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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHETRS( 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: * ZHETRS solves a system of linear equations A*X = B with a complex 21: * Hermitian matrix A using the factorization A = U*D*U**H or 22: * A = L*D*L**H computed by ZHETRF. 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: * 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 ZHETRF. 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 ZHETRF. 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: DOUBLE PRECISION S 72: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM 73: * .. 74: * .. External Functions .. 75: LOGICAL LSAME 76: EXTERNAL LSAME 77: * .. 78: * .. External Subroutines .. 79: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP 80: * .. 81: * .. Intrinsic Functions .. 82: INTRINSIC DBLE, DCONJG, MAX 83: * .. 84: * .. Executable Statements .. 85: * 86: INFO = 0 87: UPPER = LSAME( UPLO, 'U' ) 88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 89: INFO = -1 90: ELSE IF( N.LT.0 ) THEN 91: INFO = -2 92: ELSE IF( NRHS.LT.0 ) THEN 93: INFO = -3 94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 95: INFO = -5 96: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 97: INFO = -8 98: END IF 99: IF( INFO.NE.0 ) THEN 100: CALL XERBLA( 'ZHETRS', -INFO ) 101: RETURN 102: END IF 103: * 104: * Quick return if possible 105: * 106: IF( N.EQ.0 .OR. NRHS.EQ.0 ) 107: $ RETURN 108: * 109: IF( UPPER ) THEN 110: * 111: * Solve A*X = B, where A = U*D*U'. 112: * 113: * First solve U*D*X = B, overwriting B with X. 114: * 115: * K is the main loop index, decreasing from N to 1 in steps of 116: * 1 or 2, depending on the size of the diagonal blocks. 117: * 118: K = N 119: 10 CONTINUE 120: * 121: * If K < 1, exit from loop. 122: * 123: IF( K.LT.1 ) 124: $ GO TO 30 125: * 126: IF( IPIV( K ).GT.0 ) THEN 127: * 128: * 1 x 1 diagonal block 129: * 130: * Interchange rows K and IPIV(K). 131: * 132: KP = IPIV( K ) 133: IF( KP.NE.K ) 134: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 135: * 136: * Multiply by inv(U(K)), where U(K) is the transformation 137: * stored in column K of A. 138: * 139: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB, 140: $ B( 1, 1 ), LDB ) 141: * 142: * Multiply by the inverse of the diagonal block. 143: * 144: S = DBLE( ONE ) / DBLE( A( K, K ) ) 145: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 146: K = K - 1 147: ELSE 148: * 149: * 2 x 2 diagonal block 150: * 151: * Interchange rows K-1 and -IPIV(K). 152: * 153: KP = -IPIV( K ) 154: IF( KP.NE.K-1 ) 155: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 156: * 157: * Multiply by inv(U(K)), where U(K) is the transformation 158: * stored in columns K-1 and K of A. 159: * 160: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB, 161: $ B( 1, 1 ), LDB ) 162: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ), 163: $ LDB, B( 1, 1 ), LDB ) 164: * 165: * Multiply by the inverse of the diagonal block. 166: * 167: AKM1K = A( K-1, K ) 168: AKM1 = A( K-1, K-1 ) / AKM1K 169: AK = A( K, K ) / DCONJG( AKM1K ) 170: DENOM = AKM1*AK - ONE 171: DO 20 J = 1, NRHS 172: BKM1 = B( K-1, J ) / AKM1K 173: BK = B( K, J ) / DCONJG( AKM1K ) 174: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM 175: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 176: 20 CONTINUE 177: K = K - 2 178: END IF 179: * 180: GO TO 10 181: 30 CONTINUE 182: * 183: * Next solve U'*X = B, overwriting B with X. 184: * 185: * K is the main loop index, increasing from 1 to N in steps of 186: * 1 or 2, depending on the size of the diagonal blocks. 187: * 188: K = 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, A( 1, K ), 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: K = K + 1 216: ELSE 217: * 218: * 2 x 2 diagonal block 219: * 220: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation 221: * stored in columns K and K+1 of A. 222: * 223: IF( K.GT.1 ) THEN 224: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 225: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 226: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB ) 227: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 228: * 229: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 230: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, 231: $ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB ) 232: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) 233: END IF 234: * 235: * Interchange rows K and -IPIV(K). 236: * 237: KP = -IPIV( K ) 238: IF( KP.NE.K ) 239: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 240: K = K + 2 241: END IF 242: * 243: GO TO 40 244: 50 CONTINUE 245: * 246: ELSE 247: * 248: * Solve A*X = B, where A = L*D*L'. 249: * 250: * First solve L*D*X = B, overwriting B with X. 251: * 252: * K is the main loop index, increasing from 1 to N in steps of 253: * 1 or 2, depending on the size of the diagonal blocks. 254: * 255: K = 1 256: 60 CONTINUE 257: * 258: * If K > N, exit from loop. 259: * 260: IF( K.GT.N ) 261: $ GO TO 80 262: * 263: IF( IPIV( K ).GT.0 ) THEN 264: * 265: * 1 x 1 diagonal block 266: * 267: * Interchange rows K and IPIV(K). 268: * 269: KP = IPIV( K ) 270: IF( KP.NE.K ) 271: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 272: * 273: * Multiply by inv(L(K)), where L(K) is the transformation 274: * stored in column K of A. 275: * 276: IF( K.LT.N ) 277: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ), 278: $ LDB, B( K+1, 1 ), LDB ) 279: * 280: * Multiply by the inverse of the diagonal block. 281: * 282: S = DBLE( ONE ) / DBLE( A( K, K ) ) 283: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB ) 284: K = K + 1 285: ELSE 286: * 287: * 2 x 2 diagonal block 288: * 289: * Interchange rows K+1 and -IPIV(K). 290: * 291: KP = -IPIV( K ) 292: IF( KP.NE.K+1 ) 293: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 294: * 295: * Multiply by inv(L(K)), where L(K) is the transformation 296: * stored in columns K and K+1 of A. 297: * 298: IF( K.LT.N-1 ) THEN 299: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ), 300: $ LDB, B( K+2, 1 ), LDB ) 301: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1, 302: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) 303: END IF 304: * 305: * Multiply by the inverse of the diagonal block. 306: * 307: AKM1K = A( K+1, K ) 308: AKM1 = A( K, K ) / DCONJG( AKM1K ) 309: AK = A( K+1, K+1 ) / AKM1K 310: DENOM = AKM1*AK - ONE 311: DO 70 J = 1, NRHS 312: BKM1 = B( K, J ) / DCONJG( AKM1K ) 313: BK = B( K+1, J ) / AKM1K 314: B( K, J ) = ( AK*BKM1-BK ) / DENOM 315: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 316: 70 CONTINUE 317: K = K + 2 318: END IF 319: * 320: GO TO 60 321: 80 CONTINUE 322: * 323: * Next solve L'*X = B, overwriting B with X. 324: * 325: * K is the main loop index, decreasing from N to 1 in steps of 326: * 1 or 2, depending on the size of the diagonal blocks. 327: * 328: K = N 329: 90 CONTINUE 330: * 331: * If K < 1, exit from loop. 332: * 333: IF( K.LT.1 ) 334: $ GO TO 100 335: * 336: IF( IPIV( K ).GT.0 ) THEN 337: * 338: * 1 x 1 diagonal block 339: * 340: * Multiply by inv(L'(K)), where L(K) is the transformation 341: * stored in column K of A. 342: * 343: IF( K.LT.N ) THEN 344: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 345: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 346: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, 347: $ B( K, 1 ), LDB ) 348: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 349: END IF 350: * 351: * Interchange rows K and IPIV(K). 352: * 353: KP = IPIV( K ) 354: IF( KP.NE.K ) 355: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 356: K = K - 1 357: ELSE 358: * 359: * 2 x 2 diagonal block 360: * 361: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation 362: * stored in columns K-1 and K of A. 363: * 364: IF( K.LT.N ) THEN 365: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 366: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 367: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, 368: $ B( K, 1 ), LDB ) 369: CALL ZLACGV( NRHS, B( K, 1 ), LDB ) 370: * 371: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 372: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, 373: $ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE, 374: $ B( K-1, 1 ), LDB ) 375: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) 376: END IF 377: * 378: * Interchange rows K and -IPIV(K). 379: * 380: KP = -IPIV( K ) 381: IF( KP.NE.K ) 382: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 383: K = K - 2 384: END IF 385: * 386: GO TO 90 387: 100 CONTINUE 388: END IF 389: * 390: RETURN 391: * 392: * End of ZHETRS 393: * 394: END