--- rpl/lapack/lapack/dlantr.f 2012/08/22 09:48:18 1.10
+++ rpl/lapack/lapack/dlantr.f 2020/05/21 21:45:59 1.18
@@ -1,26 +1,26 @@
-*> \brief \b DLANTR
+*> \brief \b DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular 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 DLANTR + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLANTR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
* WORK )
-*
+*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER LDA, M, N
@@ -28,7 +28,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -128,12 +128,12 @@
* 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 November 2011
+*> \date December 2016
*
*> \ingroup doubleOTHERauxiliary
*
@@ -141,11 +141,12 @@
DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, 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 DIAG, NORM, UPLO
INTEGER LDA, M, N
@@ -163,17 +164,20 @@
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER I, J
- DOUBLE PRECISION SCALE, SUM, VALUE
+ DOUBLE PRECISION SUM, VALUE
* ..
-* .. External Subroutines ..
- EXTERNAL DLASSQ
+* .. Local Arrays ..
+ DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLASSQ, DCOMBSSQ
* ..
* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, MIN, SQRT
+ INTRINSIC ABS, MIN, SQRT
* ..
* .. Executable Statements ..
*
@@ -188,13 +192,15 @@
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = 1, MIN( M, J-1 )
- 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 + 1, M
- 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
@@ -203,13 +209,15 @@
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
DO 50 I = 1, MIN( M, J )
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
+ SUM = ABS( A( I, J ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
50 CONTINUE
60 CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = J, M
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
+ SUM = ABS( A( I, J ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
80 CONTINUE
END IF
@@ -233,7 +241,7 @@
SUM = SUM + ABS( A( I, J ) )
100 CONTINUE
END IF
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
110 CONTINUE
ELSE
DO 140 J = 1, N
@@ -248,7 +256,7 @@
SUM = SUM + ABS( A( I, J ) )
130 CONTINUE
END IF
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
140 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
@@ -301,43 +309,62 @@
END IF
VALUE = ZERO
DO 280 I = 1, M
- VALUE = MAX( VALUE, WORK( I ) )
+ SUM = WORK( I )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
280 CONTINUE
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.
*
IF( LSAME( UPLO, 'U' ) ) THEN
IF( LSAME( DIAG, 'U' ) ) THEN
- SCALE = ONE
- SUM = MIN( M, N )
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = MIN( M, N )
DO 290 J = 2, N
- CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
290 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
DO 300 J = 1, N
- CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( MIN( M, J ), A( 1, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
300 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
- SCALE = ONE
- SUM = MIN( M, N )
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = MIN( M, N )
DO 310 J = 1, N
- CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
- $ SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
310 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
DO 320 J = 1, N
- CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( M-J+1, A( J, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
320 CONTINUE
END IF
END IF
- VALUE = SCALE*SQRT( SUM )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANTR = VALUE