LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsytri_3()

subroutine dsytri_3 ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  E,
integer, dimension( * )  IPIV,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DSYTRI_3

Download DSYTRI_3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DSYTRI_3 computes the inverse of a real symmetric indefinite
 matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK:

     A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

 where U (or L) is unit upper (or lower) triangular matrix,
 U**T (or L**T) is the transpose of U (or L), P is a permutation
 matrix, P**T is the transpose of P, and D is symmetric and block
 diagonal with 1-by-1 and 2-by-2 diagonal blocks.

 DSYTRI_3 sets the leading dimension of the workspace  before calling
 DSYTRI_3X that actually computes the inverse.  This is the blocked
 version of the algorithm, calling Level 3 BLAS.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are
          stored as an upper or lower triangular matrix.
          = '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,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, diagonal of the block diagonal matrix D and
          factors U or L as computed by DSYTRF_RK and DSYTRF_BK:
            a) ONLY diagonal elements of the symmetric block diagonal
               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
               (superdiagonal (or subdiagonal) elements of D
                should be provided on entry in array E), and
            b) If UPLO = 'U': factor U in the superdiagonal part of A.
               If UPLO = 'L': factor L in the subdiagonal part of A.

          On exit, if INFO = 0, the symmetric inverse of the original
          matrix.
             If UPLO = 'U': the upper triangular part of the inverse
             is formed and the part of A below the diagonal is not
             referenced;
             If UPLO = 'L': the lower triangular part of the inverse
             is formed and the part of A above the diagonal is not
             referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]E
          E is DOUBLE PRECISION array, dimension (N)
          On entry, contains the superdiagonal (or subdiagonal)
          elements of the symmetric block diagonal matrix D
          with 1-by-1 or 2-by-2 diagonal blocks, where
          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

          NOTE: For 1-by-1 diagonal block D(k), where
          1 <= k <= N, the element E(k) is not referenced in both
          UPLO = 'U' or UPLO = 'L' cases.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by DSYTRF_RK or DSYTRF_BK.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3).
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK. LWORK >= (N+NB+1)*(NB+3).

          If LDWORK = -1, then a workspace query is assumed;
          the routine only calculates the optimal size of 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) = 0; the matrix is singular and its
               inverse could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2017
Contributors:

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 172 of file dsytri_3.f.

172 *
173 * -- LAPACK computational routine (version 3.8.0) --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 * November 2017
177 *
178 * .. Scalar Arguments ..
179  CHARACTER uplo
180  INTEGER info, lda, lwork, n
181 * ..
182 * .. Array Arguments ..
183  INTEGER ipiv( * )
184  DOUBLE PRECISION a( lda, * ), e( * ), work( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * .. Local Scalars ..
190  LOGICAL upper, lquery
191  INTEGER lwkopt, nb
192 * ..
193 * .. External Functions ..
194  LOGICAL lsame
195  INTEGER ilaenv
196  EXTERNAL lsame, ilaenv
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL dsytri_3x, xerbla
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input parameters.
207 *
208  info = 0
209  upper = lsame( uplo, 'U' )
210  lquery = ( lwork.EQ.-1 )
211 *
212 * Determine the block size
213 *
214  nb = max( 1, ilaenv( 1, 'DSYTRI_3', uplo, n, -1, -1, -1 ) )
215  lwkopt = ( n+nb+1 ) * ( nb+3 )
216 *
217  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
218  info = -1
219  ELSE IF( n.LT.0 ) THEN
220  info = -2
221  ELSE IF( lda.LT.max( 1, n ) ) THEN
222  info = -4
223  ELSE IF ( lwork .LT. lwkopt .AND. .NOT.lquery ) THEN
224  info = -8
225  END IF
226 *
227  IF( info.NE.0 ) THEN
228  CALL xerbla( 'DSYTRI_3', -info )
229  RETURN
230  ELSE IF( lquery ) THEN
231  work( 1 ) = lwkopt
232  RETURN
233  END IF
234 *
235 * Quick return if possible
236 *
237  IF( n.EQ.0 )
238  $ RETURN
239 *
240  CALL dsytri_3x( uplo, n, a, lda, e, ipiv, work, nb, info )
241 *
242  work( 1 ) = lwkopt
243 *
244  RETURN
245 *
246 * End of DSYTRI_3
247 *
subroutine dsytri_3x(UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)
DSYTRI_3X
Definition: dsytri_3x.f:161
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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