LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhetri.f
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00001 *> \brief \b ZHETRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download ZHETRI + dependencies 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZHETRI( 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 *> ZHETRI computes the inverse of a complex Hermitian indefinite matrix
00039 *> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
00040 *> ZHETRF.
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**H;
00052 *>          = 'L':  Lower triangular, form is A = L*D*L**H.
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 ZHETRF.
00066 *>
00067 *>          On exit, if INFO = 0, the (Hermitian) 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 ZHETRF.
00086 *> \endverbatim
00087 *>
00088 *> \param[out] WORK
00089 *> \verbatim
00090 *>          WORK is COMPLEX*16 array, dimension (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 complex16HEcomputational
00113 *
00114 *  =====================================================================
00115       SUBROUTINE ZHETRI( 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       DOUBLE PRECISION   ONE
00135       COMPLEX*16         CONE, ZERO
00136       PARAMETER          ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
00137      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
00138 *     ..
00139 *     .. Local Scalars ..
00140       LOGICAL            UPPER
00141       INTEGER            J, K, KP, KSTEP
00142       DOUBLE PRECISION   AK, AKP1, D, T
00143       COMPLEX*16         AKKP1, TEMP
00144 *     ..
00145 *     .. External Functions ..
00146       LOGICAL            LSAME
00147       COMPLEX*16         ZDOTC
00148       EXTERNAL           LSAME, ZDOTC
00149 *     ..
00150 *     .. External Subroutines ..
00151       EXTERNAL           XERBLA, ZCOPY, ZHEMV, ZSWAP
00152 *     ..
00153 *     .. Intrinsic Functions ..
00154       INTRINSIC          ABS, DBLE, DCONJG, MAX
00155 *     ..
00156 *     .. Executable Statements ..
00157 *
00158 *     Test the input parameters.
00159 *
00160       INFO = 0
00161       UPPER = LSAME( UPLO, 'U' )
00162       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00163          INFO = -1
00164       ELSE IF( N.LT.0 ) THEN
00165          INFO = -2
00166       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00167          INFO = -4
00168       END IF
00169       IF( INFO.NE.0 ) THEN
00170          CALL XERBLA( 'ZHETRI', -INFO )
00171          RETURN
00172       END IF
00173 *
00174 *     Quick return if possible
00175 *
00176       IF( N.EQ.0 )
00177      $   RETURN
00178 *
00179 *     Check that the diagonal matrix D is nonsingular.
00180 *
00181       IF( UPPER ) THEN
00182 *
00183 *        Upper triangular storage: examine D from bottom to top
00184 *
00185          DO 10 INFO = N, 1, -1
00186             IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
00187      $         RETURN
00188    10    CONTINUE
00189       ELSE
00190 *
00191 *        Lower triangular storage: examine D from top to bottom.
00192 *
00193          DO 20 INFO = 1, N
00194             IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
00195      $         RETURN
00196    20    CONTINUE
00197       END IF
00198       INFO = 0
00199 *
00200       IF( UPPER ) THEN
00201 *
00202 *        Compute inv(A) from the factorization A = U*D*U**H.
00203 *
00204 *        K is the main loop index, increasing from 1 to N in steps of
00205 *        1 or 2, depending on the size of the diagonal blocks.
00206 *
00207          K = 1
00208    30    CONTINUE
00209 *
00210 *        If K > N, exit from loop.
00211 *
00212          IF( K.GT.N )
00213      $      GO TO 50
00214 *
00215          IF( IPIV( K ).GT.0 ) THEN
00216 *
00217 *           1 x 1 diagonal block
00218 *
00219 *           Invert the diagonal block.
00220 *
00221             A( K, K ) = ONE / DBLE( A( K, K ) )
00222 *
00223 *           Compute column K of the inverse.
00224 *
00225             IF( K.GT.1 ) THEN
00226                CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
00227                CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
00228      $                     A( 1, K ), 1 )
00229                A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1,
00230      $                     K ), 1 ) )
00231             END IF
00232             KSTEP = 1
00233          ELSE
00234 *
00235 *           2 x 2 diagonal block
00236 *
00237 *           Invert the diagonal block.
00238 *
00239             T = ABS( A( K, K+1 ) )
00240             AK = DBLE( A( K, K ) ) / T
00241             AKP1 = DBLE( A( K+1, K+1 ) ) / T
00242             AKKP1 = A( K, K+1 ) / T
00243             D = T*( AK*AKP1-ONE )
00244             A( K, K ) = AKP1 / D
00245             A( K+1, K+1 ) = AK / D
00246             A( K, K+1 ) = -AKKP1 / D
00247 *
00248 *           Compute columns K and K+1 of the inverse.
00249 *
00250             IF( K.GT.1 ) THEN
00251                CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
00252                CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
00253      $                     A( 1, K ), 1 )
00254                A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1,
00255      $                     K ), 1 ) )
00256                A( K, K+1 ) = A( K, K+1 ) -
00257      $                       ZDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
00258                CALL ZCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
00259                CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
00260      $                     A( 1, K+1 ), 1 )
00261                A( K+1, K+1 ) = A( K+1, K+1 ) -
00262      $                         DBLE( ZDOTC( K-1, WORK, 1, A( 1, K+1 ),
00263      $                         1 ) )
00264             END IF
00265             KSTEP = 2
00266          END IF
00267 *
00268          KP = ABS( IPIV( K ) )
00269          IF( KP.NE.K ) THEN
00270 *
00271 *           Interchange rows and columns K and KP in the leading
00272 *           submatrix A(1:k+1,1:k+1)
00273 *
00274             CALL ZSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
00275             DO 40 J = KP + 1, K - 1
00276                TEMP = DCONJG( A( J, K ) )
00277                A( J, K ) = DCONJG( A( KP, J ) )
00278                A( KP, J ) = TEMP
00279    40       CONTINUE
00280             A( KP, K ) = DCONJG( A( KP, K ) )
00281             TEMP = A( K, K )
00282             A( K, K ) = A( KP, KP )
00283             A( KP, KP ) = TEMP
00284             IF( KSTEP.EQ.2 ) THEN
00285                TEMP = A( K, K+1 )
00286                A( K, K+1 ) = A( KP, K+1 )
00287                A( KP, K+1 ) = TEMP
00288             END IF
00289          END IF
00290 *
00291          K = K + KSTEP
00292          GO TO 30
00293    50    CONTINUE
00294 *
00295       ELSE
00296 *
00297 *        Compute inv(A) from the factorization A = L*D*L**H.
00298 *
00299 *        K is the main loop index, increasing from 1 to N in steps of
00300 *        1 or 2, depending on the size of the diagonal blocks.
00301 *
00302          K = N
00303    60    CONTINUE
00304 *
00305 *        If K < 1, exit from loop.
00306 *
00307          IF( K.LT.1 )
00308      $      GO TO 80
00309 *
00310          IF( IPIV( K ).GT.0 ) THEN
00311 *
00312 *           1 x 1 diagonal block
00313 *
00314 *           Invert the diagonal block.
00315 *
00316             A( K, K ) = ONE / DBLE( A( K, K ) )
00317 *
00318 *           Compute column K of the inverse.
00319 *
00320             IF( K.LT.N ) THEN
00321                CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
00322                CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
00323      $                     1, ZERO, A( K+1, K ), 1 )
00324                A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1,
00325      $                     A( K+1, K ), 1 ) )
00326             END IF
00327             KSTEP = 1
00328          ELSE
00329 *
00330 *           2 x 2 diagonal block
00331 *
00332 *           Invert the diagonal block.
00333 *
00334             T = ABS( A( K, K-1 ) )
00335             AK = DBLE( A( K-1, K-1 ) ) / T
00336             AKP1 = DBLE( A( K, K ) ) / T
00337             AKKP1 = A( K, K-1 ) / T
00338             D = T*( AK*AKP1-ONE )
00339             A( K-1, K-1 ) = AKP1 / D
00340             A( K, K ) = AK / D
00341             A( K, K-1 ) = -AKKP1 / D
00342 *
00343 *           Compute columns K-1 and K of the inverse.
00344 *
00345             IF( K.LT.N ) THEN
00346                CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
00347                CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
00348      $                     1, ZERO, A( K+1, K ), 1 )
00349                A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1,
00350      $                     A( K+1, K ), 1 ) )
00351                A( K, K-1 ) = A( K, K-1 ) -
00352      $                       ZDOTC( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
00353      $                       1 )
00354                CALL ZCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
00355                CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
00356      $                     1, ZERO, A( K+1, K-1 ), 1 )
00357                A( K-1, K-1 ) = A( K-1, K-1 ) -
00358      $                         DBLE( ZDOTC( N-K, WORK, 1, A( K+1, K-1 ),
00359      $                         1 ) )
00360             END IF
00361             KSTEP = 2
00362          END IF
00363 *
00364          KP = ABS( IPIV( K ) )
00365          IF( KP.NE.K ) THEN
00366 *
00367 *           Interchange rows and columns K and KP in the trailing
00368 *           submatrix A(k-1:n,k-1:n)
00369 *
00370             IF( KP.LT.N )
00371      $         CALL ZSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
00372             DO 70 J = K + 1, KP - 1
00373                TEMP = DCONJG( A( J, K ) )
00374                A( J, K ) = DCONJG( A( KP, J ) )
00375                A( KP, J ) = TEMP
00376    70       CONTINUE
00377             A( KP, K ) = DCONJG( A( KP, K ) )
00378             TEMP = A( K, K )
00379             A( K, K ) = A( KP, KP )
00380             A( KP, KP ) = TEMP
00381             IF( KSTEP.EQ.2 ) THEN
00382                TEMP = A( K, K-1 )
00383                A( K, K-1 ) = A( KP, K-1 )
00384                A( KP, K-1 ) = TEMP
00385             END IF
00386          END IF
00387 *
00388          K = K - KSTEP
00389          GO TO 60
00390    80    CONTINUE
00391       END IF
00392 *
00393       RETURN
00394 *
00395 *     End of ZHETRI
00396 *
00397       END
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