LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zsysv_aa_2stage()

 subroutine zsysv_aa_2stage ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV, integer, dimension( * ) IPIV2, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

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Purpose:
``` ZSYSV_AA_2STAGE 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 2-stage algorithm is used to factor A as
A = U * T * U**H,  if UPLO = 'U', or
A = L * T * L**H,  if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in,out] A ``` 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, L is stored below (or above) the subdiaonal blocks, when UPLO is 'L' (or 'U').``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] TB ``` TB is COMPLEX*16 array, dimension (LTB) On exit, details of the LU factorization of the band matrix.``` [in] LTB ``` 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.``` [out] IPIV ``` 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).``` [out] IPIV2 ``` IPIV 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).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] WORK ` WORK is COMPLEX*16 workspace of size LWORK` [in] LWORK ``` 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.``` [out] INFO ``` 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```
Date
November 2017

Definition at line 186 of file zsysv_aa_2stage.f.

186 *
187 * -- LAPACK computational routine (version 3.8.0) --
188 * -- LAPACK is a software package provided by Univ. of Tennessee, --
189 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190 * November 2017
191 *
192  IMPLICIT NONE
193 *
194 * .. Scalar Arguments ..
195  CHARACTER uplo
196  INTEGER n, nrhs, lda, ldb, ltb, lwork, info
197 * ..
198 * .. Array Arguments ..
199  INTEGER ipiv( * ), ipiv2( * )
200  COMPLEX*16 a( lda, * ), b( ldb, * ), tb( * ), work( * )
201 * ..
202 *
203 * =====================================================================
204 *
205 * .. Local Scalars ..
206  LOGICAL upper, tquery, wquery
207  INTEGER lwkopt
208 * ..
209 * .. External Functions ..
210  LOGICAL lsame
211  EXTERNAL lsame
212 * ..
213 * .. External Subroutines ..
214  EXTERNAL xerbla, zsytrf_aa_2stage,
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC max
219 * ..
220 * .. Executable Statements ..
221 *
222 * Test the input parameters.
223 *
224  info = 0
225  upper = lsame( uplo, 'U' )
226  wquery = ( lwork.EQ.-1 )
227  tquery = ( ltb.EQ.-1 )
228  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
229  info = -1
230  ELSE IF( n.LT.0 ) THEN
231  info = -2
232  ELSE IF( nrhs.LT.0 ) THEN
233  info = -3
234  ELSE IF( lda.LT.max( 1, n ) ) THEN
235  info = -5
236  ELSE IF( ldb.LT.max( 1, n ) ) THEN
237  info = -11
238  END IF
239 *
240  IF( info.EQ.0 ) THEN
241  CALL zsytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
242  \$ ipiv2, work, -1, info )
243  lwkopt = int( work(1) )
244  IF( ltb.LT.int( tb(1) ) .AND. .NOT.tquery ) THEN
245  info = -7
246  ELSE IF( lwork.LT.lwkopt .AND. .NOT.wquery ) THEN
247  info = -13
248  END IF
249  END IF
250 *
251  IF( info.NE.0 ) THEN
252  CALL xerbla( 'ZSYSV_AA_2STAGE', -info )
253  RETURN
254  ELSE IF( wquery .OR. tquery ) THEN
255  RETURN
256  END IF
257 *
258 *
259 * Compute the factorization A = U*T*U**H or A = L*T*L**H.
260 *
261  CALL zsytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
262  \$ work, lwork, info )
263  IF( info.EQ.0 ) THEN
264 *
265 * Solve the system A*X = B, overwriting B with X.
266 *
267  CALL zsytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
268  \$ ipiv2, b, ldb, info )
269 *
270  END IF
271 *
272  work( 1 ) = lwkopt
273 *
274 * End of ZSYSV_AA_2STAGE
275 *
subroutine zsytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
ZSYTRF_AA_2STAGE
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zsytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
ZSYTRS_AA_2STAGE
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