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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsptri.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsptri.f"> 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