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|
*> \brief \b ZSYTRF_AA_2STAGE
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZSYTRF_AA_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytrf_aa_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytrf_aa_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytrf_aa_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV,
* IPIV2, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER N, LDA, LTB, LWORK, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * ), IPIV2( * )
* COMPLEX*16 A( LDA, * ), TB( * ), WORK( * )
* ..
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
*> using the Aasen's algorithm. The form of the factorization is
*>
*> A = U**T*T*U 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 band matrix with the
*> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
*> LU factorized with partial pivoting).
*>
*> 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 hermitian 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, L is stored below (or above) the subdiaonal blocks,
*> 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] TB
*> \verbatim
*> TB is COMPLEX*16 array, dimension (LTB)
*> On exit, details of the LU factorization of the band matrix.
*> \endverbatim
*>
*> \param[in] LTB
*> \verbatim
*> LTB is INTEGER
*> The size of the array TB. LTB >= 4*N, internally
*> used to select NB such that LTB >= (3*NB+1)*N.
*>
*> If LTB = -1, then a workspace query is assumed; the
*> routine only calculates the optimal size of LTB,
*> returns this value as the first entry of TB, and
*> no error message related to LTB is issued by XERBLA.
*> \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] IPIV2
*> \verbatim
*> IPIV2 is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of T were interchanged with the
*> row and column IPIV(k).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 workspace of size LWORK
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The size of WORK. LWORK >= N, internally used to select NB
*> such that LWORK >= N*NB.
*>
*> 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, band LU factorization failed on i-th column
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup complex16SYcomputational
*
* =====================================================================
SUBROUTINE ZSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV,
$ IPIV2, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.8.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2017
*
IMPLICIT NONE
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER N, LDA, LTB, LWORK, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), IPIV2( * )
COMPLEX*16 A( LDA, * ), TB( * ), WORK( * )
* ..
*
* =====================================================================
* .. Parameters ..
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
*
* .. Local Scalars ..
LOGICAL UPPER, TQUERY, WQUERY
INTEGER I, J, K, I1, I2, TD
INTEGER LDTB, NB, KB, JB, NT, IINFO
COMPLEX*16 PIV
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZCOPY, ZGBTRF, ZGEMM, ZGETRF,
$ ZLACPY, ZLASET, ZLASWP, ZTRSM, ZSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
WQUERY = ( LWORK.EQ.-1 )
TQUERY = ( LTB.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 ( LTB .LT. 4*N .AND. .NOT.TQUERY ) THEN
INFO = -6
ELSE IF ( LWORK .LT. N .AND. .NOT.WQUERY ) THEN
INFO = -10
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSYTRF_AA_2STAGE', -INFO )
RETURN
END IF
*
* Answer the query
*
NB = ILAENV( 1, 'ZSYTRF_AA_2STAGE', UPLO, N, -1, -1, -1 )
IF( INFO.EQ.0 ) THEN
IF( TQUERY ) THEN
TB( 1 ) = (3*NB+1)*N
END IF
IF( WQUERY ) THEN
WORK( 1 ) = N*NB
END IF
END IF
IF( TQUERY .OR. WQUERY ) THEN
RETURN
END IF
*
* Quick return
*
IF ( N.EQ.0 ) THEN
RETURN
ENDIF
*
* Determine the number of the block size
*
LDTB = LTB/N
IF( LDTB .LT. 3*NB+1 ) THEN
NB = (LDTB-1)/3
END IF
IF( LWORK .LT. NB*N ) THEN
NB = LWORK/N
END IF
*
* Determine the number of the block columns
*
NT = (N+NB-1)/NB
TD = 2*NB
KB = MIN(NB, N)
*
* Initialize vectors/matrices
*
DO J = 1, KB
IPIV( J ) = J
END DO
*
* Save NB
*
TB( 1 ) = NB
*
IF( UPPER ) THEN
*
* .....................................................
* Factorize A as U**T*D*U using the upper triangle of A
* .....................................................
*
DO J = 0, NT-1
*
* Generate Jth column of W and H
*
KB = MIN(NB, N-J*NB)
DO I = 1, J-1
IF( I.EQ.1 ) THEN
* H(I,J) = T(I,I)*U(I,J) + T(I+1,I)*U(I+1,J)
IF( I .EQ. (J-1) ) THEN
JB = NB+KB
ELSE
JB = 2*NB
END IF
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ NB, KB, JB,
$ CONE, TB( TD+1 + (I*NB)*LDTB ), LDTB-1,
$ A( (I-1)*NB+1, J*NB+1 ), LDA,
$ CZERO, WORK( I*NB+1 ), N )
ELSE
* H(I,J) = T(I,I-1)*U(I-1,J) + T(I,I)*U(I,J) + T(I,I+1)*U(I+1,J)
IF( I .EQ. (J-1) ) THEN
JB = 2*NB+KB
ELSE
JB = 3*NB
END IF
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ NB, KB, JB,
$ CONE, TB( TD+NB+1 + ((I-1)*NB)*LDTB ),
$ LDTB-1,
$ A( (I-2)*NB+1, J*NB+1 ), LDA,
$ CZERO, WORK( I*NB+1 ), N )
END IF
END DO
*
* Compute T(J,J)
*
CALL ZLACPY( 'Upper', KB, KB, A( J*NB+1, J*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
IF( J.GT.1 ) THEN
* T(J,J) = U(1:J,J)'*H(1:J)
CALL ZGEMM( 'Transpose', 'NoTranspose',
$ KB, KB, (J-1)*NB,
$ -CONE, A( 1, J*NB+1 ), LDA,
$ WORK( NB+1 ), N,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
* T(J,J) += U(J,J)'*T(J,J-1)*U(J-1,J)
CALL ZGEMM( 'Transpose', 'NoTranspose',
$ KB, NB, KB,
$ CONE, A( (J-1)*NB+1, J*NB+1 ), LDA,
$ TB( TD+NB+1 + ((J-1)*NB)*LDTB ), LDTB-1,
$ CZERO, WORK( 1 ), N )
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ KB, KB, NB,
$ -CONE, WORK( 1 ), N,
$ A( (J-2)*NB+1, J*NB+1 ), LDA,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
* Expand T(J,J) into full format
*
DO I = 1, KB
DO K = I+1, KB
TB( TD+(K-I)+1 + (J*NB+I-1)*LDTB )
$ = TB( TD-(K-(I+1)) + (J*NB+K-1)*LDTB )
END DO
END DO
IF( J.GT.0 ) THEN
c CALL CHEGST( 1, 'Upper', KB,
c $ TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
c $ A( (J-1)*NB+1, J*NB+1 ), LDA, IINFO )
CALL ZTRSM( 'L', 'U', 'T', 'N', KB, KB, CONE,
$ A( (J-1)*NB+1, J*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
CALL ZTRSM( 'R', 'U', 'N', 'N', KB, KB, CONE,
$ A( (J-1)*NB+1, J*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
IF( J.LT.NT-1 ) THEN
IF( J.GT.0 ) THEN
*
* Compute H(J,J)
*
IF( J.EQ.1 ) THEN
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ KB, KB, KB,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
$ A( (J-1)*NB+1, J*NB+1 ), LDA,
$ CZERO, WORK( J*NB+1 ), N )
ELSE
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ KB, KB, NB+KB,
$ CONE, TB( TD+NB+1 + ((J-1)*NB)*LDTB ),
$ LDTB-1,
$ A( (J-2)*NB+1, J*NB+1 ), LDA,
$ CZERO, WORK( J*NB+1 ), N )
END IF
*
* Update with the previous column
*
CALL ZGEMM( 'Transpose', 'NoTranspose',
$ NB, N-(J+1)*NB, J*NB,
$ -CONE, WORK( NB+1 ), N,
$ A( 1, (J+1)*NB+1 ), LDA,
$ CONE, A( J*NB+1, (J+1)*NB+1 ), LDA )
END IF
*
* Copy panel to workspace to call ZGETRF
*
DO K = 1, NB
CALL ZCOPY( N-(J+1)*NB,
$ A( J*NB+K, (J+1)*NB+1 ), LDA,
$ WORK( 1+(K-1)*N ), 1 )
END DO
*
* Factorize panel
*
CALL ZGETRF( N-(J+1)*NB, NB,
$ WORK, N,
$ IPIV( (J+1)*NB+1 ), IINFO )
c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
c INFO = IINFO+(J+1)*NB
c END IF
*
* Copy panel back
*
DO K = 1, NB
CALL ZCOPY( N-(J+1)*NB,
$ WORK( 1+(K-1)*N ), 1,
$ A( J*NB+K, (J+1)*NB+1 ), LDA )
END DO
*
* Compute T(J+1, J), zero out for GEMM update
*
KB = MIN(NB, N-(J+1)*NB)
CALL ZLASET( 'Full', KB, NB, CZERO, CZERO,
$ TB( TD+NB+1 + (J*NB)*LDTB), LDTB-1 )
CALL ZLACPY( 'Upper', KB, NB,
$ WORK, N,
$ TB( TD+NB+1 + (J*NB)*LDTB ), LDTB-1 )
IF( J.GT.0 ) THEN
CALL ZTRSM( 'R', 'U', 'N', 'U', KB, NB, CONE,
$ A( (J-1)*NB+1, J*NB+1 ), LDA,
$ TB( TD+NB+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
* Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM
* updates
*
DO K = 1, NB
DO I = 1, KB
TB( TD-NB+K-I+1 + (J*NB+NB+I-1)*LDTB )
$ = TB( TD+NB+I-K+1 + (J*NB+K-1)*LDTB )
END DO
END DO
CALL ZLASET( 'Lower', KB, NB, CZERO, CONE,
$ A( J*NB+1, (J+1)*NB+1), LDA )
*
* Apply pivots to trailing submatrix of A
*
DO K = 1, KB
* > Adjust ipiv
IPIV( (J+1)*NB+K ) = IPIV( (J+1)*NB+K ) + (J+1)*NB
*
I1 = (J+1)*NB+K
I2 = IPIV( (J+1)*NB+K )
IF( I1.NE.I2 ) THEN
* > Apply pivots to previous columns of L
CALL ZSWAP( K-1, A( (J+1)*NB+1, I1 ), 1,
$ A( (J+1)*NB+1, I2 ), 1 )
* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
IF( I2.GT.(I1+1) )
$ CALL ZSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
$ A( I1+1, I2 ), 1 )
* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
IF( I2.LT.N )
$ CALL ZSWAP( N-I2, A( I1, I2+1 ), LDA,
$ A( I2, I2+1 ), LDA )
* > Swap A(I1, I1) with A(I2, I2)
PIV = A( I1, I1 )
A( I1, I1 ) = A( I2, I2 )
A( I2, I2 ) = PIV
* > Apply pivots to previous columns of L
IF( J.GT.0 ) THEN
CALL ZSWAP( J*NB, A( 1, I1 ), 1,
$ A( 1, I2 ), 1 )
END IF
ENDIF
END DO
END IF
END DO
ELSE
*
* .....................................................
* Factorize A as L*D*L**T using the lower triangle of A
* .....................................................
*
DO J = 0, NT-1
*
* Generate Jth column of W and H
*
KB = MIN(NB, N-J*NB)
DO I = 1, J-1
IF( I.EQ.1 ) THEN
* H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)'
IF( I .EQ. (J-1) ) THEN
JB = NB+KB
ELSE
JB = 2*NB
END IF
CALL ZGEMM( 'NoTranspose', 'Transpose',
$ NB, KB, JB,
$ CONE, TB( TD+1 + (I*NB)*LDTB ), LDTB-1,
$ A( J*NB+1, (I-1)*NB+1 ), LDA,
$ CZERO, WORK( I*NB+1 ), N )
ELSE
* H(I,J) = T(I,I-1)*L(J,I-1)' + T(I,I)*L(J,I)' + T(I,I+1)*L(J,I+1)'
IF( I .EQ. (J-1) ) THEN
JB = 2*NB+KB
ELSE
JB = 3*NB
END IF
CALL ZGEMM( 'NoTranspose', 'Transpose',
$ NB, KB, JB,
$ CONE, TB( TD+NB+1 + ((I-1)*NB)*LDTB ),
$ LDTB-1,
$ A( J*NB+1, (I-2)*NB+1 ), LDA,
$ CZERO, WORK( I*NB+1 ), N )
END IF
END DO
*
* Compute T(J,J)
*
CALL ZLACPY( 'Lower', KB, KB, A( J*NB+1, J*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
IF( J.GT.1 ) THEN
* T(J,J) = L(J,1:J)*H(1:J)
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ KB, KB, (J-1)*NB,
$ -CONE, A( J*NB+1, 1 ), LDA,
$ WORK( NB+1 ), N,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
* T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)'
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ KB, NB, KB,
$ CONE, A( J*NB+1, (J-1)*NB+1 ), LDA,
$ TB( TD+NB+1 + ((J-1)*NB)*LDTB ), LDTB-1,
$ CZERO, WORK( 1 ), N )
CALL ZGEMM( 'NoTranspose', 'Transpose',
$ KB, KB, NB,
$ -CONE, WORK( 1 ), N,
$ A( J*NB+1, (J-2)*NB+1 ), LDA,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
* Expand T(J,J) into full format
*
DO I = 1, KB
DO K = I+1, KB
TB( TD-(K-(I+1)) + (J*NB+K-1)*LDTB )
$ = TB( TD+(K-I)+1 + (J*NB+I-1)*LDTB )
END DO
END DO
IF( J.GT.0 ) THEN
c CALL CHEGST( 1, 'Lower', KB,
c $ TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
c $ A( J*NB+1, (J-1)*NB+1 ), LDA, IINFO )
CALL ZTRSM( 'L', 'L', 'N', 'N', KB, KB, CONE,
$ A( J*NB+1, (J-1)*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
CALL ZTRSM( 'R', 'L', 'T', 'N', KB, KB, CONE,
$ A( J*NB+1, (J-1)*NB+1 ), LDA,
$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
* Symmetrize T(J,J)
*
DO I = 1, KB
DO K = I+1, KB
TB( TD-(K-(I+1)) + (J*NB+K-1)*LDTB )
$ = TB( TD+(K-I)+1 + (J*NB+I-1)*LDTB )
END DO
END DO
*
IF( J.LT.NT-1 ) THEN
IF( J.GT.0 ) THEN
*
* Compute H(J,J)
*
IF( J.EQ.1 ) THEN
CALL ZGEMM( 'NoTranspose', 'Transpose',
$ KB, KB, KB,
$ CONE, TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
$ A( J*NB+1, (J-1)*NB+1 ), LDA,
$ CZERO, WORK( J*NB+1 ), N )
ELSE
CALL ZGEMM( 'NoTranspose', 'Transpose',
$ KB, KB, NB+KB,
$ CONE, TB( TD+NB+1 + ((J-1)*NB)*LDTB ),
$ LDTB-1,
$ A( J*NB+1, (J-2)*NB+1 ), LDA,
$ CZERO, WORK( J*NB+1 ), N )
END IF
*
* Update with the previous column
*
CALL ZGEMM( 'NoTranspose', 'NoTranspose',
$ N-(J+1)*NB, NB, J*NB,
$ -CONE, A( (J+1)*NB+1, 1 ), LDA,
$ WORK( NB+1 ), N,
$ CONE, A( (J+1)*NB+1, J*NB+1 ), LDA )
END IF
*
* Factorize panel
*
CALL ZGETRF( N-(J+1)*NB, NB,
$ A( (J+1)*NB+1, J*NB+1 ), LDA,
$ IPIV( (J+1)*NB+1 ), IINFO )
c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
c INFO = IINFO+(J+1)*NB
c END IF
*
* Compute T(J+1, J), zero out for GEMM update
*
KB = MIN(NB, N-(J+1)*NB)
CALL ZLASET( 'Full', KB, NB, CZERO, CZERO,
$ TB( TD+NB+1 + (J*NB)*LDTB), LDTB-1 )
CALL ZLACPY( 'Upper', KB, NB,
$ A( (J+1)*NB+1, J*NB+1 ), LDA,
$ TB( TD+NB+1 + (J*NB)*LDTB ), LDTB-1 )
IF( J.GT.0 ) THEN
CALL ZTRSM( 'R', 'L', 'T', 'U', KB, NB, CONE,
$ A( J*NB+1, (J-1)*NB+1 ), LDA,
$ TB( TD+NB+1 + (J*NB)*LDTB ), LDTB-1 )
END IF
*
* Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM
* updates
*
DO K = 1, NB
DO I = 1, KB
TB( TD-NB+K-I+1 + (J*NB+NB+I-1)*LDTB ) =
$ TB( TD+NB+I-K+1 + (J*NB+K-1)*LDTB )
END DO
END DO
CALL ZLASET( 'Upper', KB, NB, CZERO, CONE,
$ A( (J+1)*NB+1, J*NB+1 ), LDA )
*
* Apply pivots to trailing submatrix of A
*
DO K = 1, KB
* > Adjust ipiv
IPIV( (J+1)*NB+K ) = IPIV( (J+1)*NB+K ) + (J+1)*NB
*
I1 = (J+1)*NB+K
I2 = IPIV( (J+1)*NB+K )
IF( I1.NE.I2 ) THEN
* > Apply pivots to previous columns of L
CALL ZSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA,
$ A( I2, (J+1)*NB+1 ), LDA )
* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
IF( I2.GT.(I1+1) )
$ CALL ZSWAP( I2-I1-1, A( I1+1, I1 ), 1,
$ A( I2, I1+1 ), LDA )
* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
IF( I2.LT.N )
$ CALL ZSWAP( N-I2, A( I2+1, I1 ), 1,
$ A( I2+1, I2 ), 1 )
* > Swap A(I1, I1) with A(I2, I2)
PIV = A( I1, I1 )
A( I1, I1 ) = A( I2, I2 )
A( I2, I2 ) = PIV
* > Apply pivots to previous columns of L
IF( J.GT.0 ) THEN
CALL ZSWAP( J*NB, A( I1, 1 ), LDA,
$ A( I2, 1 ), LDA )
END IF
ENDIF
END DO
*
* Apply pivots to previous columns of L
*
c CALL ZLASWP( J*NB, A( 1, 1 ), LDA,
c $ (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 )
END IF
END DO
END IF
*
* Factor the band matrix
CALL ZGBTRF( N, N, NB, NB, TB, LDTB, IPIV2, INFO )
*
RETURN
*
* End of ZSYTRF_AA_2STAGE
*
END
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