LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zsptri.f
Go to the documentation of this file.
00001 *> \brief \b ZSPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZSPTRI + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptri.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * )
00029 *       COMPLEX*16         AP( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
00039 *> A in packed storage using the factorization A = U*D*U**T or
00040 *> A = L*D*L**T computed by ZSPTRF.
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] AP
00062 *> \verbatim
00063 *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
00064 *>          On entry, the block diagonal matrix D and the multipliers
00065 *>          used to obtain the factor U or L as computed by ZSPTRF,
00066 *>          stored as a packed triangular matrix.
00067 *>
00068 *>          On exit, if INFO = 0, the (symmetric) inverse of the original
00069 *>          matrix, stored as a packed triangular matrix. The j-th column
00070 *>          of inv(A) is stored in the array AP as follows:
00071 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
00072 *>          if UPLO = 'L',
00073 *>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] IPIV
00077 *> \verbatim
00078 *>          IPIV is INTEGER array, dimension (N)
00079 *>          Details of the interchanges and the block structure of D
00080 *>          as determined by ZSPTRF.
00081 *> \endverbatim
00082 *>
00083 *> \param[out] WORK
00084 *> \verbatim
00085 *>          WORK is COMPLEX*16 array, dimension (N)
00086 *> \endverbatim
00087 *>
00088 *> \param[out] INFO
00089 *> \verbatim
00090 *>          INFO is INTEGER
00091 *>          = 0: successful exit
00092 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00093 *>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
00094 *>               inverse could not be computed.
00095 *> \endverbatim
00096 *
00097 *  Authors:
00098 *  ========
00099 *
00100 *> \author Univ. of Tennessee 
00101 *> \author Univ. of California Berkeley 
00102 *> \author Univ. of Colorado Denver 
00103 *> \author NAG Ltd. 
00104 *
00105 *> \date November 2011
00106 *
00107 *> \ingroup complex16OTHERcomputational
00108 *
00109 *  =====================================================================
00110       SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
00111 *
00112 *  -- LAPACK computational routine (version 3.4.0) --
00113 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00114 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00115 *     November 2011
00116 *
00117 *     .. Scalar Arguments ..
00118       CHARACTER          UPLO
00119       INTEGER            INFO, N
00120 *     ..
00121 *     .. Array Arguments ..
00122       INTEGER            IPIV( * )
00123       COMPLEX*16         AP( * ), WORK( * )
00124 *     ..
00125 *
00126 *  =====================================================================
00127 *
00128 *     .. Parameters ..
00129       COMPLEX*16         ONE, ZERO
00130       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
00131      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
00132 *     ..
00133 *     .. Local Scalars ..
00134       LOGICAL            UPPER
00135       INTEGER            J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
00136       COMPLEX*16         AK, AKKP1, AKP1, D, T, TEMP
00137 *     ..
00138 *     .. External Functions ..
00139       LOGICAL            LSAME
00140       COMPLEX*16         ZDOTU
00141       EXTERNAL           LSAME, ZDOTU
00142 *     ..
00143 *     .. External Subroutines ..
00144       EXTERNAL           XERBLA, ZCOPY, ZSPMV, ZSWAP
00145 *     ..
00146 *     .. Intrinsic Functions ..
00147       INTRINSIC          ABS
00148 *     ..
00149 *     .. Executable Statements ..
00150 *
00151 *     Test the input parameters.
00152 *
00153       INFO = 0
00154       UPPER = LSAME( UPLO, 'U' )
00155       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00156          INFO = -1
00157       ELSE IF( N.LT.0 ) THEN
00158          INFO = -2
00159       END IF
00160       IF( INFO.NE.0 ) THEN
00161          CALL XERBLA( 'ZSPTRI', -INFO )
00162          RETURN
00163       END IF
00164 *
00165 *     Quick return if possible
00166 *
00167       IF( N.EQ.0 )
00168      $   RETURN
00169 *
00170 *     Check that the diagonal matrix D is nonsingular.
00171 *
00172       IF( UPPER ) THEN
00173 *
00174 *        Upper triangular storage: examine D from bottom to top
00175 *
00176          KP = N*( N+1 ) / 2
00177          DO 10 INFO = N, 1, -1
00178             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00179      $         RETURN
00180             KP = KP - INFO
00181    10    CONTINUE
00182       ELSE
00183 *
00184 *        Lower triangular storage: examine D from top to bottom.
00185 *
00186          KP = 1
00187          DO 20 INFO = 1, N
00188             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00189      $         RETURN
00190             KP = KP + N - INFO + 1
00191    20    CONTINUE
00192       END IF
00193       INFO = 0
00194 *
00195       IF( UPPER ) THEN
00196 *
00197 *        Compute inv(A) from the factorization A = U*D*U**T.
00198 *
00199 *        K is the main loop index, increasing from 1 to N in steps of
00200 *        1 or 2, depending on the size of the diagonal blocks.
00201 *
00202          K = 1
00203          KC = 1
00204    30    CONTINUE
00205 *
00206 *        If K > N, exit from loop.
00207 *
00208          IF( K.GT.N )
00209      $      GO TO 50
00210 *
00211          KCNEXT = KC + K
00212          IF( IPIV( K ).GT.0 ) THEN
00213 *
00214 *           1 x 1 diagonal block
00215 *
00216 *           Invert the diagonal block.
00217 *
00218             AP( KC+K-1 ) = ONE / AP( KC+K-1 )
00219 *
00220 *           Compute column K of the inverse.
00221 *
00222             IF( K.GT.1 ) THEN
00223                CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
00224                CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
00225      $                     1 )
00226                AP( KC+K-1 ) = AP( KC+K-1 ) -
00227      $                        ZDOTU( K-1, WORK, 1, AP( KC ), 1 )
00228             END IF
00229             KSTEP = 1
00230          ELSE
00231 *
00232 *           2 x 2 diagonal block
00233 *
00234 *           Invert the diagonal block.
00235 *
00236             T = AP( KCNEXT+K-1 )
00237             AK = AP( KC+K-1 ) / T
00238             AKP1 = AP( KCNEXT+K ) / T
00239             AKKP1 = AP( KCNEXT+K-1 ) / T
00240             D = T*( AK*AKP1-ONE )
00241             AP( KC+K-1 ) = AKP1 / D
00242             AP( KCNEXT+K ) = AK / D
00243             AP( KCNEXT+K-1 ) = -AKKP1 / D
00244 *
00245 *           Compute columns K and K+1 of the inverse.
00246 *
00247             IF( K.GT.1 ) THEN
00248                CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
00249                CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
00250      $                     1 )
00251                AP( KC+K-1 ) = AP( KC+K-1 ) -
00252      $                        ZDOTU( K-1, WORK, 1, AP( KC ), 1 )
00253                AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
00254      $                            ZDOTU( K-1, AP( KC ), 1, AP( KCNEXT ),
00255      $                            1 )
00256                CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
00257                CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO,
00258      $                     AP( KCNEXT ), 1 )
00259                AP( KCNEXT+K ) = AP( KCNEXT+K ) -
00260      $                          ZDOTU( K-1, WORK, 1, AP( KCNEXT ), 1 )
00261             END IF
00262             KSTEP = 2
00263             KCNEXT = KCNEXT + K + 1
00264          END IF
00265 *
00266          KP = ABS( IPIV( K ) )
00267          IF( KP.NE.K ) THEN
00268 *
00269 *           Interchange rows and columns K and KP in the leading
00270 *           submatrix A(1:k+1,1:k+1)
00271 *
00272             KPC = ( KP-1 )*KP / 2 + 1
00273             CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
00274             KX = KPC + KP - 1
00275             DO 40 J = KP + 1, K - 1
00276                KX = KX + J - 1
00277                TEMP = AP( KC+J-1 )
00278                AP( KC+J-1 ) = AP( KX )
00279                AP( KX ) = TEMP
00280    40       CONTINUE
00281             TEMP = AP( KC+K-1 )
00282             AP( KC+K-1 ) = AP( KPC+KP-1 )
00283             AP( KPC+KP-1 ) = TEMP
00284             IF( KSTEP.EQ.2 ) THEN
00285                TEMP = AP( KC+K+K-1 )
00286                AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
00287                AP( KC+K+KP-1 ) = TEMP
00288             END IF
00289          END IF
00290 *
00291          K = K + KSTEP
00292          KC = KCNEXT
00293          GO TO 30
00294    50    CONTINUE
00295 *
00296       ELSE
00297 *
00298 *        Compute inv(A) from the factorization A = L*D*L**T.
00299 *
00300 *        K is the main loop index, increasing from 1 to N in steps of
00301 *        1 or 2, depending on the size of the diagonal blocks.
00302 *
00303          NPP = N*( N+1 ) / 2
00304          K = N
00305          KC = NPP
00306    60    CONTINUE
00307 *
00308 *        If K < 1, exit from loop.
00309 *
00310          IF( K.LT.1 )
00311      $      GO TO 80
00312 *
00313          KCNEXT = KC - ( N-K+2 )
00314          IF( IPIV( K ).GT.0 ) THEN
00315 *
00316 *           1 x 1 diagonal block
00317 *
00318 *           Invert the diagonal block.
00319 *
00320             AP( KC ) = ONE / AP( KC )
00321 *
00322 *           Compute column K of the inverse.
00323 *
00324             IF( K.LT.N ) THEN
00325                CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00326                CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1,
00327      $                     ZERO, AP( KC+1 ), 1 )
00328                AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ),
00329      $                    1 )
00330             END IF
00331             KSTEP = 1
00332          ELSE
00333 *
00334 *           2 x 2 diagonal block
00335 *
00336 *           Invert the diagonal block.
00337 *
00338             T = AP( KCNEXT+1 )
00339             AK = AP( KCNEXT ) / T
00340             AKP1 = AP( KC ) / T
00341             AKKP1 = AP( KCNEXT+1 ) / T
00342             D = T*( AK*AKP1-ONE )
00343             AP( KCNEXT ) = AKP1 / D
00344             AP( KC ) = AK / D
00345             AP( KCNEXT+1 ) = -AKKP1 / D
00346 *
00347 *           Compute columns K-1 and K of the inverse.
00348 *
00349             IF( K.LT.N ) THEN
00350                CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00351                CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
00352      $                     ZERO, AP( KC+1 ), 1 )
00353                AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ),
00354      $                    1 )
00355                AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
00356      $                          ZDOTU( N-K, AP( KC+1 ), 1,
00357      $                          AP( KCNEXT+2 ), 1 )
00358                CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
00359                CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
00360      $                     ZERO, AP( KCNEXT+2 ), 1 )
00361                AP( KCNEXT ) = AP( KCNEXT ) -
00362      $                        ZDOTU( N-K, WORK, 1, AP( KCNEXT+2 ), 1 )
00363             END IF
00364             KSTEP = 2
00365             KCNEXT = KCNEXT - ( N-K+3 )
00366          END IF
00367 *
00368          KP = ABS( IPIV( K ) )
00369          IF( KP.NE.K ) THEN
00370 *
00371 *           Interchange rows and columns K and KP in the trailing
00372 *           submatrix A(k-1:n,k-1:n)
00373 *
00374             KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
00375             IF( KP.LT.N )
00376      $         CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
00377             KX = KC + KP - K
00378             DO 70 J = K + 1, KP - 1
00379                KX = KX + N - J + 1
00380                TEMP = AP( KC+J-K )
00381                AP( KC+J-K ) = AP( KX )
00382                AP( KX ) = TEMP
00383    70       CONTINUE
00384             TEMP = AP( KC )
00385             AP( KC ) = AP( KPC )
00386             AP( KPC ) = TEMP
00387             IF( KSTEP.EQ.2 ) THEN
00388                TEMP = AP( KC-N+K-1 )
00389                AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
00390                AP( KC-N+KP-1 ) = TEMP
00391             END IF
00392          END IF
00393 *
00394          K = K - KSTEP
00395          KC = KCNEXT
00396          GO TO 60
00397    80    CONTINUE
00398       END IF
00399 *
00400       RETURN
00401 *
00402 *     End of ZSPTRI
00403 *
00404       END
 All Files Functions