LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ssytri_3()

subroutine ssytri_3 ( character  UPLO,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  E,
integer, dimension( * )  IPIV,
real, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

SSYTRI_3

Download SSYTRI_3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SSYTRI_3 computes the inverse of a real symmetric indefinite
 matrix A using the factorization computed by SSYTRF_RK or SSYTRF_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.

 SSYTRI_3 sets the leading dimension of the workspace  before calling
 SSYTRI_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 REAL array, dimension (LDA,N)
          On entry, diagonal of the block diagonal matrix D and
          factors U or L as computed by SSYTRF_RK and SSYTRF_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 REAL 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 SSYTRF_RK or SSYTRF_BK.
[out]WORK
          WORK is REAL 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.
Contributors:
  November 2017,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

Definition at line 168 of file ssytri_3.f.

170 *
171 * -- LAPACK computational routine --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 *
175 * .. Scalar Arguments ..
176  CHARACTER UPLO
177  INTEGER INFO, LDA, LWORK, N
178 * ..
179 * .. Array Arguments ..
180  INTEGER IPIV( * )
181  REAL A( LDA, * ), E( * ), WORK( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * .. Local Scalars ..
187  LOGICAL UPPER, LQUERY
188  INTEGER LWKOPT, NB
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  INTEGER ILAENV
193  EXTERNAL lsame, ilaenv
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL ssytri_3x, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input parameters.
204 *
205  info = 0
206  upper = lsame( uplo, 'U' )
207  lquery = ( lwork.EQ.-1 )
208 *
209 * Determine the block size
210 *
211  nb = max( 1, ilaenv( 1, 'SSYTRI_3', uplo, n, -1, -1, -1 ) )
212  lwkopt = ( n+nb+1 ) * ( nb+3 )
213 *
214  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
215  info = -1
216  ELSE IF( n.LT.0 ) THEN
217  info = -2
218  ELSE IF( lda.LT.max( 1, n ) ) THEN
219  info = -4
220  ELSE IF ( lwork .LT. lwkopt .AND. .NOT.lquery ) THEN
221  info = -8
222  END IF
223 *
224  IF( info.NE.0 ) THEN
225  CALL xerbla( 'SSYTRI_3', -info )
226  RETURN
227  ELSE IF( lquery ) THEN
228  work( 1 ) = lwkopt
229  RETURN
230  END IF
231 *
232 * Quick return if possible
233 *
234  IF( n.EQ.0 )
235  $ RETURN
236 *
237  CALL ssytri_3x( uplo, n, a, lda, e, ipiv, work, nb, info )
238 *
239  work( 1 ) = lwkopt
240 *
241  RETURN
242 *
243 * End of SSYTRI_3
244 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssytri_3x(UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)
SSYTRI_3X
Definition: ssytri_3x.f:159
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