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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CHPTRI 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CHPTRI + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chptri.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chptri.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chptri.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHPTRI( 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 AP( * ), WORK( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CHPTRI 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 CHPTRF. 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 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 CHPTRF, 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 CHPTRF. 00081 *> \endverbatim 00082 *> 00083 *> \param[out] WORK 00084 *> \verbatim 00085 *> WORK is COMPLEX 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 complexOTHERcomputational 00108 * 00109 * ===================================================================== 00110 SUBROUTINE CHPTRI( 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 AP( * ), WORK( * ) 00124 * .. 00125 * 00126 * ===================================================================== 00127 * 00128 * .. Parameters .. 00129 REAL ONE 00130 COMPLEX CONE, ZERO 00131 PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ), 00132 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 00133 * .. 00134 * .. Local Scalars .. 00135 LOGICAL UPPER 00136 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 00137 REAL AK, AKP1, D, T 00138 COMPLEX AKKP1, TEMP 00139 * .. 00140 * .. External Functions .. 00141 LOGICAL LSAME 00142 COMPLEX CDOTC 00143 EXTERNAL LSAME, CDOTC 00144 * .. 00145 * .. External Subroutines .. 00146 EXTERNAL CCOPY, CHPMV, CSWAP, XERBLA 00147 * .. 00148 * .. Intrinsic Functions .. 00149 INTRINSIC ABS, CONJG, REAL 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( 'CHPTRI', -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 / REAL( AP( KC+K-1 ) ) 00221 * 00222 * Compute column K of the inverse. 00223 * 00224 IF( K.GT.1 ) THEN 00225 CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00226 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00227 $ AP( KC ), 1 ) 00228 AP( KC+K-1 ) = AP( KC+K-1 ) - 00229 $ REAL( CDOTC( 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 = REAL( AP( KC+K-1 ) ) / T 00240 AKP1 = REAL( 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 CCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00251 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00252 $ AP( KC ), 1 ) 00253 AP( KC+K-1 ) = AP( KC+K-1 ) - 00254 $ REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) 00255 AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 00256 $ CDOTC( K-1, AP( KC ), 1, AP( KCNEXT ), 00257 $ 1 ) 00258 CALL CCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 00259 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00260 $ AP( KCNEXT ), 1 ) 00261 AP( KCNEXT+K ) = AP( KCNEXT+K ) - 00262 $ REAL( CDOTC( K-1, WORK, 1, AP( KCNEXT ), $ 1 ) ) 00263 END IF 00264 KSTEP = 2 00265 KCNEXT = KCNEXT + K + 1 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 KPC = ( KP-1 )*KP / 2 + 1 00275 CALL CSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 00276 KX = KPC + KP - 1 00277 DO 40 J = KP + 1, K - 1 00278 KX = KX + J - 1 00279 TEMP = CONJG( AP( KC+J-1 ) ) 00280 AP( KC+J-1 ) = CONJG( AP( KX ) ) 00281 AP( KX ) = TEMP 00282 40 CONTINUE 00283 AP( KC+KP-1 ) = CONJG( AP( KC+KP-1 ) ) 00284 TEMP = AP( KC+K-1 ) 00285 AP( KC+K-1 ) = AP( KPC+KP-1 ) 00286 AP( KPC+KP-1 ) = TEMP 00287 IF( KSTEP.EQ.2 ) THEN 00288 TEMP = AP( KC+K+K-1 ) 00289 AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 00290 AP( KC+K+KP-1 ) = TEMP 00291 END IF 00292 END IF 00293 * 00294 K = K + KSTEP 00295 KC = KCNEXT 00296 GO TO 30 00297 50 CONTINUE 00298 * 00299 ELSE 00300 * 00301 * Compute inv(A) from the factorization A = L*D*L**H. 00302 * 00303 * K is the main loop index, increasing from 1 to N in steps of 00304 * 1 or 2, depending on the size of the diagonal blocks. 00305 * 00306 NPP = N*( N+1 ) / 2 00307 K = N 00308 KC = NPP 00309 60 CONTINUE 00310 * 00311 * If K < 1, exit from loop. 00312 * 00313 IF( K.LT.1 ) 00314 $ GO TO 80 00315 * 00316 KCNEXT = KC - ( N-K+2 ) 00317 IF( IPIV( K ).GT.0 ) THEN 00318 * 00319 * 1 x 1 diagonal block 00320 * 00321 * Invert the diagonal block. 00322 * 00323 AP( KC ) = ONE / REAL( AP( KC ) ) 00324 * 00325 * Compute column K of the inverse. 00326 * 00327 IF( K.LT.N ) THEN 00328 CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00329 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1, 00330 $ ZERO, AP( KC+1 ), 1 ) 00331 AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) 00332 END IF 00333 KSTEP = 1 00334 ELSE 00335 * 00336 * 2 x 2 diagonal block 00337 * 00338 * Invert the diagonal block. 00339 * 00340 T = ABS( AP( KCNEXT+1 ) ) 00341 AK = REAL( AP( KCNEXT ) ) / T 00342 AKP1 = REAL( AP( KC ) ) / T 00343 AKKP1 = AP( KCNEXT+1 ) / T 00344 D = T*( AK*AKP1-ONE ) 00345 AP( KCNEXT ) = AKP1 / D 00346 AP( KC ) = AK / D 00347 AP( KCNEXT+1 ) = -AKKP1 / D 00348 * 00349 * Compute columns K-1 and K of the inverse. 00350 * 00351 IF( K.LT.N ) THEN 00352 CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00353 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00354 $ 1, ZERO, AP( KC+1 ), 1 ) 00355 AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) 00356 AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 00357 $ CDOTC( N-K, AP( KC+1 ), 1, 00358 $ AP( KCNEXT+2 ), 1 ) 00359 CALL CCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 00360 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00361 $ 1, ZERO, AP( KCNEXT+2 ), 1 ) 00362 AP( KCNEXT ) = AP( KCNEXT ) - 00363 $ REAL( CDOTC( N-K, WORK, 1, AP( KCNEXT+2 ), $ 1 ) ) 00364 END IF 00365 KSTEP = 2 00366 KCNEXT = KCNEXT - ( N-K+3 ) 00367 END IF 00368 * 00369 KP = ABS( IPIV( K ) ) 00370 IF( KP.NE.K ) THEN 00371 * 00372 * Interchange rows and columns K and KP in the trailing 00373 * submatrix A(k-1:n,k-1:n) 00374 * 00375 KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 00376 IF( KP.LT.N ) 00377 $ CALL CSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 00378 KX = KC + KP - K 00379 DO 70 J = K + 1, KP - 1 00380 KX = KX + N - J + 1 00381 TEMP = CONJG( AP( KC+J-K ) ) 00382 AP( KC+J-K ) = CONJG( AP( KX ) ) 00383 AP( KX ) = TEMP 00384 70 CONTINUE 00385 AP( KC+KP-K ) = CONJG( AP( KC+KP-K ) ) 00386 TEMP = AP( KC ) 00387 AP( KC ) = AP( KPC ) 00388 AP( KPC ) = TEMP 00389 IF( KSTEP.EQ.2 ) THEN 00390 TEMP = AP( KC-N+K-1 ) 00391 AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 00392 AP( KC-N+KP-1 ) = TEMP 00393 END IF 00394 END IF 00395 * 00396 K = K - KSTEP 00397 KC = KCNEXT 00398 GO TO 60 00399 80 CONTINUE 00400 END IF 00401 * 00402 RETURN 00403 * 00404 * End of CHPTRI 00405 * 00406 END 00407