version 1.11, 2012/08/22 09:48:38
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version 1.20, 2023/08/07 08:39:32
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*> \brief \b ZLATRS |
*> \brief \b ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZLATRS + dependencies |
*> Download ZLATRS + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatrs.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatrs.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatrs.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatrs.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatrs.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatrs.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, |
* SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, |
* CNORM, INFO ) |
* CNORM, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER DIAG, NORMIN, TRANS, UPLO |
* CHARACTER DIAG, NORMIN, TRANS, UPLO |
* INTEGER INFO, LDA, N |
* INTEGER INFO, LDA, N |
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* DOUBLE PRECISION CNORM( * ) |
* DOUBLE PRECISION CNORM( * ) |
* COMPLEX*16 A( LDA, * ), X( * ) |
* COMPLEX*16 A( LDA, * ), X( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
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*> \date April 2012 |
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* |
* |
*> \ingroup complex16OTHERauxiliary |
*> \ingroup complex16OTHERauxiliary |
* |
* |
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SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, |
SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, |
$ CNORM, INFO ) |
$ CNORM, INFO ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.1) -- |
* -- LAPACK auxiliary routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* April 2012 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER DIAG, NORMIN, TRANS, UPLO |
CHARACTER DIAG, NORMIN, TRANS, UPLO |
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* |
* |
* Quick return if possible |
* Quick return if possible |
* |
* |
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SCALE = ONE |
IF( N.EQ.0 ) |
IF( N.EQ.0 ) |
$ RETURN |
$ RETURN |
* |
* |
* Determine machine dependent parameters to control overflow. |
* Determine machine dependent parameters to control overflow. |
* |
* |
SMLNUM = DLAMCH( 'Safe minimum' ) |
SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) |
BIGNUM = ONE / SMLNUM |
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CALL DLABAD( SMLNUM, BIGNUM ) |
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SMLNUM = SMLNUM / DLAMCH( 'Precision' ) |
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BIGNUM = ONE / SMLNUM |
BIGNUM = ONE / SMLNUM |
SCALE = ONE |
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* |
* |
IF( LSAME( NORMIN, 'N' ) ) THEN |
IF( LSAME( NORMIN, 'N' ) ) THEN |
* |
* |
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IF( TMAX.LE.BIGNUM*HALF ) THEN |
IF( TMAX.LE.BIGNUM*HALF ) THEN |
TSCAL = ONE |
TSCAL = ONE |
ELSE |
ELSE |
TSCAL = HALF / ( SMLNUM*TMAX ) |
* |
CALL DSCAL( N, TSCAL, CNORM, 1 ) |
* Avoid NaN generation if entries in CNORM exceed the |
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* overflow threshold |
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* |
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IF ( TMAX.LE.DLAMCH('Overflow') ) THEN |
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* Case 1: All entries in CNORM are valid floating-point numbers |
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TSCAL = HALF / ( SMLNUM*TMAX ) |
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CALL DSCAL( N, TSCAL, CNORM, 1 ) |
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ELSE |
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* Case 2: At least one column norm of A cannot be |
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* represented as a floating-point number. Find the |
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* maximum offdiagonal absolute value |
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* max( |Re(A(I,J))|, |Im(A(I,J)| ). If this entry is |
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* not +/- Infinity, use this value as TSCAL. |
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TMAX = ZERO |
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IF( UPPER ) THEN |
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* |
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* A is upper triangular. |
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* |
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DO J = 2, N |
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DO I = 1, J - 1 |
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TMAX = MAX( TMAX, ABS( DBLE( A( I, J ) ) ), |
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$ ABS( DIMAG(A ( I, J ) ) ) ) |
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END DO |
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END DO |
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ELSE |
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* |
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* A is lower triangular. |
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* |
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DO J = 1, N - 1 |
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DO I = J + 1, N |
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TMAX = MAX( TMAX, ABS( DBLE( A( I, J ) ) ), |
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$ ABS( DIMAG(A ( I, J ) ) ) ) |
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END DO |
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END DO |
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END IF |
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* |
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IF( TMAX.LE.DLAMCH('Overflow') ) THEN |
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TSCAL = ONE / ( SMLNUM*TMAX ) |
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DO J = 1, N |
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IF( CNORM( J ).LE.DLAMCH('Overflow') ) THEN |
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CNORM( J ) = CNORM( J )*TSCAL |
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ELSE |
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* Recompute the 1-norm of each column without |
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* introducing Infinity in the summation. |
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TSCAL = TWO * TSCAL |
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CNORM( J ) = ZERO |
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IF( UPPER ) THEN |
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DO I = 1, J - 1 |
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CNORM( J ) = CNORM( J ) + |
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$ TSCAL * CABS2( A( I, J ) ) |
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END DO |
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ELSE |
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DO I = J + 1, N |
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CNORM( J ) = CNORM( J ) + |
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$ TSCAL * CABS2( A( I, J ) ) |
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END DO |
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END IF |
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TSCAL = TSCAL * HALF |
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END IF |
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END DO |
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ELSE |
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* At least one entry of A is not a valid floating-point |
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* entry. Rely on TRSV to propagate Inf and NaN. |
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CALL ZTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 ) |
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RETURN |
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END IF |
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END IF |
END IF |
END IF |
* |
* |
* Compute a bound on the computed solution vector to see if the |
* Compute a bound on the computed solution vector to see if the |