LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ ssysv_aa()

subroutine ssysv_aa ( character  UPLO,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

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

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Purpose:
 SSYSV computes the solution to a real 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 * 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 tridiagonal. The factored
 form of A is then used to solve the system of equations A * X = B.
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 number of linear equations, i.e., 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 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*T*U or A = L*T*L**T as computed by
          SSYTRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[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).
[in,out]B
          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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
          the best performance, LWORK >= MAX(1,N*NB), where NB is
          the optimal blocksize for SSYTRF_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.
[out]INFO
          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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 160 of file ssysv_aa.f.

162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER UPLO
169  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170 * ..
171 * .. Array Arguments ..
172  INTEGER IPIV( * )
173  REAL A( LDA, * ), B( LDB, * ), WORK( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Local Scalars ..
179  LOGICAL LQUERY
180  INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
181 * ..
182 * .. External Functions ..
183  LOGICAL LSAME
184  EXTERNAL lsame
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL xerbla, ssytrs_aa, ssytrf_aa
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC max
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  lquery = ( lwork.EQ.-1 )
198  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
199  info = -1
200  ELSE IF( n.LT.0 ) THEN
201  info = -2
202  ELSE IF( nrhs.LT.0 ) THEN
203  info = -3
204  ELSE IF( lda.LT.max( 1, n ) ) THEN
205  info = -5
206  ELSE IF( ldb.LT.max( 1, n ) ) THEN
207  info = -8
208  ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
209  info = -10
210  END IF
211 *
212  IF( info.EQ.0 ) THEN
213  CALL ssytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
214  lwkopt_sytrf = int( work(1) )
215  CALL ssytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
216  $ -1, info )
217  lwkopt_sytrs = int( work(1) )
218  lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
219  work( 1 ) = lwkopt
220  END IF
221 *
222  IF( info.NE.0 ) THEN
223  CALL xerbla( 'SSYSV_AA', -info )
224  RETURN
225  ELSE IF( lquery ) THEN
226  RETURN
227  END IF
228 *
229 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
230 *
231  CALL ssytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
232  IF( info.EQ.0 ) THEN
233 *
234 * Solve the system A*X = B, overwriting B with X.
235 *
236  CALL ssytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
237  $ lwork, info )
238 *
239  END IF
240 *
241  work( 1 ) = lwkopt
242 *
243  RETURN
244 *
245 * End of SSYSV_AA
246 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_AA
Definition: ssytrf_aa.f:132
subroutine ssytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYTRS_AA
Definition: ssytrs_aa.f:131
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