--- rpl/lapack/lapack/dlansp.f 2012/12/14 14:22:33 1.12
+++ rpl/lapack/lapack/dlansp.f 2020/05/21 21:45:59 1.18
@@ -2,24 +2,24 @@
*
* =========== 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 DLANSP + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLANSP + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
-*
+*
* .. Scalar Arguments ..
* CHARACTER NORM, UPLO
* INTEGER N
@@ -27,7 +27,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -102,23 +102,24 @@
* 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 September 2012
+*> \date December 2016
*
*> \ingroup doubleOTHERauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, 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 N
@@ -135,15 +136,18 @@
* ..
* .. Local Scalars ..
INTEGER I, J, K
- 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, SQRT
* ..
@@ -217,31 +221,48 @@
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
K = 2
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
- CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + J
110 CONTINUE
ELSE
DO 120 J = 1, N - 1
- CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + N - J + 1
120 CONTINUE
END IF
- SUM = 2*SUM
+ SSQ( 2 ) = 2*SSQ( 2 )
+*
+* Sum diagonal
+*
K = 1
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
DO 130 I = 1, N
IF( AP( K ).NE.ZERO ) THEN
ABSA = ABS( AP( K ) )
- IF( SCALE.LT.ABSA ) THEN
- SUM = ONE + SUM*( SCALE / ABSA )**2
- SCALE = ABSA
+ IF( COLSSQ( 1 ).LT.ABSA ) THEN
+ COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+ COLSSQ( 1 ) = ABSA
ELSE
- SUM = SUM + ( ABSA / SCALE )**2
+ COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
END IF
END IF
IF( LSAME( UPLO, 'U' ) ) THEN
@@ -250,7 +271,8 @@
K = K + N - I + 1
END IF
130 CONTINUE
- VALUE = SCALE*SQRT( SUM )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANSP = VALUE