--- rpl/lapack/lapack/dlansb.f 2012/12/14 12:30:23 1.11
+++ rpl/lapack/lapack/dlansb.f 2020/05/21 21:45:59 1.18
@@ -2,25 +2,25 @@
*
* =========== 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 DLANSB + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLANSB + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
-*
+*
* .. Scalar Arguments ..
* CHARACTER NORM, UPLO
* INTEGER K, LDAB, N
@@ -28,7 +28,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -116,12 +116,12 @@
* 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 September 2012
+*> \date December 2016
*
*> \ingroup doubleOTHERauxiliary
*
@@ -129,11 +129,12 @@
DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
$ 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, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
+* December 2016
*
+ IMPLICIT NONE
* .. Scalar Arguments ..
CHARACTER NORM, UPLO
INTEGER K, LDAB, N
@@ -150,15 +151,18 @@
* ..
* .. Local Scalars ..
INTEGER I, J, L
- DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
+ DOUBLE PRECISION ABSA, SUM, VALUE
* ..
-* .. External Subroutines ..
- EXTERNAL DLASSQ
+* .. Local Arrays ..
+ DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME, DISNAN
EXTERNAL LSAME, DISNAN
* ..
+* .. External Subroutines ..
+ EXTERNAL DLASSQ, DCOMBSSQ
+* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
* ..
@@ -225,29 +229,47 @@
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( K.GT.0 ) THEN
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
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
L = K + 1
ELSE
DO 120 J = 1, N - 1
- CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
- $ SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
120 CONTINUE
L = 1
END IF
- SUM = 2*SUM
+ SSQ( 2 ) = 2*SSQ( 2 )
ELSE
L = 1
END IF
- CALL DLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
- VALUE = SCALE*SQRT( SUM )
+*
+* Sum diagonal
+*
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( N, AB( L, 1 ), LDAB, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANSB = VALUE