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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) 2: * 3: * -- LAPACK routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER UPLO 10: INTEGER INFO, LDB, N, NRHS 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: COMPLEX*16 AP( * ), B( LDB, * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * ZHPTRS solves a system of linear equations A*X = B with a complex 21: * Hermitian matrix A stored in packed format using the factorization 22: * A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 23: * 24: * Arguments 25: * ========= 26: * 27: * UPLO (input) CHARACTER*1 28: * Specifies whether the details of the factorization are stored 29: * as an upper or lower triangular matrix. 30: * = 'U': Upper triangular, form is A = U*D*U**H; 31: * = 'L': Lower triangular, form is A = L*D*L**H. 32: * 33: * N (input) INTEGER 34: * The order of the matrix A. N >= 0. 35: * 36: * NRHS (input) INTEGER 37: * The number of right hand sides, i.e., the number of columns 38: * of the matrix B. NRHS >= 0. 39: * 40: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) 41: * The block diagonal matrix D and the multipliers used to 42: * obtain the factor U or L as computed by ZHPTRF, stored as a 43: * packed triangular matrix. 44: * 45: * IPIV (input) INTEGER array, dimension (N) 46: * Details of the interchanges and the block structure of D 47: * as determined by ZHPTRF. 48: * 49: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) 50: * On entry, the right hand side matrix B. 51: * On exit, the solution matrix X. 52: * 53: * LDB (input) INTEGER 54: * The leading dimension of the array B. LDB >= max(1,N). 55: * 56: * INFO (output) INTEGER 57: * = 0: successful exit 58: * < 0: if INFO = -i, the i-th argument had an illegal value 59: * 60: * ===================================================================== 61: * 62: * .. Parameters .. 63: COMPLEX*16 ONE 64: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 65: * .. 66: * .. Local Scalars .. 67: LOGICAL UPPER 68: INTEGER J, K, KC, KP 69: DOUBLE PRECISION S 70: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM 71: * .. 72: * .. External Functions .. 73: LOGICAL LSAME 74: EXTERNAL LSAME 75: * .. 76: * .. External Subroutines .. 77: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP 78: * .. 79: * .. Intrinsic Functions .. 80: INTRINSIC DBLE, DCONJG, MAX 81: * .. 82: * .. Executable Statements .. 83: * 84: INFO = 0 85: UPPER = LSAME( UPLO, 'U' ) 86: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 87: INFO = -1 88: ELSE IF( N.LT.0 ) THEN 89: INFO = -2 90: ELSE IF( NRHS.LT.0 ) THEN 91: INFO = -3 92: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 93: INFO = -7 94: END IF 95: IF( INFO.NE.0 ) THEN 96: CALL XERBLA( 'ZHPTRS', -INFO ) 97: RETURN 98: END IF 99: * 100: * Quick return if possible 101: * 102: IF( N.EQ.0 .OR. NRHS.EQ.0 ) 103: $ RETURN 104: * 105: IF( UPPER ) THEN 106: * 107: * Solve A*X = B, where A = U*D*U'. 108: * 109: * First solve U*D*X = B, overwriting B with X. 110: * 111: * K is the main loop index, decreasing from N to 1 in steps of 112: * 1 or 2, depending on the size of the diagonal blocks. 113: * 114: K = N 115: KC = N*( N+1 ) / 2 + 1 116: 10 CONTINUE 117: * 118: * If K < 1, exit from loop. 119: * 120: IF( K.LT.1 ) 121: $ GO TO 30 122: * 123: KC = KC - K 124: IF( IPIV( K ).GT.0 ) THEN 125: * 126: * 1 x 1 diagonal block 127: * 128: * Interchange rows K and IPIV(K). 129: * 130: KP = IPIV( K ) 131: IF( KP.NE.K ) 132: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 133: * 134: * Multiply by inv(U(K)), where U(K) is the transformation 135: * stored in column K of A. 136: * 137: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 138: $ B( 1, 1 ), LDB ) 139: * 140: * Multiply by the inverse of the diagonal block. 141: * 142: S = DBLE( ONE ) / DBLE( AP( KC+K-1 ) ) 143: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 144: K = K - 1 145: ELSE 146: * 147: * 2 x 2 diagonal block 148: * 149: * Interchange rows K-1 and -IPIV(K). 150: * 151: KP = -IPIV( K ) 152: IF( KP.NE.K-1 ) 153: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 154: * 155: * Multiply by inv(U(K)), where U(K) is the transformation 156: * stored in columns K-1 and K of A. 157: * 158: CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 159: $ B( 1, 1 ), LDB ) 160: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1, 161: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB ) 162: * 163: * Multiply by the inverse of the diagonal block. 164: * 165: AKM1K = AP( KC+K-2 ) 166: AKM1 = AP( KC-1 ) / AKM1K 167: AK = AP( KC+K-1 ) / DCONJG( AKM1K ) 168: DENOM = AKM1*AK - ONE 169: DO 20 J = 1, NRHS 170: BKM1 = B( K-1, J ) / AKM1K 171: BK = B( K, J ) / DCONJG( AKM1K ) 172: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 173: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 174: 20 CONTINUE 175: KC = KC - K + 1 176: K = K - 2 177: END IF 178: * 179: GO TO 10 180: 30 CONTINUE 181: * 182: * Next solve U'*X = B, overwriting B with X. 183: * 184: * K is the main loop index, increasing from 1 to N in steps of 185: * 1 or 2, depending on the size of the diagonal blocks. 186: * 187: K = 1 188: KC = 1 189: 40 CONTINUE 190: * 191: * If K > N, exit from loop. 192: * 193: IF( K.GT.N ) 194: $ GO TO 50 195: * 196: IF( IPIV( K ).GT.0 ) THEN 197: * 198: * 1 x 1 diagonal block 199: * 200: * Multiply by inv(U'(K)), where U(K) is the transformation 201: * stored in column K of A. 202: * 203: IF( K.GT.1 ) THEN 204: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 205: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 206: $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB ) 207: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 208: END IF 209: * 210: * Interchange rows K and IPIV(K). 211: * 212: KP = IPIV( K ) 213: IF( KP.NE.K ) 214: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 215: KC = KC + K 216: K = K + 1 217: ELSE 218: * 219: * 2 x 2 diagonal block 220: * 221: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation 222: * stored in columns K and K+1 of A. 223: * 224: IF( K.GT.1 ) THEN 225: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 226: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 227: $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB ) 228: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 229: * 230: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 231: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 232: $ LDB, AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB ) 233: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 234: END IF 235: * 236: * Interchange rows K and -IPIV(K). 237: * 238: KP = -IPIV( K ) 239: IF( KP.NE.K ) 240: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 241: KC = KC + 2*K + 1 242: K = K + 2 243: END IF 244: * 245: GO TO 40 246: 50 CONTINUE 247: * 248: ELSE 249: * 250: * Solve A*X = B, where A = L*D*L'. 251: * 252: * First solve L*D*X = B, overwriting B with X. 253: * 254: * K is the main loop index, increasing from 1 to N in steps of 255: * 1 or 2, depending on the size of the diagonal blocks. 256: * 257: K = 1 258: KC = 1 259: 60 CONTINUE 260: * 261: * If K > N, exit from loop. 262: * 263: IF( K.GT.N ) 264: $ GO TO 80 265: * 266: IF( IPIV( K ).GT.0 ) THEN 267: * 268: * 1 x 1 diagonal block 269: * 270: * Interchange rows K and IPIV(K). 271: * 272: KP = IPIV( K ) 273: IF( KP.NE.K ) 274: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 275: * 276: * Multiply by inv(L(K)), where L(K) is the transformation 277: * stored in column K of A. 278: * 279: IF( K.LT.N ) 280: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ), 281: $ LDB, B( K+1, 1 ), LDB ) 282: * 283: * Multiply by the inverse of the diagonal block. 284: * 285: S = DBLE( ONE ) / DBLE( AP( KC ) ) 286: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 287: KC = KC + N - K + 1 288: K = K + 1 289: ELSE 290: * 291: * 2 x 2 diagonal block 292: * 293: * Interchange rows K+1 and -IPIV(K). 294: * 295: KP = -IPIV( K ) 296: IF( KP.NE.K+1 ) 297: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 298: * 299: * Multiply by inv(L(K)), where L(K) is the transformation 300: * stored in columns K and K+1 of A. 301: * 302: IF( K.LT.N-1 ) THEN 303: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ), 304: $ LDB, B( K+2, 1 ), LDB ) 305: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1, 306: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 307: END IF 308: * 309: * Multiply by the inverse of the diagonal block. 310: * 311: AKM1K = AP( KC+1 ) 312: AKM1 = AP( KC ) / DCONJG( AKM1K ) 313: AK = AP( KC+N-K+1 ) / AKM1K 314: DENOM = AKM1*AK - ONE 315: DO 70 J = 1, NRHS 316: BKM1 = B( K, J ) / DCONJG( AKM1K ) 317: BK = B( K+1, J ) / AKM1K 318: B( K, J ) = ( AK*BKM1-BK ) / DENOM 319: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 320: 70 CONTINUE 321: KC = KC + 2*( N-K ) + 1 322: K = K + 2 323: END IF 324: * 325: GO TO 60 326: 80 CONTINUE 327: * 328: * Next solve L'*X = B, overwriting B with X. 329: * 330: * K is the main loop index, decreasing from N to 1 in steps of 331: * 1 or 2, depending on the size of the diagonal blocks. 332: * 333: K = N 334: KC = N*( N+1 ) / 2 + 1 335: 90 CONTINUE 336: * 337: * If K < 1, exit from loop. 338: * 339: IF( K.LT.1 ) 340: $ GO TO 100 341: * 342: KC = KC - ( N-K+1 ) 343: IF( IPIV( K ).GT.0 ) THEN 344: * 345: * 1 x 1 diagonal block 346: * 347: * Multiply by inv(L'(K)), where L(K) is the transformation 348: * stored in column K of A. 349: * 350: IF( K.LT.N ) THEN 351: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 352: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 353: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE, 354: $ B( K, 1 ), LDB ) 355: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 356: END IF 357: * 358: * Interchange rows K and IPIV(K). 359: * 360: KP = IPIV( K ) 361: IF( KP.NE.K ) 362: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 363: K = K - 1 364: ELSE 365: * 366: * 2 x 2 diagonal block 367: * 368: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation 369: * stored in columns K-1 and K of A. 370: * 371: IF( K.LT.N ) THEN 372: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 373: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 374: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE, 375: $ B( K, 1 ), LDB ) 376: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 377: * 378: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 379: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 380: $ B( K+1, 1 ), LDB, AP( KC-( N-K ) ), 1, ONE, 381: $ B( K-1, 1 ), LDB ) 382: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 383: END IF 384: * 385: * Interchange rows K and -IPIV(K). 386: * 387: KP = -IPIV( K ) 388: IF( KP.NE.K ) 389: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 390: KC = KC - ( N-K+2 ) 391: K = K - 2 392: END IF 393: * 394: GO TO 90 395: 100 CONTINUE 396: END IF 397: * 398: RETURN 399: * 400: * End of ZHPTRS 401: * 402: END