--- rpl/lapack/lapack/dlatrs.f 2012/12/14 14:22:36 1.14
+++ rpl/lapack/lapack/dlatrs.f 2023/08/07 08:39:00 1.20
@@ -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 DLATRS + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLATRS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
-*
+*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORMIN, TRANS, UPLO
* INTEGER INFO, LDA, N
@@ -29,7 +29,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -153,12 +153,10 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date September 2012
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup doubleOTHERauxiliary
*
@@ -238,10 +236,9 @@
SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
$ CNORM, INFO )
*
-* -- LAPACK auxiliary routine (version 3.4.2) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORMIN, TRANS, UPLO
@@ -267,8 +264,8 @@
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
- DOUBLE PRECISION DASUM, DDOT, DLAMCH
- EXTERNAL LSAME, IDAMAX, DASUM, DDOT, DLAMCH
+ DOUBLE PRECISION DASUM, DDOT, DLAMCH, DLANGE
+ EXTERNAL LSAME, IDAMAX, DASUM, DDOT, DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DSCAL, DTRSV, XERBLA
@@ -307,6 +304,7 @@
*
* Quick return if possible
*
+ SCALE = ONE
IF( N.EQ.0 )
$ RETURN
*
@@ -314,7 +312,6 @@
*
SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
BIGNUM = ONE / SMLNUM
- SCALE = ONE
*
IF( LSAME( NORMIN, 'N' ) ) THEN
*
@@ -346,8 +343,67 @@
IF( TMAX.LE.BIGNUM ) THEN
TSCAL = ONE
ELSE
- TSCAL = ONE / ( SMLNUM*TMAX )
- CALL DSCAL( N, TSCAL, CNORM, 1 )
+*
+* Avoid NaN generation if entries in CNORM exceed the
+* overflow threshold
+*
+ IF( TMAX.LE.DLAMCH('Overflow') ) THEN
+* Case 1: All entries in CNORM are valid floating-point numbers
+ TSCAL = ONE / ( SMLNUM*TMAX )
+ CALL DSCAL( N, TSCAL, CNORM, 1 )
+ ELSE
+* Case 2: At least one column norm of A cannot be represented
+* as floating-point number. Find the offdiagonal entry A( I, J )
+* with the largest absolute value. If this entry is not +/- Infinity,
+* use this value as TSCAL.
+ TMAX = ZERO
+ IF( UPPER ) THEN
+*
+* A is upper triangular.
+*
+ DO J = 2, N
+ TMAX = MAX( DLANGE( 'M', J-1, 1, A( 1, J ), 1, SUMJ ),
+ $ TMAX )
+ END DO
+ ELSE
+*
+* A is lower triangular.
+*
+ DO J = 1, N - 1
+ TMAX = MAX( DLANGE( 'M', N-J, 1, A( J+1, J ), 1,
+ $ SUMJ ), TMAX )
+ END DO
+ END IF
+*
+ IF( TMAX.LE.DLAMCH('Overflow') ) THEN
+ TSCAL = ONE / ( SMLNUM*TMAX )
+ DO J = 1, N
+ IF( CNORM( J ).LE.DLAMCH('Overflow') ) THEN
+ CNORM( J ) = CNORM( J )*TSCAL
+ ELSE
+* Recompute the 1-norm without introducing Infinity
+* in the summation
+ CNORM( J ) = ZERO
+ IF( UPPER ) THEN
+ DO I = 1, J - 1
+ CNORM( J ) = CNORM( J ) +
+ $ TSCAL * ABS( A( I, J ) )
+ END DO
+ ELSE
+ DO I = J + 1, N
+ CNORM( J ) = CNORM( J ) +
+ $ TSCAL * ABS( A( I, J ) )
+ END DO
+ END IF
+ END IF
+ END DO
+ ELSE
+* At least one entry of A is not a valid floating-point entry.
+* Rely on TRSV to propagate Inf and NaN.
+ CALL DTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 )
+ RETURN
+ END IF
+ END IF
END IF
*
* Compute a bound on the computed solution vector to see if the