--- /dev/null
+*> \brief \b CLASYF_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CLASYF_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clasyf_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clasyf_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clasyf_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AA factorizes a panel of a complex symmetric matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by CSYTRF_AA, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is REAL workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* =====================================================================
+ SUBROUTINE CLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ COMPLEX PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ICAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, ICAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from CSYTRF_AA,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* 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)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL CGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL CCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -A( K-1, J )
+ CALL CAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( K.GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL CAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ICAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL CSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL CSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL CSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL CSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ ENDIF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL CCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* 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)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL CCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL CSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL CLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from CSYTRF_AA,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* 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)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL CGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL CCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -A( J, K-1 )
+ CALL CAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( K.GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL CAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ICAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL CSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL CSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL CSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL CSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL CCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* 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)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL CCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL CSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL CLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of CLASYF_AA
+*
+ END
--- /dev/null
+*> \brief <b> CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CSYSV_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csysv_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csysv_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csysv_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CSYSV computes the solution to a complex system of linear equations
+*> A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**T, if UPLO = 'U', or
+*> A = L * T * L**T, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is symmetric tridiagonal. The factored
+*> form of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**T or A = L*T*L**T as computed by
+*> CSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is REAL array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= MAX(2*N, 3*N-2), and for
+*> the best performance, LWORK >= max(1,N*NB), where NB is
+*> the optimal blocksize for CSYTRF_AA.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYsolve
+*
+* =====================================================================
+ SUBROUTINE CSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL ILAENV, LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, CSYTRF, CSYTRS, CSYTRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ CALL CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
+ LWKOPT_SYTRF = INT( WORK(1) )
+ CALL CSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ -1, INFO )
+ LWKOPT_SYTRS = INT( WORK(1) )
+ LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
+ WORK( 1 ) = LWKOPT
+ IF( LWORK.LT.LWKOPT .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CSYSV_AA ', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*
+ CALL CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL CSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of CSYSV_AA
+*
+ END
--- /dev/null
+*> \brief \b CSYTRF_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CSYTRF_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytrf_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytrf_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytrf_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CSYTRF_AA computes the factorization of a complex symmetric matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a complex symmetric tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >=2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* =====================================================================
+ SUBROUTINE CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ COMPLEX ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'CSYTRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CSYTRF_AA', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* Copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL CCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by CLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL CLASYF_AA( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL CSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* If first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J, J+1 )
+ A( J, J+1 ) = ONE
+ CALL CCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL CSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with CGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL CGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J1-K2, J3 ), 1,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with CGEMM
+*
+ CALL CGEMM( 'Transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( J3-J1+1+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL CCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL CCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by CLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL CLASYF_AA( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL CSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J+1, J )
+ A( J+1, J ) = ONE
+ CALL CCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL CSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with CGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL CGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), 1 )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block in J2-th block column with CGEMM
+*
+ CALL CGEMM( 'No transpose', 'Transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL CCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of CSYTRF_AA
+*
+ END
--- /dev/null
+*> \brief \b CSYTRS_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CSYTRS_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytrs_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytrs_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytrs_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CSYTRS_AA solves a system of linear equations A*X = B with a complex
+*> symmetric matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by CSYTRF_AA.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> Details of factors computed by CSYTRF_AA.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by CSYTRF_AA.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is REAL array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* =====================================================================
+ SUBROUTINE CSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ COMPLEX ONE
+ PARAMETER ( ONE = 1.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER K, KP, LWKOPT
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL CGTSV, CSWAP, CTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CSYTRS_AA', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ LWKOPT = (3*N-2)
+ WORK( 1 ) = LWKOPT
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL CTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL CLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
+ IF( N.GT.1 ) THEN
+ CALL CLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
+ CALL CLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL CGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
+ $ INFO )
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL CTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL CTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
+ CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL CGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL CTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of CSYTRS_AA
+*
+ END
--- /dev/null
+*> \brief \b ZLASYF_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLASYF_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlasyf_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlasyf_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlasyf_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AA factorizes a panel of a complex symmetric matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by ZSYTRF_AA, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is COMPLEX*16 workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* =====================================================================
+ SUBROUTINE ZLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ COMPLEX*16 PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER IZAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, IZAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from ZSYTRF_AA,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* 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)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL ZGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -A( K-1, J )
+ CALL ZAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( K.GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL ZAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IZAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL ZSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL ZSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL ZSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ ENDIF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL ZCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* 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)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from ZSYTRF_AA,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* 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)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL ZGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -A( J, K-1 )
+ CALL ZAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( K.GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL ZAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IZAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL ZSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL ZSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL ZSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL ZCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* 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)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of ZLASYF_AA
+*
+ END
--- /dev/null
+*> \brief <b> ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZSYSV_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsysv_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsysv_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsysv_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZSYSV computes the solution to a complex system of linear equations
+*> A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**T, if UPLO = 'U', or
+*> A = L * T * L**T, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is symmetric tridiagonal. The factored
+*> form of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**T or A = L*T*L**T as computed by
+*> ZSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= MAX(2*N, 3*N-2), and for
+*> the best performance, LWORK >= max(1,N*NB), where NB is
+*> the optimal blocksize for ZSYTRF_AA.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYsolve
+*
+* =====================================================================
+ SUBROUTINE ZSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL ILAENV, LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, ZSYTRF, ZSYTRS, ZSYTRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ CALL ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
+ LWKOPT_SYTRF = INT( WORK(1) )
+ CALL ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ -1, INFO )
+ LWKOPT_SYTRS = INT( WORK(1) )
+ LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
+ WORK( 1 ) = LWKOPT
+ IF( LWORK.LT.LWKOPT .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZSYSV_AA ', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*
+ CALL ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of ZSYSV_AA
+*
+ END
--- /dev/null
+*> \brief \b ZSYTRF_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZSYTRF_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrf_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrf_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZSYTRF_AA computes the factorization of a complex symmetric matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a complex symmetric tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >=2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* =====================================================================
+ SUBROUTINE ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ COMPLEX*16 ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZSYTRF_AA', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* Copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL ZCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by ZLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL ZLASYF_AA( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL ZSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* If first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J, J+1 )
+ A( J, J+1 ) = ONE
+ CALL ZCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL ZSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with ZGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL ZGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J1-K2, J3 ), 1,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with ZGEMM
+*
+ CALL ZGEMM( 'Transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( J3-J1+1+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL ZCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL ZCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by ZLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL ZLASYF_AA( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL ZSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J+1, J )
+ A( J+1, J ) = ONE
+ CALL ZCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL ZSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with ZGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL ZGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), 1 )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block in J2-th block column with ZGEMM
+*
+ CALL ZGEMM( 'No transpose', 'Transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL ZCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of ZSYTRF_AA
+*
+ END
--- /dev/null
+*> \brief \b ZSYTRS_AA
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZSYTRS_AA + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrs_aa.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrs_aa.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrs_aa.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZSYTRS_AA solves a system of linear equations A*X = B with a complex
+*> symmetric matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by ZSYTRF_AA.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> Details of factors computed by ZSYTRF_AA.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by ZSYTRF_AA.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* =====================================================================
+ SUBROUTINE ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ COMPLEX*16 ONE
+ PARAMETER ( ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER K, KP, LWKOPT
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL ZGTSV, ZSWAP, ZTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZSYTRS_AA', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ LWKOPT = (3*N-2)
+ WORK( 1 ) = LWKOPT
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL ZTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL ZLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
+ IF( N.GT.1 ) THEN
+ CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
+ CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL ZGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
+ $ INFO )
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
+ CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL ZGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL ZTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of ZSYTRS_AA
+*
+ END
projects / platform / upstream / lapack.git / commitdiff