LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhptri.f
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00001 *> \brief \b ZHPTRI
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 ZHPTRI + dependencies 
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00011 *> [TGZ]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZHPTRI( 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 *> ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
00039 *> A in packed storage using the factorization A = U*D*U**H or
00040 *> A = L*D*L**H computed by ZHPTRF.
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] 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 ZHPTRF,
00066 *>          stored as a packed triangular matrix.
00067 *>
00068 *>          On exit, if INFO = 0, the (Hermitian) 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 ZHPTRF.
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 ZHPTRI( 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       DOUBLE PRECISION   ONE
00130       COMPLEX*16         CONE, ZERO
00131       PARAMETER          ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
00132      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
00133 *     ..
00134 *     .. Local Scalars ..
00135       LOGICAL            UPPER
00136       INTEGER            J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
00137       DOUBLE PRECISION   AK, AKP1, D, T
00138       COMPLEX*16         AKKP1, TEMP
00139 *     ..
00140 *     .. External Functions ..
00141       LOGICAL            LSAME
00142       COMPLEX*16         ZDOTC
00143       EXTERNAL           LSAME, ZDOTC
00144 *     ..
00145 *     .. External Subroutines ..
00146       EXTERNAL           XERBLA, ZCOPY, ZHPMV, ZSWAP
00147 *     ..
00148 *     .. Intrinsic Functions ..
00149       INTRINSIC          ABS, DBLE, DCONJG
00150 *     ..
00151 *     .. Executable Statements ..
00152 *
00153 *     Test the input parameters.
00154 *
00155       INFO = 0
00156       UPPER = LSAME( UPLO, 'U' )
00157       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00158          INFO = -1
00159       ELSE IF( N.LT.0 ) THEN
00160          INFO = -2
00161       END IF
00162       IF( INFO.NE.0 ) THEN
00163          CALL XERBLA( 'ZHPTRI', -INFO )
00164          RETURN
00165       END IF
00166 *
00167 *     Quick return if possible
00168 *
00169       IF( N.EQ.0 )
00170      $   RETURN
00171 *
00172 *     Check that the diagonal matrix D is nonsingular.
00173 *
00174       IF( UPPER ) THEN
00175 *
00176 *        Upper triangular storage: examine D from bottom to top
00177 *
00178          KP = N*( N+1 ) / 2
00179          DO 10 INFO = N, 1, -1
00180             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00181      $         RETURN
00182             KP = KP - INFO
00183    10    CONTINUE
00184       ELSE
00185 *
00186 *        Lower triangular storage: examine D from top to bottom.
00187 *
00188          KP = 1
00189          DO 20 INFO = 1, N
00190             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00191      $         RETURN
00192             KP = KP + N - INFO + 1
00193    20    CONTINUE
00194       END IF
00195       INFO = 0
00196 *
00197       IF( UPPER ) THEN
00198 *
00199 *        Compute inv(A) from the factorization A = U*D*U**H.
00200 *
00201 *        K is the main loop index, increasing from 1 to N in steps of
00202 *        1 or 2, depending on the size of the diagonal blocks.
00203 *
00204          K = 1
00205          KC = 1
00206    30    CONTINUE
00207 *
00208 *        If K > N, exit from loop.
00209 *
00210          IF( K.GT.N )
00211      $      GO TO 50
00212 *
00213          KCNEXT = KC + K
00214          IF( IPIV( K ).GT.0 ) THEN
00215 *
00216 *           1 x 1 diagonal block
00217 *
00218 *           Invert the diagonal block.
00219 *
00220             AP( KC+K-1 ) = ONE / DBLE( AP( KC+K-1 ) )
00221 *
00222 *           Compute column K of the inverse.
00223 *
00224             IF( K.GT.1 ) THEN
00225                CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
00226                CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
00227      $                     AP( KC ), 1 )
00228                AP( KC+K-1 ) = AP( KC+K-1 ) -
00229      $                        DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
00230             END IF
00231             KSTEP = 1
00232          ELSE
00233 *
00234 *           2 x 2 diagonal block
00235 *
00236 *           Invert the diagonal block.
00237 *
00238             T = ABS( AP( KCNEXT+K-1 ) )
00239             AK = DBLE( AP( KC+K-1 ) ) / T
00240             AKP1 = DBLE( AP( KCNEXT+K ) ) / T
00241             AKKP1 = AP( KCNEXT+K-1 ) / T
00242             D = T*( AK*AKP1-ONE )
00243             AP( KC+K-1 ) = AKP1 / D
00244             AP( KCNEXT+K ) = AK / D
00245             AP( KCNEXT+K-1 ) = -AKKP1 / D
00246 *
00247 *           Compute columns K and K+1 of the inverse.
00248 *
00249             IF( K.GT.1 ) THEN
00250                CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
00251                CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
00252      $                     AP( KC ), 1 )
00253                AP( KC+K-1 ) = AP( KC+K-1 ) -
00254      $                        DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
00255                AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
00256      $                            ZDOTC( K-1, AP( KC ), 1, AP( KCNEXT ),
00257      $                            1 )
00258                CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
00259                CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
00260      $                     AP( KCNEXT ), 1 )
00261                AP( KCNEXT+K ) = AP( KCNEXT+K ) -
00262      $                          DBLE( ZDOTC( K-1, WORK, 1, AP( KCNEXT ),
00263      $                          1 ) )
00264             END IF
00265             KSTEP = 2
00266             KCNEXT = KCNEXT + K + 1
00267          END IF
00268 *
00269          KP = ABS( IPIV( K ) )
00270          IF( KP.NE.K ) THEN
00271 *
00272 *           Interchange rows and columns K and KP in the leading
00273 *           submatrix A(1:k+1,1:k+1)
00274 *
00275             KPC = ( KP-1 )*KP / 2 + 1
00276             CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
00277             KX = KPC + KP - 1
00278             DO 40 J = KP + 1, K - 1
00279                KX = KX + J - 1
00280                TEMP = DCONJG( AP( KC+J-1 ) )
00281                AP( KC+J-1 ) = DCONJG( AP( KX ) )
00282                AP( KX ) = TEMP
00283    40       CONTINUE
00284             AP( KC+KP-1 ) = DCONJG( AP( KC+KP-1 ) )
00285             TEMP = AP( KC+K-1 )
00286             AP( KC+K-1 ) = AP( KPC+KP-1 )
00287             AP( KPC+KP-1 ) = TEMP
00288             IF( KSTEP.EQ.2 ) THEN
00289                TEMP = AP( KC+K+K-1 )
00290                AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
00291                AP( KC+K+KP-1 ) = TEMP
00292             END IF
00293          END IF
00294 *
00295          K = K + KSTEP
00296          KC = KCNEXT
00297          GO TO 30
00298    50    CONTINUE
00299 *
00300       ELSE
00301 *
00302 *        Compute inv(A) from the factorization A = L*D*L**H.
00303 *
00304 *        K is the main loop index, increasing from 1 to N in steps of
00305 *        1 or 2, depending on the size of the diagonal blocks.
00306 *
00307          NPP = N*( N+1 ) / 2
00308          K = N
00309          KC = NPP
00310    60    CONTINUE
00311 *
00312 *        If K < 1, exit from loop.
00313 *
00314          IF( K.LT.1 )
00315      $      GO TO 80
00316 *
00317          KCNEXT = KC - ( N-K+2 )
00318          IF( IPIV( K ).GT.0 ) THEN
00319 *
00320 *           1 x 1 diagonal block
00321 *
00322 *           Invert the diagonal block.
00323 *
00324             AP( KC ) = ONE / DBLE( AP( KC ) )
00325 *
00326 *           Compute column K of the inverse.
00327 *
00328             IF( K.LT.N ) THEN
00329                CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00330                CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1,
00331      $                     ZERO, AP( KC+1 ), 1 )
00332                AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
00333      $                    AP( KC+1 ), 1 ) )
00334             END IF
00335             KSTEP = 1
00336          ELSE
00337 *
00338 *           2 x 2 diagonal block
00339 *
00340 *           Invert the diagonal block.
00341 *
00342             T = ABS( AP( KCNEXT+1 ) )
00343             AK = DBLE( AP( KCNEXT ) ) / T
00344             AKP1 = DBLE( AP( KC ) ) / T
00345             AKKP1 = AP( KCNEXT+1 ) / T
00346             D = T*( AK*AKP1-ONE )
00347             AP( KCNEXT ) = AKP1 / D
00348             AP( KC ) = AK / D
00349             AP( KCNEXT+1 ) = -AKKP1 / D
00350 *
00351 *           Compute columns K-1 and K of the inverse.
00352 *
00353             IF( K.LT.N ) THEN
00354                CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00355                CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
00356      $                     1, ZERO, AP( KC+1 ), 1 )
00357                AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
00358      $                    AP( KC+1 ), 1 ) )
00359                AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
00360      $                          ZDOTC( N-K, AP( KC+1 ), 1,
00361      $                          AP( KCNEXT+2 ), 1 )
00362                CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
00363                CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
00364      $                     1, ZERO, AP( KCNEXT+2 ), 1 )
00365                AP( KCNEXT ) = AP( KCNEXT ) -
00366      $                        DBLE( ZDOTC( N-K, WORK, 1, AP( KCNEXT+2 ),
00367      $                        1 ) )
00368             END IF
00369             KSTEP = 2
00370             KCNEXT = KCNEXT - ( N-K+3 )
00371          END IF
00372 *
00373          KP = ABS( IPIV( K ) )
00374          IF( KP.NE.K ) THEN
00375 *
00376 *           Interchange rows and columns K and KP in the trailing
00377 *           submatrix A(k-1:n,k-1:n)
00378 *
00379             KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
00380             IF( KP.LT.N )
00381      $         CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
00382             KX = KC + KP - K
00383             DO 70 J = K + 1, KP - 1
00384                KX = KX + N - J + 1
00385                TEMP = DCONJG( AP( KC+J-K ) )
00386                AP( KC+J-K ) = DCONJG( AP( KX ) )
00387                AP( KX ) = TEMP
00388    70       CONTINUE
00389             AP( KC+KP-K ) = DCONJG( AP( KC+KP-K ) )
00390             TEMP = AP( KC )
00391             AP( KC ) = AP( KPC )
00392             AP( KPC ) = TEMP
00393             IF( KSTEP.EQ.2 ) THEN
00394                TEMP = AP( KC-N+K-1 )
00395                AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
00396                AP( KC-N+KP-1 ) = TEMP
00397             END IF
00398          END IF
00399 *
00400          K = K - KSTEP
00401          KC = KCNEXT
00402          GO TO 60
00403    80    CONTINUE
00404       END IF
00405 *
00406       RETURN
00407 *
00408 *     End of ZHPTRI
00409 *
00410       END
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