 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ csysv_aa_2stage()

 subroutine csysv_aa_2stage ( character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV, integer, dimension( * ) IPIV2, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, integer LWORK, integer INFO )

CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:
CSYSV_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 * T * U,  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 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 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 array, dimension (LTB) On exit, details of the LU factorization of the band matrix. [in] LTB 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. [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 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). [in,out] B B is COMPLEX 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 workspace of size LWORK [in] LWORK 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. [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

Definition at line 183 of file csysv_aa_2stage.f.

186 *
187 * -- LAPACK computational routine --
188 * -- LAPACK is a software package provided by Univ. of Tennessee, --
189 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190 *
191  IMPLICIT NONE
192 *
193 * .. Scalar Arguments ..
194  CHARACTER UPLO
195  INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
196 * ..
197 * .. Array Arguments ..
198  INTEGER IPIV( * ), IPIV2( * )
199  COMPLEX A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
200 * ..
201 *
202 * =====================================================================
203 *
204 * .. Local Scalars ..
205  LOGICAL UPPER, TQUERY, WQUERY
206  INTEGER LWKOPT
207 * ..
208 * .. External Functions ..
209  LOGICAL LSAME
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL csytrf_aa_2stage,
215 * ..
216 * .. Intrinsic Functions ..
217  INTRINSIC max
218 * ..
219 * .. Executable Statements ..
220 *
221 * Test the input parameters.
222 *
223  info = 0
224  upper = lsame( uplo, 'U' )
225  wquery = ( lwork.EQ.-1 )
226  tquery = ( ltb.EQ.-1 )
227  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
228  info = -1
229  ELSE IF( n.LT.0 ) THEN
230  info = -2
231  ELSE IF( nrhs.LT.0 ) THEN
232  info = -3
233  ELSE IF( lda.LT.max( 1, n ) ) THEN
234  info = -5
235  ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
236  info = -7
237  ELSE IF( ldb.LT.max( 1, n ) ) THEN
238  info = -11
239  ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
240  info = -13
241  END IF
242 *
243  IF( info.EQ.0 ) THEN
244  CALL csytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
245  \$ ipiv2, work, -1, info )
246  lwkopt = int( work(1) )
247  END IF
248 *
249  IF( info.NE.0 ) THEN
250  CALL xerbla( 'CSYSV_AA_2STAGE', -info )
251  RETURN
252  ELSE IF( wquery .OR. tquery ) THEN
253  RETURN
254  END IF
255 *
256 *
257 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
258 *
259  CALL csytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
260  \$ work, lwork, info )
261  IF( info.EQ.0 ) THEN
262 *
263 * Solve the system A*X = B, overwriting B with X.
264 *
265  CALL csytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
266  \$ ipiv2, b, ldb, info )
267 *
268  END IF
269 *
270  work( 1 ) = lwkopt
271 *
272  RETURN
273 *
274 * End of CSYSV_AA_2STAGE
275 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine csytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
CSYTRF_AA_2STAGE
subroutine csytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
CSYTRS_AA_2STAGE
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