--- rpl/lapack/lapack/dlantp.f 2011/11/21 22:19:32 1.9
+++ rpl/lapack/lapack/dlantp.f 2020/05/21 21:45:59 1.18
@@ -1,25 +1,25 @@
-*> \brief \b DLANTP
+*> \brief \b DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
*
* =========== 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 DLANTP + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLANTP + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
-*
+*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER N
@@ -27,7 +27,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -112,23 +112,24 @@
* 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 doubleOTHERauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, 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 N
@@ -146,17 +147,20 @@
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER I, J, K
- 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, SQRT
+ INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
@@ -172,14 +176,16 @@
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = K, K + J - 2
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
K = K + J
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = K + 1, K + N - J
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
30 CONTINUE
K = K + N - J + 1
40 CONTINUE
@@ -189,14 +195,16 @@
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
DO 50 I = K, K + J - 1
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
50 CONTINUE
K = K + J
60 CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = K, K + N - J
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
K = K + N - J + 1
80 CONTINUE
@@ -223,7 +231,7 @@
100 CONTINUE
END IF
K = K + J
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
110 CONTINUE
ELSE
DO 140 J = 1, N
@@ -239,7 +247,7 @@
130 CONTINUE
END IF
K = K + N - J + 1
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
140 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
@@ -296,50 +304,70 @@
END IF
VALUE = ZERO
DO 270 I = 1, N
- VALUE = MAX( VALUE, WORK( I ) )
+ SUM = WORK( I )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
270 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 = N
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = N
K = 2
DO 280 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
280 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
K = 1
DO 290 J = 1, N
- CALL DLASSQ( J, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( J, AP( K ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + J
290 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
- SCALE = ONE
- SUM = N
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = N
K = 2
DO 300 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
300 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
K = 1
DO 310 J = 1, N
- CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( N-J+1, AP( K ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + N - J + 1
310 CONTINUE
END IF
END IF
- VALUE = SCALE*SQRT( SUM )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANTP = VALUE