version 1.19, 2018/05/29 07:18:31
|
version 1.20, 2023/08/07 08:39:32
|
Line 159
|
Line 159
|
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date November 2017 |
|
* |
|
*> \ingroup complex16OTHERauxiliary |
*> \ingroup complex16OTHERauxiliary |
* |
* |
*> \par Further Details: |
*> \par Further Details: |
Line 239
|
Line 237
|
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 3.8.0) -- |
* -- 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..-- |
* November 2017 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER DIAG, NORMIN, TRANS, UPLO |
CHARACTER DIAG, NORMIN, TRANS, UPLO |
Line 277
|
Line 274
|
$ ZDOTU, ZLADIV |
$ ZDOTU, ZLADIV |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DSCAL, XERBLA, ZAXPY, ZDSCAL, ZTRSV, DLABAD |
EXTERNAL DSCAL, XERBLA, ZAXPY, ZDSCAL, ZTRSV |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN |
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN |
Line 321
|
Line 318
|
* |
* |
* Quick return if possible |
* Quick return if possible |
* |
* |
|
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 |
BIGNUM = ONE / SMLNUM |
CALL DLABAD( SMLNUM, BIGNUM ) |
|
SMLNUM = SMLNUM / DLAMCH( 'Precision' ) |
|
BIGNUM = ONE / SMLNUM |
|
SCALE = ONE |
|
* |
* |
IF( LSAME( NORMIN, 'N' ) ) THEN |
IF( LSAME( NORMIN, 'N' ) ) THEN |
* |
* |
Line 363
|
Line 357
|
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 |
|
* 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 |
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 |