LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dsptri.f
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00001 *> \brief \b DSPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DSPTRI + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DSPTRI( 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 *       DOUBLE PRECISION   AP( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DSPTRI computes the inverse of a real 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 DSPTRF.
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 DOUBLE PRECISION 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 DSPTRF,
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 DSPTRF.
00081 *> \endverbatim
00082 *>
00083 *> \param[out] WORK
00084 *> \verbatim
00085 *>          WORK is DOUBLE PRECISION 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 doubleOTHERcomputational
00108 *
00109 *  =====================================================================
00110       SUBROUTINE DSPTRI( 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       DOUBLE PRECISION   AP( * ), WORK( * )
00124 *     ..
00125 *
00126 *  =====================================================================
00127 *
00128 *     .. Parameters ..
00129       DOUBLE PRECISION   ONE, ZERO
00130       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00131 *     ..
00132 *     .. Local Scalars ..
00133       LOGICAL            UPPER
00134       INTEGER            J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
00135       DOUBLE PRECISION   AK, AKKP1, AKP1, D, T, TEMP
00136 *     ..
00137 *     .. External Functions ..
00138       LOGICAL            LSAME
00139       DOUBLE PRECISION   DDOT
00140       EXTERNAL           LSAME, DDOT
00141 *     ..
00142 *     .. External Subroutines ..
00143       EXTERNAL           DCOPY, DSPMV, DSWAP, XERBLA
00144 *     ..
00145 *     .. Intrinsic Functions ..
00146       INTRINSIC          ABS
00147 *     ..
00148 *     .. Executable Statements ..
00149 *
00150 *     Test the input parameters.
00151 *
00152       INFO = 0
00153       UPPER = LSAME( UPLO, 'U' )
00154       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00155          INFO = -1
00156       ELSE IF( N.LT.0 ) THEN
00157          INFO = -2
00158       END IF
00159       IF( INFO.NE.0 ) THEN
00160          CALL XERBLA( 'DSPTRI', -INFO )
00161          RETURN
00162       END IF
00163 *
00164 *     Quick return if possible
00165 *
00166       IF( N.EQ.0 )
00167      $   RETURN
00168 *
00169 *     Check that the diagonal matrix D is nonsingular.
00170 *
00171       IF( UPPER ) THEN
00172 *
00173 *        Upper triangular storage: examine D from bottom to top
00174 *
00175          KP = N*( N+1 ) / 2
00176          DO 10 INFO = N, 1, -1
00177             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00178      $         RETURN
00179             KP = KP - INFO
00180    10    CONTINUE
00181       ELSE
00182 *
00183 *        Lower triangular storage: examine D from top to bottom.
00184 *
00185          KP = 1
00186          DO 20 INFO = 1, N
00187             IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
00188      $         RETURN
00189             KP = KP + N - INFO + 1
00190    20    CONTINUE
00191       END IF
00192       INFO = 0
00193 *
00194       IF( UPPER ) THEN
00195 *
00196 *        Compute inv(A) from the factorization A = U*D*U**T.
00197 *
00198 *        K is the main loop index, increasing from 1 to N in steps of
00199 *        1 or 2, depending on the size of the diagonal blocks.
00200 *
00201          K = 1
00202          KC = 1
00203    30    CONTINUE
00204 *
00205 *        If K > N, exit from loop.
00206 *
00207          IF( K.GT.N )
00208      $      GO TO 50
00209 *
00210          KCNEXT = KC + K
00211          IF( IPIV( K ).GT.0 ) THEN
00212 *
00213 *           1 x 1 diagonal block
00214 *
00215 *           Invert the diagonal block.
00216 *
00217             AP( KC+K-1 ) = ONE / AP( KC+K-1 )
00218 *
00219 *           Compute column K of the inverse.
00220 *
00221             IF( K.GT.1 ) THEN
00222                CALL DCOPY( K-1, AP( KC ), 1, WORK, 1 )
00223                CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
00224      $                     1 )
00225                AP( KC+K-1 ) = AP( KC+K-1 ) -
00226      $                        DDOT( K-1, WORK, 1, AP( KC ), 1 )
00227             END IF
00228             KSTEP = 1
00229          ELSE
00230 *
00231 *           2 x 2 diagonal block
00232 *
00233 *           Invert the diagonal block.
00234 *
00235             T = ABS( AP( KCNEXT+K-1 ) )
00236             AK = AP( KC+K-1 ) / T
00237             AKP1 = AP( KCNEXT+K ) / T
00238             AKKP1 = AP( KCNEXT+K-1 ) / T
00239             D = T*( AK*AKP1-ONE )
00240             AP( KC+K-1 ) = AKP1 / D
00241             AP( KCNEXT+K ) = AK / D
00242             AP( KCNEXT+K-1 ) = -AKKP1 / D
00243 *
00244 *           Compute columns K and K+1 of the inverse.
00245 *
00246             IF( K.GT.1 ) THEN
00247                CALL DCOPY( K-1, AP( KC ), 1, WORK, 1 )
00248                CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
00249      $                     1 )
00250                AP( KC+K-1 ) = AP( KC+K-1 ) -
00251      $                        DDOT( K-1, WORK, 1, AP( KC ), 1 )
00252                AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
00253      $                            DDOT( K-1, AP( KC ), 1, AP( KCNEXT ),
00254      $                            1 )
00255                CALL DCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
00256                CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO,
00257      $                     AP( KCNEXT ), 1 )
00258                AP( KCNEXT+K ) = AP( KCNEXT+K ) -
00259      $                          DDOT( K-1, WORK, 1, AP( KCNEXT ), 1 )
00260             END IF
00261             KSTEP = 2
00262             KCNEXT = KCNEXT + K + 1
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             KPC = ( KP-1 )*KP / 2 + 1
00272             CALL DSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
00273             KX = KPC + KP - 1
00274             DO 40 J = KP + 1, K - 1
00275                KX = KX + J - 1
00276                TEMP = AP( KC+J-1 )
00277                AP( KC+J-1 ) = AP( KX )
00278                AP( KX ) = TEMP
00279    40       CONTINUE
00280             TEMP = AP( KC+K-1 )
00281             AP( KC+K-1 ) = AP( KPC+KP-1 )
00282             AP( KPC+KP-1 ) = TEMP
00283             IF( KSTEP.EQ.2 ) THEN
00284                TEMP = AP( KC+K+K-1 )
00285                AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
00286                AP( KC+K+KP-1 ) = TEMP
00287             END IF
00288          END IF
00289 *
00290          K = K + KSTEP
00291          KC = KCNEXT
00292          GO TO 30
00293    50    CONTINUE
00294 *
00295       ELSE
00296 *
00297 *        Compute inv(A) from the factorization A = L*D*L**T.
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          NPP = N*( N+1 ) / 2
00303          K = N
00304          KC = NPP
00305    60    CONTINUE
00306 *
00307 *        If K < 1, exit from loop.
00308 *
00309          IF( K.LT.1 )
00310      $      GO TO 80
00311 *
00312          KCNEXT = KC - ( N-K+2 )
00313          IF( IPIV( K ).GT.0 ) THEN
00314 *
00315 *           1 x 1 diagonal block
00316 *
00317 *           Invert the diagonal block.
00318 *
00319             AP( KC ) = ONE / AP( KC )
00320 *
00321 *           Compute column K of the inverse.
00322 *
00323             IF( K.LT.N ) THEN
00324                CALL DCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00325                CALL DSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1,
00326      $                     ZERO, AP( KC+1 ), 1 )
00327                AP( KC ) = AP( KC ) - DDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
00328             END IF
00329             KSTEP = 1
00330          ELSE
00331 *
00332 *           2 x 2 diagonal block
00333 *
00334 *           Invert the diagonal block.
00335 *
00336             T = ABS( AP( KCNEXT+1 ) )
00337             AK = AP( KCNEXT ) / T
00338             AKP1 = AP( KC ) / T
00339             AKKP1 = AP( KCNEXT+1 ) / T
00340             D = T*( AK*AKP1-ONE )
00341             AP( KCNEXT ) = AKP1 / D
00342             AP( KC ) = AK / D
00343             AP( KCNEXT+1 ) = -AKKP1 / D
00344 *
00345 *           Compute columns K-1 and K of the inverse.
00346 *
00347             IF( K.LT.N ) THEN
00348                CALL DCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
00349                CALL DSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
00350      $                     ZERO, AP( KC+1 ), 1 )
00351                AP( KC ) = AP( KC ) - DDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
00352                AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
00353      $                          DDOT( N-K, AP( KC+1 ), 1,
00354      $                          AP( KCNEXT+2 ), 1 )
00355                CALL DCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
00356                CALL DSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
00357      $                     ZERO, AP( KCNEXT+2 ), 1 )
00358                AP( KCNEXT ) = AP( KCNEXT ) -
00359      $                        DDOT( N-K, WORK, 1, AP( KCNEXT+2 ), 1 )
00360             END IF
00361             KSTEP = 2
00362             KCNEXT = KCNEXT - ( N-K+3 )
00363          END IF
00364 *
00365          KP = ABS( IPIV( K ) )
00366          IF( KP.NE.K ) THEN
00367 *
00368 *           Interchange rows and columns K and KP in the trailing
00369 *           submatrix A(k-1:n,k-1:n)
00370 *
00371             KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
00372             IF( KP.LT.N )
00373      $         CALL DSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
00374             KX = KC + KP - K
00375             DO 70 J = K + 1, KP - 1
00376                KX = KX + N - J + 1
00377                TEMP = AP( KC+J-K )
00378                AP( KC+J-K ) = AP( KX )
00379                AP( KX ) = TEMP
00380    70       CONTINUE
00381             TEMP = AP( KC )
00382             AP( KC ) = AP( KPC )
00383             AP( KPC ) = TEMP
00384             IF( KSTEP.EQ.2 ) THEN
00385                TEMP = AP( KC-N+K-1 )
00386                AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
00387                AP( KC-N+KP-1 ) = TEMP
00388             END IF
00389          END IF
00390 *
00391          K = K - KSTEP
00392          KC = KCNEXT
00393          GO TO 60
00394    80    CONTINUE
00395       END IF
00396 *
00397       RETURN
00398 *
00399 *     End of DSPTRI
00400 *
00401       END
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