LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zsytri.f
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00001 *> \brief \b ZSYTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * )
00029 *       COMPLEX*16         A( LDA, * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> ZSYTRI computes the inverse of a complex symmetric indefinite matrix
00039 *> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
00040 *> ZSYTRF.
00041 *> \endverbatim
00042 *
00043 *  Arguments:
00044 *  ==========
00045 *
00046 *> \param[in] UPLO
00047 *> \verbatim
00048 *>          UPLO is CHARACTER*1
00049 *>          Specifies whether the details of the factorization are stored
00050 *>          as an upper or lower triangular matrix.
00051 *>          = 'U':  Upper triangular, form is A = U*D*U**T;
00052 *>          = 'L':  Lower triangular, form is A = L*D*L**T.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] N
00056 *> \verbatim
00057 *>          N is INTEGER
00058 *>          The order of the matrix A.  N >= 0.
00059 *> \endverbatim
00060 *>
00061 *> \param[in,out] A
00062 *> \verbatim
00063 *>          A is COMPLEX*16 array, dimension (LDA,N)
00064 *>          On entry, the block diagonal matrix D and the multipliers
00065 *>          used to obtain the factor U or L as computed by ZSYTRF.
00066 *>
00067 *>          On exit, if INFO = 0, the (symmetric) inverse of the original
00068 *>          matrix.  If UPLO = 'U', the upper triangular part of the
00069 *>          inverse is formed and the part of A below the diagonal is not
00070 *>          referenced; if UPLO = 'L' the lower triangular part of the
00071 *>          inverse is formed and the part of A above the diagonal is
00072 *>          not referenced.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] LDA
00076 *> \verbatim
00077 *>          LDA is INTEGER
00078 *>          The leading dimension of the array A.  LDA >= max(1,N).
00079 *> \endverbatim
00080 *>
00081 *> \param[in] IPIV
00082 *> \verbatim
00083 *>          IPIV is INTEGER array, dimension (N)
00084 *>          Details of the interchanges and the block structure of D
00085 *>          as determined by ZSYTRF.
00086 *> \endverbatim
00087 *>
00088 *> \param[out] WORK
00089 *> \verbatim
00090 *>          WORK is COMPLEX*16 array, dimension (2*N)
00091 *> \endverbatim
00092 *>
00093 *> \param[out] INFO
00094 *> \verbatim
00095 *>          INFO is INTEGER
00096 *>          = 0: successful exit
00097 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00098 *>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
00099 *>               inverse could not be computed.
00100 *> \endverbatim
00101 *
00102 *  Authors:
00103 *  ========
00104 *
00105 *> \author Univ. of Tennessee 
00106 *> \author Univ. of California Berkeley 
00107 *> \author Univ. of Colorado Denver 
00108 *> \author NAG Ltd. 
00109 *
00110 *> \date November 2011
00111 *
00112 *> \ingroup complex16SYcomputational
00113 *
00114 *  =====================================================================
00115       SUBROUTINE ZSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
00116 *
00117 *  -- LAPACK computational routine (version 3.4.0) --
00118 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00119 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00120 *     November 2011
00121 *
00122 *     .. Scalar Arguments ..
00123       CHARACTER          UPLO
00124       INTEGER            INFO, LDA, N
00125 *     ..
00126 *     .. Array Arguments ..
00127       INTEGER            IPIV( * )
00128       COMPLEX*16         A( LDA, * ), WORK( * )
00129 *     ..
00130 *
00131 *  =====================================================================
00132 *
00133 *     .. Parameters ..
00134       COMPLEX*16         ONE, ZERO
00135       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
00136      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
00137 *     ..
00138 *     .. Local Scalars ..
00139       LOGICAL            UPPER
00140       INTEGER            K, KP, KSTEP
00141       COMPLEX*16         AK, AKKP1, AKP1, D, T, TEMP
00142 *     ..
00143 *     .. External Functions ..
00144       LOGICAL            LSAME
00145       COMPLEX*16         ZDOTU
00146       EXTERNAL           LSAME, ZDOTU
00147 *     ..
00148 *     .. External Subroutines ..
00149       EXTERNAL           XERBLA, ZCOPY, ZSWAP, ZSYMV
00150 *     ..
00151 *     .. Intrinsic Functions ..
00152       INTRINSIC          ABS, MAX
00153 *     ..
00154 *     .. Executable Statements ..
00155 *
00156 *     Test the input parameters.
00157 *
00158       INFO = 0
00159       UPPER = LSAME( UPLO, 'U' )
00160       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00161          INFO = -1
00162       ELSE IF( N.LT.0 ) THEN
00163          INFO = -2
00164       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00165          INFO = -4
00166       END IF
00167       IF( INFO.NE.0 ) THEN
00168          CALL XERBLA( 'ZSYTRI', -INFO )
00169          RETURN
00170       END IF
00171 *
00172 *     Quick return if possible
00173 *
00174       IF( N.EQ.0 )
00175      $   RETURN
00176 *
00177 *     Check that the diagonal matrix D is nonsingular.
00178 *
00179       IF( UPPER ) THEN
00180 *
00181 *        Upper triangular storage: examine D from bottom to top
00182 *
00183          DO 10 INFO = N, 1, -1
00184             IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
00185      $         RETURN
00186    10    CONTINUE
00187       ELSE
00188 *
00189 *        Lower triangular storage: examine D from top to bottom.
00190 *
00191          DO 20 INFO = 1, N
00192             IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
00193      $         RETURN
00194    20    CONTINUE
00195       END IF
00196       INFO = 0
00197 *
00198       IF( UPPER ) THEN
00199 *
00200 *        Compute inv(A) from the factorization A = U*D*U**T.
00201 *
00202 *        K is the main loop index, increasing from 1 to N in steps of
00203 *        1 or 2, depending on the size of the diagonal blocks.
00204 *
00205          K = 1
00206    30    CONTINUE
00207 *
00208 *        If K > N, exit from loop.
00209 *
00210          IF( K.GT.N )
00211      $      GO TO 40
00212 *
00213          IF( IPIV( K ).GT.0 ) THEN
00214 *
00215 *           1 x 1 diagonal block
00216 *
00217 *           Invert the diagonal block.
00218 *
00219             A( K, K ) = ONE / A( K, K )
00220 *
00221 *           Compute column K of the inverse.
00222 *
00223             IF( K.GT.1 ) THEN
00224                CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
00225                CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
00226      $                     A( 1, K ), 1 )
00227                A( K, K ) = A( K, K ) - ZDOTU( K-1, WORK, 1, A( 1, K ),
00228      $                     1 )
00229             END IF
00230             KSTEP = 1
00231          ELSE
00232 *
00233 *           2 x 2 diagonal block
00234 *
00235 *           Invert the diagonal block.
00236 *
00237             T = A( K, K+1 )
00238             AK = A( K, K ) / T
00239             AKP1 = A( K+1, K+1 ) / T
00240             AKKP1 = A( K, K+1 ) / T
00241             D = T*( AK*AKP1-ONE )
00242             A( K, K ) = AKP1 / D
00243             A( K+1, K+1 ) = AK / D
00244             A( K, K+1 ) = -AKKP1 / D
00245 *
00246 *           Compute columns K and K+1 of the inverse.
00247 *
00248             IF( K.GT.1 ) THEN
00249                CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
00250                CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
00251      $                     A( 1, K ), 1 )
00252                A( K, K ) = A( K, K ) - ZDOTU( K-1, WORK, 1, A( 1, K ),
00253      $                     1 )
00254                A( K, K+1 ) = A( K, K+1 ) -
00255      $                       ZDOTU( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
00256                CALL ZCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
00257                CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
00258      $                     A( 1, K+1 ), 1 )
00259                A( K+1, K+1 ) = A( K+1, K+1 ) -
00260      $                         ZDOTU( K-1, WORK, 1, A( 1, K+1 ), 1 )
00261             END IF
00262             KSTEP = 2
00263          END IF
00264 *
00265          KP = ABS( IPIV( K ) )
00266          IF( KP.NE.K ) THEN
00267 *
00268 *           Interchange rows and columns K and KP in the leading
00269 *           submatrix A(1:k+1,1:k+1)
00270 *
00271             CALL ZSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
00272             CALL ZSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
00273             TEMP = A( K, K )
00274             A( K, K ) = A( KP, KP )
00275             A( KP, KP ) = TEMP
00276             IF( KSTEP.EQ.2 ) THEN
00277                TEMP = A( K, K+1 )
00278                A( K, K+1 ) = A( KP, K+1 )
00279                A( KP, K+1 ) = TEMP
00280             END IF
00281          END IF
00282 *
00283          K = K + KSTEP
00284          GO TO 30
00285    40    CONTINUE
00286 *
00287       ELSE
00288 *
00289 *        Compute inv(A) from the factorization A = L*D*L**T.
00290 *
00291 *        K is the main loop index, increasing from 1 to N in steps of
00292 *        1 or 2, depending on the size of the diagonal blocks.
00293 *
00294          K = N
00295    50    CONTINUE
00296 *
00297 *        If K < 1, exit from loop.
00298 *
00299          IF( K.LT.1 )
00300      $      GO TO 60
00301 *
00302          IF( IPIV( K ).GT.0 ) THEN
00303 *
00304 *           1 x 1 diagonal block
00305 *
00306 *           Invert the diagonal block.
00307 *
00308             A( K, K ) = ONE / A( K, K )
00309 *
00310 *           Compute column K of the inverse.
00311 *
00312             IF( K.LT.N ) THEN
00313                CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
00314                CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
00315      $                     ZERO, A( K+1, K ), 1 )
00316                A( K, K ) = A( K, K ) - ZDOTU( N-K, WORK, 1, A( K+1, K ),
00317      $                     1 )
00318             END IF
00319             KSTEP = 1
00320          ELSE
00321 *
00322 *           2 x 2 diagonal block
00323 *
00324 *           Invert the diagonal block.
00325 *
00326             T = A( K, K-1 )
00327             AK = A( K-1, K-1 ) / T
00328             AKP1 = A( K, K ) / T
00329             AKKP1 = A( K, K-1 ) / T
00330             D = T*( AK*AKP1-ONE )
00331             A( K-1, K-1 ) = AKP1 / D
00332             A( K, K ) = AK / D
00333             A( K, K-1 ) = -AKKP1 / D
00334 *
00335 *           Compute columns K-1 and K of the inverse.
00336 *
00337             IF( K.LT.N ) THEN
00338                CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
00339                CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
00340      $                     ZERO, A( K+1, K ), 1 )
00341                A( K, K ) = A( K, K ) - ZDOTU( N-K, WORK, 1, A( K+1, K ),
00342      $                     1 )
00343                A( K, K-1 ) = A( K, K-1 ) -
00344      $                       ZDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
00345      $                       1 )
00346                CALL ZCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
00347                CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
00348      $                     ZERO, A( K+1, K-1 ), 1 )
00349                A( K-1, K-1 ) = A( K-1, K-1 ) -
00350      $                         ZDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 )
00351             END IF
00352             KSTEP = 2
00353          END IF
00354 *
00355          KP = ABS( IPIV( K ) )
00356          IF( KP.NE.K ) THEN
00357 *
00358 *           Interchange rows and columns K and KP in the trailing
00359 *           submatrix A(k-1:n,k-1:n)
00360 *
00361             IF( KP.LT.N )
00362      $         CALL ZSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
00363             CALL ZSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
00364             TEMP = A( K, K )
00365             A( K, K ) = A( KP, KP )
00366             A( KP, KP ) = TEMP
00367             IF( KSTEP.EQ.2 ) THEN
00368                TEMP = A( K, K-1 )
00369                A( K, K-1 ) = A( KP, K-1 )
00370                A( KP, K-1 ) = TEMP
00371             END IF
00372          END IF
00373 *
00374          K = K - KSTEP
00375          GO TO 50
00376    60    CONTINUE
00377       END IF
00378 *
00379       RETURN
00380 *
00381 *     End of ZSYTRI
00382 *
00383       END
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