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

Download ZSYSV_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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
Here is the call graph for this function:
Here is the caller graph for this function: