--- rpl/lapack/lapack/zlatrs.f 2011/11/21 22:19:54 1.9
+++ rpl/lapack/lapack/zlatrs.f 2023/08/07 08:39:32 1.20
@@ -1,26 +1,26 @@
-*> \brief \b ZLATRS
+*> \brief \b ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
*
* =========== 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 ZLATRS + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download ZLATRS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
-*
+*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORMIN, TRANS, UPLO
* INTEGER INFO, LDA, N
@@ -30,7 +30,7 @@
* DOUBLE PRECISION CNORM( * )
* COMPLEX*16 A( LDA, * ), X( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -131,7 +131,7 @@
*>
*> \param[in,out] CNORM
*> \verbatim
-*> CNORM is or output) DOUBLE PRECISION array, dimension (N)
+*> CNORM is DOUBLE PRECISION array, dimension (N)
*>
*> If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
*> contains the norm of the off-diagonal part of the j-th column
@@ -154,12 +154,10 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date November 2011
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup complex16OTHERauxiliary
*
@@ -239,10 +237,9 @@
SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
$ CNORM, INFO )
*
-* -- LAPACK auxiliary routine (version 3.4.0) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORMIN, TRANS, UPLO
@@ -321,17 +318,14 @@
*
* Quick return if possible
*
+ SCALE = ONE
IF( N.EQ.0 )
$ RETURN
*
* Determine machine dependent parameters to control overflow.
*
- SMLNUM = DLAMCH( 'Safe minimum' )
- BIGNUM = ONE / SMLNUM
- CALL DLABAD( SMLNUM, BIGNUM )
- SMLNUM = SMLNUM / DLAMCH( 'Precision' )
+ SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
BIGNUM = ONE / SMLNUM
- SCALE = ONE
*
IF( LSAME( NORMIN, 'N' ) ) THEN
*
@@ -363,8 +357,74 @@
IF( TMAX.LE.BIGNUM*HALF ) THEN
TSCAL = ONE
ELSE
- TSCAL = HALF / ( 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 = HALF / ( SMLNUM*TMAX )
+ CALL DSCAL( N, TSCAL, CNORM, 1 )
+ ELSE
+* Case 2: At least one column norm of A cannot be
+* represented as a floating-point number. Find the
+* maximum offdiagonal absolute value
+* max( |Re(A(I,J))|, |Im(A(I,J)| ). If this entry is
+* not +/- Infinity, use this value as TSCAL.
+ TMAX = ZERO
+ IF( UPPER ) THEN
+*
+* A is upper triangular.
+*
+ DO J = 2, N
+ DO I = 1, J - 1
+ TMAX = MAX( TMAX, ABS( DBLE( A( I, J ) ) ),
+ $ ABS( DIMAG(A ( I, J ) ) ) )
+ END DO
+ END DO
+ ELSE
+*
+* A is lower triangular.
+*
+ DO J = 1, N - 1
+ DO I = J + 1, N
+ TMAX = MAX( TMAX, ABS( DBLE( A( I, J ) ) ),
+ $ ABS( DIMAG(A ( I, J ) ) ) )
+ END DO
+ 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 of each column without
+* introducing Infinity in the summation.
+ TSCAL = TWO * TSCAL
+ CNORM( J ) = ZERO
+ IF( UPPER ) THEN
+ DO I = 1, J - 1
+ CNORM( J ) = CNORM( J ) +
+ $ TSCAL * CABS2( A( I, J ) )
+ END DO
+ ELSE
+ DO I = J + 1, N
+ CNORM( J ) = CNORM( J ) +
+ $ TSCAL * CABS2( A( I, J ) )
+ END DO
+ END IF
+ TSCAL = TSCAL * HALF
+ 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 ZTRSV( 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