|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 |
SUBROUTINE CHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX AP( * ), WORK( * ) * .. * * Purpose * ======= * * CHPTRI computes the inverse of a complex Hermitian indefinite matrix * A in packed storage using the factorization A = U*D*U**H or * A = L*D*L**H computed by CHPTRF. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the details of the factorization are stored * as an upper or lower triangular matrix. * = 'U': Upper triangular, form is A = U*D*U**H; * = 'L': Lower triangular, form is A = L*D*L**H. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input/output) COMPLEX array, dimension (N*(N+1)/2) * On entry, the block diagonal matrix D and the multipliers * used to obtain the factor U or L as computed by CHPTRF, * stored as a packed triangular matrix. * * On exit, if INFO = 0, the (Hermitian) inverse of the original * matrix, stored as a packed triangular matrix. The j-th column * of inv(A) is stored in the array AP as follows: * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; * if UPLO = 'L', * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. * * IPIV (input) INTEGER array, dimension (N) * Details of the interchanges and the block structure of D * as determined by CHPTRF. * * WORK (workspace) COMPLEX array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its * inverse could not be computed. * * ===================================================================== * * .. Parameters .. REAL ONE COMPLEX CONE, ZERO PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ), $ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP REAL AK, AKP1, D, T COMPLEX AKKP1, TEMP * .. * .. External Functions .. LOGICAL LSAME COMPLEX CDOTC EXTERNAL LSAME, CDOTC * .. * .. External Subroutines .. EXTERNAL CCOPY, CHPMV, CSWAP, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHPTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Check that the diagonal matrix D is nonsingular. * IF( UPPER ) THEN * * Upper triangular storage: examine D from bottom to top * KP = N*( N+1 ) / 2 DO 10 INFO = N, 1, -1 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) $ RETURN KP = KP - INFO 10 CONTINUE ELSE * * Lower triangular storage: examine D from top to bottom. * KP = 1 DO 20 INFO = 1, N IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) $ RETURN KP = KP + N - INFO + 1 20 CONTINUE END IF INFO = 0 * IF( UPPER ) THEN * * Compute inv(A) from the factorization A = U*D*U**H. * * K is the main loop index, increasing from 1 to N in steps of * 1 or 2, depending on the size of the diagonal blocks. * K = 1 KC = 1 30 CONTINUE * * If K > N, exit from loop. * IF( K.GT.N ) $ GO TO 50 * KCNEXT = KC + K IF( IPIV( K ).GT.0 ) THEN * * 1 x 1 diagonal block * * Invert the diagonal block. * AP( KC+K-1 ) = ONE / REAL( AP( KC+K-1 ) ) * * Compute column K of the inverse. * IF( K.GT.1 ) THEN CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 ) CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, $ AP( KC ), 1 ) AP( KC+K-1 ) = AP( KC+K-1 ) - $ REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) END IF KSTEP = 1 ELSE * * 2 x 2 diagonal block * * Invert the diagonal block. * T = ABS( AP( KCNEXT+K-1 ) ) AK = REAL( AP( KC+K-1 ) ) / T AKP1 = REAL( AP( KCNEXT+K ) ) / T AKKP1 = AP( KCNEXT+K-1 ) / T D = T*( AK*AKP1-ONE ) AP( KC+K-1 ) = AKP1 / D AP( KCNEXT+K ) = AK / D AP( KCNEXT+K-1 ) = -AKKP1 / D * * Compute columns K and K+1 of the inverse. * IF( K.GT.1 ) THEN CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 ) CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, $ AP( KC ), 1 ) AP( KC+K-1 ) = AP( KC+K-1 ) - $ REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - $ CDOTC( K-1, AP( KC ), 1, AP( KCNEXT ), $ 1 ) CALL CCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, $ AP( KCNEXT ), 1 ) AP( KCNEXT+K ) = AP( KCNEXT+K ) - $ REAL( CDOTC( K-1, WORK, 1, AP( KCNEXT ), $ 1 ) ) END IF KSTEP = 2 KCNEXT = KCNEXT + K + 1 END IF * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) THEN * * Interchange rows and columns K and KP in the leading * submatrix A(1:k+1,1:k+1) * KPC = ( KP-1 )*KP / 2 + 1 CALL CSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) KX = KPC + KP - 1 DO 40 J = KP + 1, K - 1 KX = KX + J - 1 TEMP = CONJG( AP( KC+J-1 ) ) AP( KC+J-1 ) = CONJG( AP( KX ) ) AP( KX ) = TEMP 40 CONTINUE AP( KC+KP-1 ) = CONJG( AP( KC+KP-1 ) ) TEMP = AP( KC+K-1 ) AP( KC+K-1 ) = AP( KPC+KP-1 ) AP( KPC+KP-1 ) = TEMP IF( KSTEP.EQ.2 ) THEN TEMP = AP( KC+K+K-1 ) AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) AP( KC+K+KP-1 ) = TEMP END IF END IF * K = K + KSTEP KC = KCNEXT GO TO 30 50 CONTINUE * ELSE * * Compute inv(A) from the factorization A = L*D*L**H. * * K is the main loop index, increasing from 1 to N in steps of * 1 or 2, depending on the size of the diagonal blocks. * NPP = N*( N+1 ) / 2 K = N KC = NPP 60 CONTINUE * * If K < 1, exit from loop. * IF( K.LT.1 ) $ GO TO 80 * KCNEXT = KC - ( N-K+2 ) IF( IPIV( K ).GT.0 ) THEN * * 1 x 1 diagonal block * * Invert the diagonal block. * AP( KC ) = ONE / REAL( AP( KC ) ) * * Compute column K of the inverse. * IF( K.LT.N ) THEN CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) CALL CHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1, $ ZERO, AP( KC+1 ), 1 ) AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) END IF KSTEP = 1 ELSE * * 2 x 2 diagonal block * * Invert the diagonal block. * T = ABS( AP( KCNEXT+1 ) ) AK = REAL( AP( KCNEXT ) ) / T AKP1 = REAL( AP( KC ) ) / T AKKP1 = AP( KCNEXT+1 ) / T D = T*( AK*AKP1-ONE ) AP( KCNEXT ) = AKP1 / D AP( KC ) = AK / D AP( KCNEXT+1 ) = -AKKP1 / D * * Compute columns K-1 and K of the inverse. * IF( K.LT.N ) THEN CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, $ 1, ZERO, AP( KC+1 ), 1 ) AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - $ CDOTC( N-K, AP( KC+1 ), 1, $ AP( KCNEXT+2 ), 1 ) CALL CCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, $ 1, ZERO, AP( KCNEXT+2 ), 1 ) AP( KCNEXT ) = AP( KCNEXT ) - $ REAL( CDOTC( N-K, WORK, 1, AP( KCNEXT+2 ), $ 1 ) ) END IF KSTEP = 2 KCNEXT = KCNEXT - ( N-K+3 ) END IF * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) THEN * * Interchange rows and columns K and KP in the trailing * submatrix A(k-1:n,k-1:n) * KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 IF( KP.LT.N ) $ CALL CSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) KX = KC + KP - K DO 70 J = K + 1, KP - 1 KX = KX + N - J + 1 TEMP = CONJG( AP( KC+J-K ) ) AP( KC+J-K ) = CONJG( AP( KX ) ) AP( KX ) = TEMP 70 CONTINUE AP( KC+KP-K ) = CONJG( AP( KC+KP-K ) ) TEMP = AP( KC ) AP( KC ) = AP( KPC ) AP( KPC ) = TEMP IF( KSTEP.EQ.2 ) THEN TEMP = AP( KC-N+K-1 ) AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) AP( KC-N+KP-1 ) = TEMP END IF END IF * K = K - KSTEP KC = KCNEXT GO TO 60 80 CONTINUE END IF * RETURN * * End of CHPTRI * END |