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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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