version 1.1, 2017/06/17 11:02:55
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version 1.6, 2023/08/07 08:39:29
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* =========== |
* =========== |
* |
* |
* SUBROUTINE ZLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, |
* SUBROUTINE ZLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, |
* H, LDH, WORK, INFO ) |
* H, LDH, WORK ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER UPLO |
* CHARACTER UPLO |
* INTEGER J1, M, NB, LDA, LDH, INFO |
* INTEGER J1, M, NB, LDA, LDH |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
* INTEGER IPIV( * ) |
* INTEGER IPIV( * ) |
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*> WORK is COMPLEX*16 workspace, dimension (M). |
*> WORK is COMPLEX*16 workspace, dimension (M). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization |
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*> has been completed, but the block diagonal matrix D is |
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*> exactly singular, and division by zero will occur if it |
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*> is used to solve a system of equations. |
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*> \endverbatim |
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* |
* |
* Authors: |
* Authors: |
* ======== |
* ======== |
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*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date December 2016 |
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* |
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*> \ingroup complex16HEcomputational |
*> \ingroup complex16HEcomputational |
* |
* |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE ZLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, |
SUBROUTINE ZLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, |
$ H, LDH, WORK, INFO ) |
$ H, LDH, WORK ) |
* |
* |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK computational 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..-- |
* December 2016 |
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* |
* |
IMPLICIT NONE |
IMPLICIT NONE |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
INTEGER M, NB, J1, LDA, LDH, INFO |
INTEGER M, NB, J1, LDA, LDH |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
INTEGER IPIV( * ) |
INTEGER IPIV( * ) |
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PARAMETER ( ZERO = (0.0D+0, 0.0D+0), ONE = (1.0D+0, 0.0D+0) ) |
PARAMETER ( ZERO = (0.0D+0, 0.0D+0), ONE = (1.0D+0, 0.0D+0) ) |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER J, K, K1, I1, I2 |
INTEGER J, K, K1, I1, I2, MJ |
COMPLEX*16 PIV, ALPHA |
COMPLEX*16 PIV, ALPHA |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
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EXTERNAL LSAME, ILAENV, IZAMAX |
EXTERNAL LSAME, ILAENV, IZAMAX |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL XERBLA |
EXTERNAL ZGEMM, ZGEMV, ZAXPY, ZLACGV, ZCOPY, ZSCAL, ZSWAP, |
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$ ZLASET, XERBLA |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC DBLE, DCONJG, MAX |
INTRINSIC DBLE, DCONJG, MAX |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
INFO = 0 |
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J = 1 |
J = 1 |
* |
* |
* K1 is the first column of the panel to be factorized |
* K1 is the first column of the panel to be factorized |
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* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, |
* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, |
* |
* |
K = J1+J-1 |
K = J1+J-1 |
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IF( J.EQ.M ) THEN |
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* |
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* Only need to compute T(J, J) |
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* |
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MJ = 1 |
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ELSE |
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MJ = M-J+1 |
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END IF |
* |
* |
* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J), |
* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J), |
* where H(J:N, J) has been initialized to be A(J, J:N) |
* where H(J:N, J) has been initialized to be A(J, J:N) |
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* first column |
* first column |
* |
* |
CALL ZLACGV( J-K1, A( 1, J ), 1 ) |
CALL ZLACGV( J-K1, A( 1, J ), 1 ) |
CALL ZGEMV( 'No transpose', M-J+1, J-K1, |
CALL ZGEMV( 'No transpose', MJ, J-K1, |
$ -ONE, H( J, K1 ), LDH, |
$ -ONE, H( J, K1 ), LDH, |
$ A( 1, J ), 1, |
$ A( 1, J ), 1, |
$ ONE, H( J, J ), 1 ) |
$ ONE, H( J, J ), 1 ) |
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* |
* |
* Copy H(i:n, i) into WORK |
* Copy H(i:n, i) into WORK |
* |
* |
CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 ) |
CALL ZCOPY( MJ, H( J, J ), 1, WORK( 1 ), 1 ) |
* |
* |
IF( J.GT.K1 ) THEN |
IF( J.GT.K1 ) THEN |
* |
* |
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* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N) |
* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N) |
* |
* |
ALPHA = -DCONJG( A( K-1, J ) ) |
ALPHA = -DCONJG( A( K-1, J ) ) |
CALL ZAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 ) |
CALL ZAXPY( MJ, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 ) |
END IF |
END IF |
* |
* |
* Set A(J, J) = T(J, J) |
* Set A(J, J) = T(J, J) |
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* |
* |
* Swap A(I1, I2+1:N) with A(I2, I2+1:N) |
* Swap A(I1, I2+1:N) with A(I2, I2+1:N) |
* |
* |
CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA, |
IF( I2.LT.M ) |
$ A( J1+I2-1, I2+1 ), LDA ) |
$ CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA, |
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$ A( J1+I2-1, I2+1 ), LDA ) |
* |
* |
* Swap A(I1, I1) with A(I2,I2) |
* Swap A(I1, I1) with A(I2,I2) |
* |
* |
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* Set A(J, J+1) = T(J, J+1) |
* Set A(J, J+1) = T(J, J+1) |
* |
* |
A( K, J+1 ) = WORK( 2 ) |
A( K, J+1 ) = WORK( 2 ) |
IF( (A( K, J ).EQ.ZERO ) .AND. |
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$ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN |
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IF(INFO .EQ. 0) THEN |
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INFO = J |
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END IF |
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END IF |
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* |
* |
IF( J.LT.NB ) THEN |
IF( J.LT.NB ) THEN |
* |
* |
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* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), |
* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), |
* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) |
* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) |
* |
* |
IF( A( K, J+1 ).NE.ZERO ) THEN |
IF( J.LT.(M-1) ) THEN |
ALPHA = ONE / A( K, J+1 ) |
IF( A( K, J+1 ).NE.ZERO ) THEN |
CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA ) |
ALPHA = ONE / A( K, J+1 ) |
CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA ) |
CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA ) |
ELSE |
CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA ) |
CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO, |
ELSE |
$ A( K, J+2 ), LDA) |
CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO, |
END IF |
$ A( K, J+2 ), LDA) |
ELSE |
END IF |
IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN |
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INFO = J |
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END IF |
END IF |
END IF |
END IF |
J = J + 1 |
J = J + 1 |
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* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, |
* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, |
* |
* |
K = J1+J-1 |
K = J1+J-1 |
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IF( J.EQ.M ) THEN |
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* |
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* Only need to compute T(J, J) |
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* |
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MJ = 1 |
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ELSE |
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MJ = M-J+1 |
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END IF |
* |
* |
* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T, |
* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T, |
* where H(J:N, J) has been initialized to be A(J:N, J) |
* where H(J:N, J) has been initialized to be A(J:N, J) |
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* first column |
* first column |
* |
* |
CALL ZLACGV( J-K1, A( J, 1 ), LDA ) |
CALL ZLACGV( J-K1, A( J, 1 ), LDA ) |
CALL ZGEMV( 'No transpose', M-J+1, J-K1, |
CALL ZGEMV( 'No transpose', MJ, J-K1, |
$ -ONE, H( J, K1 ), LDH, |
$ -ONE, H( J, K1 ), LDH, |
$ A( J, 1 ), LDA, |
$ A( J, 1 ), LDA, |
$ ONE, H( J, J ), 1 ) |
$ ONE, H( J, J ), 1 ) |
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* |
* |
* Copy H(J:N, J) into WORK |
* Copy H(J:N, J) into WORK |
* |
* |
CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 ) |
CALL ZCOPY( MJ, H( J, J ), 1, WORK( 1 ), 1 ) |
* |
* |
IF( J.GT.K1 ) THEN |
IF( J.GT.K1 ) THEN |
* |
* |
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* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) |
* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) |
* |
* |
ALPHA = -DCONJG( A( J, K-1 ) ) |
ALPHA = -DCONJG( A( J, K-1 ) ) |
CALL ZAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 ) |
CALL ZAXPY( MJ, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 ) |
END IF |
END IF |
* |
* |
* Set A(J, J) = T(J, J) |
* Set A(J, J) = T(J, J) |
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* |
* |
* Swap A(I2+1:N, I1) with A(I2+1:N, I2) |
* Swap A(I2+1:N, I1) with A(I2+1:N, I2) |
* |
* |
CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1, |
IF( I2.LT.M ) |
$ A( I2+1, J1+I2-1 ), 1 ) |
$ CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1, |
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$ A( I2+1, J1+I2-1 ), 1 ) |
* |
* |
* Swap A(I1, I1) with A(I2, I2) |
* Swap A(I1, I1) with A(I2, I2) |
* |
* |
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* Set A(J+1, J) = T(J+1, J) |
* Set A(J+1, J) = T(J+1, J) |
* |
* |
A( J+1, K ) = WORK( 2 ) |
A( J+1, K ) = WORK( 2 ) |
IF( (A( J, K ).EQ.ZERO) .AND. |
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$ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN |
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IF (INFO .EQ. 0) |
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$ INFO = J |
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END IF |
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* |
* |
IF( J.LT.NB ) THEN |
IF( J.LT.NB ) THEN |
* |
* |
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* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), |
* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), |
* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) |
* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) |
* |
* |
IF( A( J+1, K ).NE.ZERO ) THEN |
IF( J.LT.(M-1) ) THEN |
ALPHA = ONE / A( J+1, K ) |
IF( A( J+1, K ).NE.ZERO ) THEN |
CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 ) |
ALPHA = ONE / A( J+1, K ) |
CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 ) |
CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 ) |
ELSE |
CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 ) |
CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO, |
ELSE |
$ A( J+2, K ), LDA ) |
CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO, |
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$ A( J+2, K ), LDA ) |
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END IF |
END IF |
END IF |
ELSE |
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IF( (A( J, K ).EQ.ZERO) .AND. (J.EQ.M) |
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$ .AND. (INFO.EQ.0) ) INFO = J |
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END IF |
END IF |
J = J + 1 |
J = J + 1 |
GO TO 30 |
GO TO 30 |