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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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 * 00008 *> \htmlonly 00009 *> Download ZHETRI + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetri.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetri.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetri.f"> 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