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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZSPTRS( 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: * ZSPTRS solves a system of linear equations A*X = B with a complex 21: * symmetric matrix A stored in packed format using the factorization 22: * A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. 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**T; 31: * = 'L': Lower triangular, form is A = L*D*L**T. 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 ZSPTRF, 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 ZSPTRF. 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: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM 70: * .. 71: * .. External Functions .. 72: LOGICAL LSAME 73: EXTERNAL LSAME 74: * .. 75: * .. External Subroutines .. 76: EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP 77: * .. 78: * .. Intrinsic Functions .. 79: INTRINSIC MAX 80: * .. 81: * .. Executable Statements .. 82: * 83: INFO = 0 84: UPPER = LSAME( UPLO, 'U' ) 85: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 86: INFO = -1 87: ELSE IF( N.LT.0 ) THEN 88: INFO = -2 89: ELSE IF( NRHS.LT.0 ) THEN 90: INFO = -3 91: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 92: INFO = -7 93: END IF 94: IF( INFO.NE.0 ) THEN 95: CALL XERBLA( 'ZSPTRS', -INFO ) 96: RETURN 97: END IF 98: * 99: * Quick return if possible 100: * 101: IF( N.EQ.0 .OR. NRHS.EQ.0 ) 102: $ RETURN 103: * 104: IF( UPPER ) THEN 105: * 106: * Solve A*X = B, where A = U*D*U'. 107: * 108: * First solve U*D*X = B, overwriting B with X. 109: * 110: * K is the main loop index, decreasing from N to 1 in steps of 111: * 1 or 2, depending on the size of the diagonal blocks. 112: * 113: K = N 114: KC = N*( N+1 ) / 2 + 1 115: 10 CONTINUE 116: * 117: * If K < 1, exit from loop. 118: * 119: IF( K.LT.1 ) 120: $ GO TO 30 121: * 122: KC = KC - K 123: IF( IPIV( K ).GT.0 ) THEN 124: * 125: * 1 x 1 diagonal block 126: * 127: * Interchange rows K and IPIV(K). 128: * 129: KP = IPIV( K ) 130: IF( KP.NE.K ) 131: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 132: * 133: * Multiply by inv(U(K)), where U(K) is the transformation 134: * stored in column K of A. 135: * 136: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 137: $ B( 1, 1 ), LDB ) 138: * 139: * Multiply by the inverse of the diagonal block. 140: * 141: CALL ZSCAL( NRHS, ONE / AP( KC+K-1 ), B( K, 1 ), LDB ) 142: K = K - 1 143: ELSE 144: * 145: * 2 x 2 diagonal block 146: * 147: * Interchange rows K-1 and -IPIV(K). 148: * 149: KP = -IPIV( K ) 150: IF( KP.NE.K-1 ) 151: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 152: * 153: * Multiply by inv(U(K)), where U(K) is the transformation 154: * stored in columns K-1 and K of A. 155: * 156: CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB, 157: $ B( 1, 1 ), LDB ) 158: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1, 159: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB ) 160: * 161: * Multiply by the inverse of the diagonal block. 162: * 163: AKM1K = AP( KC+K-2 ) 164: AKM1 = AP( KC-1 ) / AKM1K 165: AK = AP( KC+K-1 ) / AKM1K 166: DENOM = AKM1*AK - ONE 167: DO 20 J = 1, NRHS 168: BKM1 = B( K-1, J ) / AKM1K 169: BK = B( K, J ) / AKM1K 170: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 171: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 172: 20 CONTINUE 173: KC = KC - K + 1 174: K = K - 2 175: END IF 176: * 177: GO TO 10 178: 30 CONTINUE 179: * 180: * Next solve U'*X = B, overwriting B with X. 181: * 182: * K is the main loop index, increasing from 1 to N in steps of 183: * 1 or 2, depending on the size of the diagonal blocks. 184: * 185: K = 1 186: KC = 1 187: 40 CONTINUE 188: * 189: * If K > N, exit from loop. 190: * 191: IF( K.GT.N ) 192: $ GO TO 50 193: * 194: IF( IPIV( K ).GT.0 ) THEN 195: * 196: * 1 x 1 diagonal block 197: * 198: * Multiply by inv(U'(K)), where U(K) is the transformation 199: * stored in column K of A. 200: * 201: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ), 202: $ 1, ONE, B( K, 1 ), LDB ) 203: * 204: * Interchange rows K and IPIV(K). 205: * 206: KP = IPIV( K ) 207: IF( KP.NE.K ) 208: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 209: KC = KC + K 210: K = K + 1 211: ELSE 212: * 213: * 2 x 2 diagonal block 214: * 215: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation 216: * stored in columns K and K+1 of A. 217: * 218: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ), 219: $ 1, ONE, B( K, 1 ), LDB ) 220: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, 221: $ AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB ) 222: * 223: * Interchange rows K and -IPIV(K). 224: * 225: KP = -IPIV( K ) 226: IF( KP.NE.K ) 227: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 228: KC = KC + 2*K + 1 229: K = K + 2 230: END IF 231: * 232: GO TO 40 233: 50 CONTINUE 234: * 235: ELSE 236: * 237: * Solve A*X = B, where A = L*D*L'. 238: * 239: * First solve L*D*X = B, overwriting B with X. 240: * 241: * K is the main loop index, increasing from 1 to N in steps of 242: * 1 or 2, depending on the size of the diagonal blocks. 243: * 244: K = 1 245: KC = 1 246: 60 CONTINUE 247: * 248: * If K > N, exit from loop. 249: * 250: IF( K.GT.N ) 251: $ GO TO 80 252: * 253: IF( IPIV( K ).GT.0 ) THEN 254: * 255: * 1 x 1 diagonal block 256: * 257: * Interchange rows K and IPIV(K). 258: * 259: KP = IPIV( K ) 260: IF( KP.NE.K ) 261: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 262: * 263: * Multiply by inv(L(K)), where L(K) is the transformation 264: * stored in column K of A. 265: * 266: IF( K.LT.N ) 267: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ), 268: $ LDB, B( K+1, 1 ), LDB ) 269: * 270: * Multiply by the inverse of the diagonal block. 271: * 272: CALL ZSCAL( NRHS, ONE / AP( KC ), B( K, 1 ), LDB ) 273: KC = KC + N - K + 1 274: K = K + 1 275: ELSE 276: * 277: * 2 x 2 diagonal block 278: * 279: * Interchange rows K+1 and -IPIV(K). 280: * 281: KP = -IPIV( K ) 282: IF( KP.NE.K+1 ) 283: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 284: * 285: * Multiply by inv(L(K)), where L(K) is the transformation 286: * stored in columns K and K+1 of A. 287: * 288: IF( K.LT.N-1 ) THEN 289: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ), 290: $ LDB, B( K+2, 1 ), LDB ) 291: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1, 292: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 293: END IF 294: * 295: * Multiply by the inverse of the diagonal block. 296: * 297: AKM1K = AP( KC+1 ) 298: AKM1 = AP( KC ) / AKM1K 299: AK = AP( KC+N-K+1 ) / AKM1K 300: DENOM = AKM1*AK - ONE 301: DO 70 J = 1, NRHS 302: BKM1 = B( K, J ) / AKM1K 303: BK = B( K+1, J ) / AKM1K 304: B( K, J ) = ( AK*BKM1-BK ) / DENOM 305: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 306: 70 CONTINUE 307: KC = KC + 2*( N-K ) + 1 308: K = K + 2 309: END IF 310: * 311: GO TO 60 312: 80 CONTINUE 313: * 314: * Next solve L'*X = B, overwriting B with X. 315: * 316: * K is the main loop index, decreasing from N to 1 in steps of 317: * 1 or 2, depending on the size of the diagonal blocks. 318: * 319: K = N 320: KC = N*( N+1 ) / 2 + 1 321: 90 CONTINUE 322: * 323: * If K < 1, exit from loop. 324: * 325: IF( K.LT.1 ) 326: $ GO TO 100 327: * 328: KC = KC - ( N-K+1 ) 329: IF( IPIV( K ).GT.0 ) THEN 330: * 331: * 1 x 1 diagonal block 332: * 333: * Multiply by inv(L'(K)), where L(K) is the transformation 334: * stored in column K of A. 335: * 336: IF( K.LT.N ) 337: $ CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 338: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB ) 339: * 340: * Interchange rows K and IPIV(K). 341: * 342: KP = IPIV( K ) 343: IF( KP.NE.K ) 344: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 345: K = K - 1 346: ELSE 347: * 348: * 2 x 2 diagonal block 349: * 350: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation 351: * stored in columns K-1 and K of A. 352: * 353: IF( K.LT.N ) THEN 354: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 355: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB ) 356: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 357: $ LDB, AP( KC-( N-K ) ), 1, ONE, B( K-1, 1 ), 358: $ LDB ) 359: END IF 360: * 361: * Interchange rows K and -IPIV(K). 362: * 363: KP = -IPIV( K ) 364: IF( KP.NE.K ) 365: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 366: KC = KC - ( N-K+2 ) 367: K = K - 2 368: END IF 369: * 370: GO TO 90 371: 100 CONTINUE 372: END IF 373: * 374: RETURN 375: * 376: * End of ZSPTRS 377: * 378: END