version 1.10, 2011/11/21 22:19:35
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version 1.15, 2014/01/27 09:28:23
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*> \brief \b DLASYF |
*> \brief \b DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. |
* |
* |
* =========== 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 DLASYF + dependencies |
*> Download DLASYF + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) |
* SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER UPLO |
* CHARACTER UPLO |
* INTEGER INFO, KB, LDA, LDW, N, NB |
* INTEGER INFO, KB, LDA, LDW, N, NB |
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* INTEGER IPIV( * ) |
* INTEGER IPIV( * ) |
* DOUBLE PRECISION A( LDA, * ), W( LDW, * ) |
* DOUBLE PRECISION A( LDA, * ), W( LDW, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> \verbatim |
*> \verbatim |
*> IPIV is INTEGER array, dimension (N) |
*> IPIV is INTEGER array, dimension (N) |
*> Details of the interchanges and the block structure of D. |
*> Details of the interchanges and the block structure of D. |
*> If UPLO = 'U', only the last KB elements of IPIV are set; |
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*> if UPLO = 'L', only the first KB elements are set. |
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*> |
*> |
*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
*> If UPLO = 'U': |
*> interchanged and D(k,k) is a 1-by-1 diagonal block. |
*> Only the last KB elements of IPIV are set. |
*> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and |
*> |
*> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) |
*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
*> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = |
*> interchanged and D(k,k) is a 1-by-1 diagonal block. |
*> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were |
*> |
*> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. |
*> If IPIV(k) = IPIV(k-1) < 0, then rows and columns |
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*> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) |
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*> is a 2-by-2 diagonal block. |
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*> |
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*> If UPLO = 'L': |
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*> Only the first KB elements of IPIV are set. |
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*> |
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
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*> interchanged and D(k,k) is a 1-by-1 diagonal block. |
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*> |
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*> If IPIV(k) = IPIV(k+1) < 0, then rows and columns |
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*> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) |
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*> is a 2-by-2 diagonal block. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] W |
*> \param[out] W |
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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. |
* |
* |
*> \date November 2011 |
*> \date November 2013 |
* |
* |
*> \ingroup doubleSYcomputational |
*> \ingroup doubleSYcomputational |
* |
* |
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*> \par Contributors: |
|
* ================== |
|
*> |
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*> \verbatim |
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*> |
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*> November 2013, Igor Kozachenko, |
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*> Computer Science Division, |
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*> University of California, Berkeley |
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*> \endverbatim |
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* |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) |
SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational routine (version 3.5.0) -- |
* -- 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 2011 |
* November 2013 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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ABSAKK = ABS( W( K, KW ) ) |
ABSAKK = ABS( W( K, KW ) ) |
* |
* |
* IMAX is the row-index of the largest off-diagonal element in |
* IMAX is the row-index of the largest off-diagonal element in |
* column K, and COLMAX is its absolute value |
* column K, and COLMAX is its absolute value. |
|
* Determine both COLMAX and IMAX. |
* |
* |
IF( K.GT.1 ) THEN |
IF( K.GT.1 ) THEN |
IMAX = IDAMAX( K-1, W( 1, KW ), 1 ) |
IMAX = IDAMAX( K-1, W( 1, KW ), 1 ) |
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* |
* |
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
* |
* |
* Column K is zero: set INFO and continue |
* Column K is zero or underflow: set INFO and continue |
* |
* |
IF( INFO.EQ.0 ) |
IF( INFO.EQ.0 ) |
$ INFO = K |
$ INFO = K |
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* |
* |
KP = IMAX |
KP = IMAX |
* |
* |
* copy column KW-1 of W to column KW |
* copy column KW-1 of W to column KW of W |
* |
* |
CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 ) |
CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 ) |
ELSE |
ELSE |
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END IF |
END IF |
END IF |
END IF |
* |
* |
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* ============================================================ |
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* |
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* KK is the column of A where pivoting step stopped |
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* |
KK = K - KSTEP + 1 |
KK = K - KSTEP + 1 |
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* |
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* KKW is the column of W which corresponds to column KK of A |
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* |
KKW = NB + KK - N |
KKW = NB + KK - N |
* |
* |
* Updated column KP is already stored in column KKW of W |
* Interchange rows and columns KP and KK. |
|
* Updated column KP is already stored in column KKW of W. |
* |
* |
IF( KP.NE.KK ) THEN |
IF( KP.NE.KK ) THEN |
* |
* |
* Copy non-updated column KK to column KP |
* Copy non-updated column KK to column KP of submatrix A |
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* at step K. No need to copy element into column K |
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* (or K and K-1 for 2-by-2 pivot) of A, since these columns |
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* will be later overwritten. |
* |
* |
A( KP, K ) = A( KK, K ) |
A( KP, KP ) = A( KK, KK ) |
CALL DCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ), |
CALL DCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ), |
$ LDA ) |
$ LDA ) |
CALL DCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 ) |
IF( KP.GT.1 ) |
|
$ CALL DCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 ) |
* |
* |
* Interchange rows KK and KP in last KK columns of A and W |
* Interchange rows KK and KP in last K+1 to N columns of A |
|
* (columns K (or K and K-1 for 2-by-2 pivot) of A will be |
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* later overwritten). Interchange rows KK and KP |
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* in last KKW to NB columns of W. |
* |
* |
CALL DSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA ) |
IF( K.LT.N ) |
|
$ CALL DSWAP( N-K, A( KK, K+1 ), LDA, A( KP, K+1 ), |
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$ LDA ) |
CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ), |
CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ), |
$ LDW ) |
$ LDW ) |
END IF |
END IF |
* |
* |
IF( KSTEP.EQ.1 ) THEN |
IF( KSTEP.EQ.1 ) THEN |
* |
* |
* 1-by-1 pivot block D(k): column KW of W now holds |
* 1-by-1 pivot block D(k): column kw of W now holds |
* |
* |
* W(k) = U(k)*D(k) |
* W(kw) = U(k)*D(k), |
* |
* |
* where U(k) is the k-th column of U |
* where U(k) is the k-th column of U |
* |
* |
* Store U(k) in column k of A |
* Store subdiag. elements of column U(k) |
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* and 1-by-1 block D(k) in column k of A. |
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* NOTE: Diagonal element U(k,k) is a UNIT element |
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* and not stored. |
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* A(k,k) := D(k,k) = W(k,kw) |
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* A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k) |
* |
* |
CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 ) |
CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 ) |
R1 = ONE / A( K, K ) |
R1 = ONE / A( K, K ) |
CALL DSCAL( K-1, R1, A( 1, K ), 1 ) |
CALL DSCAL( K-1, R1, A( 1, K ), 1 ) |
|
* |
ELSE |
ELSE |
* |
* |
* 2-by-2 pivot block D(k): columns KW and KW-1 of W now |
* 2-by-2 pivot block D(k): columns kw and kw-1 of W now hold |
* hold |
|
* |
* |
* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) |
* ( W(kw-1) W(kw) ) = ( U(k-1) U(k) )*D(k) |
* |
* |
* where U(k) and U(k-1) are the k-th and (k-1)-th columns |
* where U(k) and U(k-1) are the k-th and (k-1)-th columns |
* of U |
* of U |
* |
* |
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* Store U(1:k-2,k-1) and U(1:k-2,k) and 2-by-2 |
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* block D(k-1:k,k-1:k) in columns k-1 and k of A. |
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* NOTE: 2-by-2 diagonal block U(k-1:k,k-1:k) is a UNIT |
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* block and not stored. |
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* A(k-1:k,k-1:k) := D(k-1:k,k-1:k) = W(k-1:k,kw-1:kw) |
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* A(1:k-2,k-1:k) := U(1:k-2,k:k-1:k) = |
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* = W(1:k-2,kw-1:kw) * ( D(k-1:k,k-1:k)**(-1) ) |
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* |
IF( K.GT.2 ) THEN |
IF( K.GT.2 ) THEN |
* |
* |
* Store U(k) and U(k-1) in columns k and k-1 of A |
* Compose the columns of the inverse of 2-by-2 pivot |
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* block D in the following way to reduce the number |
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* of FLOPS when we myltiply panel ( W(kw-1) W(kw) ) by |
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* this inverse |
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* |
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* D**(-1) = ( d11 d21 )**(-1) = |
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* ( d21 d22 ) |
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* |
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* = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) = |
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* ( (-d21 ) ( d11 ) ) |
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* |
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* = 1/d21 * 1/((d11/d21)*(d22/d21)-1) * |
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* |
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* * ( ( d22/d21 ) ( -1 ) ) = |
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* ( ( -1 ) ( d11/d21 ) ) |
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* |
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* = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) ( -1 ) ) = |
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* ( ( -1 ) ( D22 ) ) |
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* |
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* = 1/d21 * T * ( ( D11 ) ( -1 ) ) |
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* ( ( -1 ) ( D22 ) ) |
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* |
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* = D21 * ( ( D11 ) ( -1 ) ) |
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* ( ( -1 ) ( D22 ) ) |
* |
* |
D21 = W( K-1, KW ) |
D21 = W( K-1, KW ) |
D11 = W( K, KW ) / D21 |
D11 = W( K, KW ) / D21 |
D22 = W( K-1, KW-1 ) / D21 |
D22 = W( K-1, KW-1 ) / D21 |
T = ONE / ( D11*D22-ONE ) |
T = ONE / ( D11*D22-ONE ) |
D21 = T / D21 |
D21 = T / D21 |
|
* |
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* Update elements in columns A(k-1) and A(k) as |
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* dot products of rows of ( W(kw-1) W(kw) ) and columns |
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* of D**(-1) |
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* |
DO 20 J = 1, K - 2 |
DO 20 J = 1, K - 2 |
A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) ) |
A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) ) |
A( J, K ) = D21*( D22*W( J, KW )-W( J, KW-1 ) ) |
A( J, K ) = D21*( D22*W( J, KW )-W( J, KW-1 ) ) |
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A( K-1, K-1 ) = W( K-1, KW-1 ) |
A( K-1, K-1 ) = W( K-1, KW-1 ) |
A( K-1, K ) = W( K-1, KW ) |
A( K-1, K ) = W( K-1, KW ) |
A( K, K ) = W( K, KW ) |
A( K, K ) = W( K, KW ) |
|
* |
END IF |
END IF |
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* |
END IF |
END IF |
* |
* |
* Store details of the interchanges in IPIV |
* Store details of the interchanges in IPIV |
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50 CONTINUE |
50 CONTINUE |
* |
* |
* Put U12 in standard form by partially undoing the interchanges |
* Put U12 in standard form by partially undoing the interchanges |
* in columns k+1:n |
* in columns k+1:n looping backwards from k+1 to n |
* |
* |
J = K + 1 |
J = K + 1 |
60 CONTINUE |
60 CONTINUE |
JJ = J |
* |
JP = IPIV( J ) |
* Undo the interchanges (if any) of rows JJ and JP at each |
IF( JP.LT.0 ) THEN |
* step J |
JP = -JP |
* |
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* (Here, J is a diagonal index) |
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JJ = J |
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JP = IPIV( J ) |
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IF( JP.LT.0 ) THEN |
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JP = -JP |
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* (Here, J is a diagonal index) |
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J = J + 1 |
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END IF |
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* (NOTE: Here, J is used to determine row length. Length N-J+1 |
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* of the rows to swap back doesn't include diagonal element) |
J = J + 1 |
J = J + 1 |
END IF |
IF( JP.NE.JJ .AND. J.LE.N ) |
J = J + 1 |
$ CALL DSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA ) |
IF( JP.NE.JJ .AND. J.LE.N ) |
IF( J.LT.N ) |
$ CALL DSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA ) |
|
IF( J.LE.N ) |
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$ GO TO 60 |
$ GO TO 60 |
* |
* |
* Set KB to the number of columns factorized |
* Set KB to the number of columns factorized |
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ABSAKK = ABS( W( K, K ) ) |
ABSAKK = ABS( W( K, K ) ) |
* |
* |
* IMAX is the row-index of the largest off-diagonal element in |
* IMAX is the row-index of the largest off-diagonal element in |
* column K, and COLMAX is its absolute value |
* column K, and COLMAX is its absolute value. |
|
* Determine both COLMAX and IMAX. |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 ) |
IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 ) |
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* |
* |
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN |
* |
* |
* Column K is zero: set INFO and continue |
* Column K is zero or underflow: set INFO and continue |
* |
* |
IF( INFO.EQ.0 ) |
IF( INFO.EQ.0 ) |
$ INFO = K |
$ INFO = K |
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* |
* |
KP = IMAX |
KP = IMAX |
* |
* |
* copy column K+1 of W to column K |
* copy column K+1 of W to column K of W |
* |
* |
CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 ) |
CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 ) |
ELSE |
ELSE |
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END IF |
END IF |
END IF |
END IF |
* |
* |
|
* ============================================================ |
|
* |
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* KK is the column of A where pivoting step stopped |
|
* |
KK = K + KSTEP - 1 |
KK = K + KSTEP - 1 |
* |
* |
* Updated column KP is already stored in column KK of W |
* Interchange rows and columns KP and KK. |
|
* Updated column KP is already stored in column KK of W. |
* |
* |
IF( KP.NE.KK ) THEN |
IF( KP.NE.KK ) THEN |
* |
* |
* Copy non-updated column KK to column KP |
* Copy non-updated column KK to column KP of submatrix A |
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* at step K. No need to copy element into column K |
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* (or K and K+1 for 2-by-2 pivot) of A, since these columns |
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* will be later overwritten. |
* |
* |
A( KP, K ) = A( KK, K ) |
A( KP, KP ) = A( KK, KK ) |
CALL DCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA ) |
CALL DCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ), |
CALL DCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 ) |
$ LDA ) |
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IF( KP.LT.N ) |
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$ CALL DCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 ) |
* |
* |
* Interchange rows KK and KP in first KK columns of A and W |
* Interchange rows KK and KP in first K-1 columns of A |
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* (columns K (or K and K+1 for 2-by-2 pivot) of A will be |
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* later overwritten). Interchange rows KK and KP |
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* in first KK columns of W. |
* |
* |
CALL DSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA ) |
IF( K.GT.1 ) |
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$ CALL DSWAP( K-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA ) |
CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW ) |
CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW ) |
END IF |
END IF |
* |
* |
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* |
* |
* 1-by-1 pivot block D(k): column k of W now holds |
* 1-by-1 pivot block D(k): column k of W now holds |
* |
* |
* W(k) = L(k)*D(k) |
* W(k) = L(k)*D(k), |
* |
* |
* where L(k) is the k-th column of L |
* where L(k) is the k-th column of L |
* |
* |
* Store L(k) in column k of A |
* Store subdiag. elements of column L(k) |
|
* and 1-by-1 block D(k) in column k of A. |
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* (NOTE: Diagonal element L(k,k) is a UNIT element |
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* and not stored) |
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* A(k,k) := D(k,k) = W(k,k) |
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* A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k) |
* |
* |
CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 ) |
CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 ) |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
R1 = ONE / A( K, K ) |
R1 = ONE / A( K, K ) |
CALL DSCAL( N-K, R1, A( K+1, K ), 1 ) |
CALL DSCAL( N-K, R1, A( K+1, K ), 1 ) |
END IF |
END IF |
|
* |
ELSE |
ELSE |
* |
* |
* 2-by-2 pivot block D(k): columns k and k+1 of W now hold |
* 2-by-2 pivot block D(k): columns k and k+1 of W now hold |
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* where L(k) and L(k+1) are the k-th and (k+1)-th columns |
* where L(k) and L(k+1) are the k-th and (k+1)-th columns |
* of L |
* of L |
* |
* |
|
* Store L(k+2:N,k) and L(k+2:N,k+1) and 2-by-2 |
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* block D(k:k+1,k:k+1) in columns k and k+1 of A. |
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* (NOTE: 2-by-2 diagonal block L(k:k+1,k:k+1) is a UNIT |
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* block and not stored) |
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* A(k:k+1,k:k+1) := D(k:k+1,k:k+1) = W(k:k+1,k:k+1) |
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* A(k+2:N,k:k+1) := L(k+2:N,k:k+1) = |
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* = W(k+2:N,k:k+1) * ( D(k:k+1,k:k+1)**(-1) ) |
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* |
IF( K.LT.N-1 ) THEN |
IF( K.LT.N-1 ) THEN |
* |
* |
* Store L(k) and L(k+1) in columns k and k+1 of A |
* Compose the columns of the inverse of 2-by-2 pivot |
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* block D in the following way to reduce the number |
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* of FLOPS when we myltiply panel ( W(k) W(k+1) ) by |
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* this inverse |
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* |
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* D**(-1) = ( d11 d21 )**(-1) = |
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* ( d21 d22 ) |
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* |
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* = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) = |
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* ( (-d21 ) ( d11 ) ) |
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* |
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* = 1/d21 * 1/((d11/d21)*(d22/d21)-1) * |
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* |
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* * ( ( d22/d21 ) ( -1 ) ) = |
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* ( ( -1 ) ( d11/d21 ) ) |
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* |
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* = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) ( -1 ) ) = |
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* ( ( -1 ) ( D22 ) ) |
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* |
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* = 1/d21 * T * ( ( D11 ) ( -1 ) ) |
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* ( ( -1 ) ( D22 ) ) |
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* |
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* = D21 * ( ( D11 ) ( -1 ) ) |
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* ( ( -1 ) ( D22 ) ) |
* |
* |
D21 = W( K+1, K ) |
D21 = W( K+1, K ) |
D11 = W( K+1, K+1 ) / D21 |
D11 = W( K+1, K+1 ) / D21 |
D22 = W( K, K ) / D21 |
D22 = W( K, K ) / D21 |
T = ONE / ( D11*D22-ONE ) |
T = ONE / ( D11*D22-ONE ) |
D21 = T / D21 |
D21 = T / D21 |
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* |
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* Update elements in columns A(k) and A(k+1) as |
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* dot products of rows of ( W(k) W(k+1) ) and columns |
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* of D**(-1) |
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* |
DO 80 J = K + 2, N |
DO 80 J = K + 2, N |
A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) ) |
A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) ) |
A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) ) |
A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) ) |
Line 593
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Line 739
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A( K, K ) = W( K, K ) |
A( K, K ) = W( K, K ) |
A( K+1, K ) = W( K+1, K ) |
A( K+1, K ) = W( K+1, K ) |
A( K+1, K+1 ) = W( K+1, K+1 ) |
A( K+1, K+1 ) = W( K+1, K+1 ) |
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* |
END IF |
END IF |
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* |
END IF |
END IF |
* |
* |
* Store details of the interchanges in IPIV |
* Store details of the interchanges in IPIV |
Line 638
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Line 786
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110 CONTINUE |
110 CONTINUE |
* |
* |
* Put L21 in standard form by partially undoing the interchanges |
* Put L21 in standard form by partially undoing the interchanges |
* in columns 1:k-1 |
* of rows in columns 1:k-1 looping backwards from k-1 to 1 |
* |
* |
J = K - 1 |
J = K - 1 |
120 CONTINUE |
120 CONTINUE |
JJ = J |
* |
JP = IPIV( J ) |
* Undo the interchanges (if any) of rows JJ and JP at each |
IF( JP.LT.0 ) THEN |
* step J |
JP = -JP |
* |
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* (Here, J is a diagonal index) |
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JJ = J |
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JP = IPIV( J ) |
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IF( JP.LT.0 ) THEN |
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JP = -JP |
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* (Here, J is a diagonal index) |
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J = J - 1 |
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END IF |
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* (NOTE: Here, J is used to determine row length. Length J |
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* of the rows to swap back doesn't include diagonal element) |
J = J - 1 |
J = J - 1 |
END IF |
IF( JP.NE.JJ .AND. J.GE.1 ) |
J = J - 1 |
$ CALL DSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA ) |
IF( JP.NE.JJ .AND. J.GE.1 ) |
IF( J.GT.1 ) |
$ CALL DSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA ) |
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IF( J.GE.1 ) |
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$ GO TO 120 |
$ GO TO 120 |
* |
* |
* Set KB to the number of columns factorized |
* Set KB to the number of columns factorized |