
END IF |
END IF |
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( K.GT.0 ) THEN |
IF( K.GT.0 ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
IF( LSAME( UPLO, 'U' ) ) THEN |
DO 110 J = 2, N |
DO 110 J = 2, N |
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COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
CALL DLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ), |
CALL DLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ), |
$ 1, SCALE, SUM ) |
$ 1, COLSSQ( 1 ), COLSSQ( 2 ) ) |
|
CALL DCOMBSSQ( SSQ, COLSSQ ) |
110 CONTINUE |
110 CONTINUE |
L = K + 1 |
L = K + 1 |
ELSE |
ELSE |
DO 120 J = 1, N - 1 |
DO 120 J = 1, N - 1 |
CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE, |
COLSSQ( 1 ) = ZERO |
$ SUM ) |
COLSSQ( 2 ) = ONE |
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CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, |
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$ COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
120 CONTINUE |
120 CONTINUE |
L = 1 |
L = 1 |
END IF |
END IF |
SUM = 2*SUM |
SSQ( 2 ) = 2*SSQ( 2 ) |
ELSE |
ELSE |
L = 1 |
L = 1 |
END IF |
END IF |
CALL DLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM ) |
* |
VALUE = SCALE*SQRT( SUM ) |
* Sum diagonal |
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* |
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COLSSQ( 1 ) = ZERO |
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COLSSQ( 2 ) = ONE |
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CALL DLASSQ( N, AB( L, 1 ), LDAB, COLSSQ( 1 ), COLSSQ( 2 ) ) |
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CALL DCOMBSSQ( SSQ, COLSSQ ) |
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VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) |
END IF |
END IF |
* |
* |
DLANSB = VALUE |
DLANSB = VALUE |