![]() ![]() | ![]() |
Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, 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, LDA, LDB, N, NRHS 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: COMPLEX*16 A( LDA, * ), B( LDB, * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * ZSYTRS solves a system of linear equations A*X = B with a complex 21: * symmetric matrix A using the factorization A = U*D*U**T or 22: * A = L*D*L**T computed by ZSYTRF. 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: * A (input) COMPLEX*16 array, dimension (LDA,N) 41: * The block diagonal matrix D and the multipliers used to 42: * obtain the factor U or L as computed by ZSYTRF. 43: * 44: * LDA (input) INTEGER 45: * The leading dimension of the array A. LDA >= max(1,N). 46: * 47: * IPIV (input) INTEGER array, dimension (N) 48: * Details of the interchanges and the block structure of D 49: * as determined by ZSYTRF. 50: * 51: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) 52: * On entry, the right hand side matrix B. 53: * On exit, the solution matrix X. 54: * 55: * LDB (input) INTEGER 56: * The leading dimension of the array B. LDB >= max(1,N). 57: * 58: * INFO (output) INTEGER 59: * = 0: successful exit 60: * < 0: if INFO = -i, the i-th argument had an illegal value 61: * 62: * ===================================================================== 63: * 64: * .. Parameters .. 65: COMPLEX*16 ONE 66: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 67: * .. 68: * .. Local Scalars .. 69: LOGICAL UPPER 70: INTEGER J, K, KP 71: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM 72: * .. 73: * .. External Functions .. 74: LOGICAL LSAME 75: EXTERNAL LSAME 76: * .. 77: * .. External Subroutines .. 78: EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP 79: * .. 80: * .. Intrinsic Functions .. 81: INTRINSIC MAX 82: * .. 83: * .. Executable Statements .. 84: * 85: INFO = 0 86: UPPER = LSAME( UPLO, 'U' ) 87: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 88: INFO = -1 89: ELSE IF( N.LT.0 ) THEN 90: INFO = -2 91: ELSE IF( NRHS.LT.0 ) THEN 92: INFO = -3 93: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 94: INFO = -5 95: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 96: INFO = -8 97: END IF 98: IF( INFO.NE.0 ) THEN 99: CALL XERBLA( 'ZSYTRS', -INFO ) 100: RETURN 101: END IF 102: * 103: * Quick return if possible 104: * 105: IF( N.EQ.0 .OR. NRHS.EQ.0 ) 106: $ RETURN 107: * 108: IF( UPPER ) THEN 109: * 110: * Solve A*X = B, where A = U*D*U'. 111: * 112: * First solve U*D*X = B, overwriting B with X. 113: * 114: * K is the main loop index, decreasing from N to 1 in steps of 115: * 1 or 2, depending on the size of the diagonal blocks. 116: * 117: K = N 118: 10 CONTINUE 119: * 120: * If K < 1, exit from loop. 121: * 122: IF( K.LT.1 ) 123: $ GO TO 30 124: * 125: IF( IPIV( K ).GT.0 ) THEN 126: * 127: * 1 x 1 diagonal block 128: * 129: * Interchange rows K and IPIV(K). 130: * 131: KP = IPIV( K ) 132: IF( KP.NE.K ) 133: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 134: * 135: * Multiply by inv(U(K)), where U(K) is the transformation 136: * stored in column K of A. 137: * 138: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB, 139: $ B( 1, 1 ), LDB ) 140: * 141: * Multiply by the inverse of the diagonal block. 142: * 143: CALL ZSCAL( NRHS, ONE / A( K, K ), 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, A( 1, K ), 1, B( K, 1 ), LDB, 159: $ B( 1, 1 ), LDB ) 160: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ), 161: $ LDB, B( 1, 1 ), LDB ) 162: * 163: * Multiply by the inverse of the diagonal block. 164: * 165: AKM1K = A( K-1, K ) 166: AKM1 = A( K-1, K-1 ) / AKM1K 167: AK = A( K, K ) / AKM1K 168: DENOM = AKM1*AK - ONE 169: DO 20 J = 1, NRHS 170: BKM1 = B( K-1, J ) / AKM1K 171: BK = B( K, J ) / AKM1K 172: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 173: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 174: 20 CONTINUE 175: K = K - 2 176: END IF 177: * 178: GO TO 10 179: 30 CONTINUE 180: * 181: * Next solve U'*X = B, overwriting B with X. 182: * 183: * K is the main loop index, increasing from 1 to N in steps of 184: * 1 or 2, depending on the size of the diagonal blocks. 185: * 186: K = 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, A( 1, K ), 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: K = K + 1 210: ELSE 211: * 212: * 2 x 2 diagonal block 213: * 214: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation 215: * stored in columns K and K+1 of A. 216: * 217: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), 218: $ 1, ONE, B( K, 1 ), LDB ) 219: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, 220: $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB ) 221: * 222: * Interchange rows K and -IPIV(K). 223: * 224: KP = -IPIV( K ) 225: IF( KP.NE.K ) 226: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 227: K = K + 2 228: END IF 229: * 230: GO TO 40 231: 50 CONTINUE 232: * 233: ELSE 234: * 235: * Solve A*X = B, where A = L*D*L'. 236: * 237: * First solve L*D*X = B, overwriting B with X. 238: * 239: * K is the main loop index, increasing from 1 to N in steps of 240: * 1 or 2, depending on the size of the diagonal blocks. 241: * 242: K = 1 243: 60 CONTINUE 244: * 245: * If K > N, exit from loop. 246: * 247: IF( K.GT.N ) 248: $ GO TO 80 249: * 250: IF( IPIV( K ).GT.0 ) THEN 251: * 252: * 1 x 1 diagonal block 253: * 254: * Interchange rows K and IPIV(K). 255: * 256: KP = IPIV( K ) 257: IF( KP.NE.K ) 258: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 259: * 260: * Multiply by inv(L(K)), where L(K) is the transformation 261: * stored in column K of A. 262: * 263: IF( K.LT.N ) 264: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ), 265: $ LDB, B( K+1, 1 ), LDB ) 266: * 267: * Multiply by the inverse of the diagonal block. 268: * 269: CALL ZSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB ) 270: K = K + 1 271: ELSE 272: * 273: * 2 x 2 diagonal block 274: * 275: * Interchange rows K+1 and -IPIV(K). 276: * 277: KP = -IPIV( K ) 278: IF( KP.NE.K+1 ) 279: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 280: * 281: * Multiply by inv(L(K)), where L(K) is the transformation 282: * stored in columns K and K+1 of A. 283: * 284: IF( K.LT.N-1 ) THEN 285: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ), 286: $ LDB, B( K+2, 1 ), LDB ) 287: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1, 288: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 289: END IF 290: * 291: * Multiply by the inverse of the diagonal block. 292: * 293: AKM1K = A( K+1, K ) 294: AKM1 = A( K, K ) / AKM1K 295: AK = A( K+1, K+1 ) / AKM1K 296: DENOM = AKM1*AK - ONE 297: DO 70 J = 1, NRHS 298: BKM1 = B( K, J ) / AKM1K 299: BK = B( K+1, J ) / AKM1K 300: B( K, J ) = ( AK*BKM1-BK ) / DENOM 301: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 302: 70 CONTINUE 303: K = K + 2 304: END IF 305: * 306: GO TO 60 307: 80 CONTINUE 308: * 309: * Next solve L'*X = B, overwriting B with X. 310: * 311: * K is the main loop index, decreasing from N to 1 in steps of 312: * 1 or 2, depending on the size of the diagonal blocks. 313: * 314: K = N 315: 90 CONTINUE 316: * 317: * If K < 1, exit from loop. 318: * 319: IF( K.LT.1 ) 320: $ GO TO 100 321: * 322: IF( IPIV( K ).GT.0 ) THEN 323: * 324: * 1 x 1 diagonal block 325: * 326: * Multiply by inv(L'(K)), where L(K) is the transformation 327: * stored in column K of A. 328: * 329: IF( K.LT.N ) 330: $ CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 331: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB ) 332: * 333: * Interchange rows K and IPIV(K). 334: * 335: KP = IPIV( K ) 336: IF( KP.NE.K ) 337: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 338: K = K - 1 339: ELSE 340: * 341: * 2 x 2 diagonal block 342: * 343: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation 344: * stored in columns K-1 and K of A. 345: * 346: IF( K.LT.N ) THEN 347: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 348: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB ) 349: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ), 350: $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ), 351: $ LDB ) 352: END IF 353: * 354: * Interchange rows K and -IPIV(K). 355: * 356: KP = -IPIV( K ) 357: IF( KP.NE.K ) 358: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 359: K = K - 2 360: END IF 361: * 362: GO TO 90 363: 100 CONTINUE 364: END IF 365: * 366: RETURN 367: * 368: * End of ZSYTRS 369: * 370: END