--- rpl/lapack/lapack/zlansy.f 2012/08/22 09:48:36 1.10
+++ rpl/lapack/lapack/zlansy.f 2020/05/21 21:46:08 1.19
@@ -1,25 +1,25 @@
-*> \brief \b ZLANSY
+*> \brief \b ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix.
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download ZLANSY + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download ZLANSY + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
-*
+*
* .. Scalar Arguments ..
* CHARACTER NORM, UPLO
* INTEGER LDA, N
@@ -28,7 +28,7 @@
* DOUBLE PRECISION WORK( * )
* COMPLEX*16 A( LDA, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -111,23 +111,24 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-*> \date November 2011
+*> \date December 2016
*
*> \ingroup complex16SYauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, 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, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
+* December 2016
*
+ IMPLICIT NONE
* .. Scalar Arguments ..
CHARACTER NORM, UPLO
INTEGER LDA, N
@@ -145,17 +146,20 @@
* ..
* .. Local Scalars ..
INTEGER I, J
- DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
+ DOUBLE PRECISION ABSA, SUM, VALUE
+* ..
+* .. Local Arrays ..
+ DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
* ..
* .. External Subroutines ..
- EXTERNAL ZLASSQ
+ EXTERNAL ZLASSQ, DCOMBSSQ
* ..
* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, SQRT
+ INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
@@ -169,13 +173,15 @@
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = 1, J
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
+ SUM = ABS( A( I, J ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = J, N
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
+ SUM = ABS( A( I, J ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
30 CONTINUE
40 CONTINUE
END IF
@@ -196,7 +202,8 @@
WORK( J ) = SUM + ABS( A( J, J ) )
60 CONTINUE
DO 70 I = 1, N
- VALUE = MAX( VALUE, WORK( I ) )
+ SUM = WORK( I )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
ELSE
DO 80 I = 1, N
@@ -209,27 +216,45 @@
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
90 CONTINUE
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
100 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
+* SSQ(1) is scale
+* SSQ(2) is sum-of-squares
+* For better accuracy, sum each column separately.
+*
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
+*
+* Sum off-diagonals
*
- SCALE = ZERO
- SUM = ONE
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
- CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL ZLASSQ( J-1, A( 1, J ), 1, COLSSQ(1), COLSSQ(2) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
110 CONTINUE
ELSE
DO 120 J = 1, N - 1
- CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL ZLASSQ( N-J, A( J+1, J ), 1, COLSSQ(1), COLSSQ(2) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
120 CONTINUE
END IF
- SUM = 2*SUM
- CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
- VALUE = SCALE*SQRT( SUM )
+ SSQ( 2 ) = 2*SSQ( 2 )
+*
+* Sum diagonal
+*
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL ZLASSQ( N, A, LDA+1, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
ZLANSY = VALUE