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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO ) 2: * 3: * -- LAPACK routine (version 3.3.0) -- 4: * 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center -- 6: * November 2010 -- 7: * 8: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 10: * 11: * .. Scalar Arguments .. 12: CHARACTER TRANSR, UPLO, DIAG 13: INTEGER INFO, N 14: * .. 15: * .. Array Arguments .. 16: DOUBLE PRECISION A( 0: * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * DTFTRI computes the inverse of a triangular matrix A stored in RFP 23: * format. 24: * 25: * This is a Level 3 BLAS version of the algorithm. 26: * 27: * Arguments 28: * ========= 29: * 30: * TRANSR (input) CHARACTER*1 31: * = 'N': The Normal TRANSR of RFP A is stored; 32: * = 'T': The Transpose TRANSR of RFP A is stored. 33: * 34: * UPLO (input) CHARACTER*1 35: * = 'U': A is upper triangular; 36: * = 'L': A is lower triangular. 37: * 38: * DIAG (input) CHARACTER*1 39: * = 'N': A is non-unit triangular; 40: * = 'U': A is unit triangular. 41: * 42: * N (input) INTEGER 43: * The order of the matrix A. N >= 0. 44: * 45: * A (input/output) DOUBLE PRECISION array, dimension (0:nt-1); 46: * nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian 47: * Positive Definite matrix A in RFP format. RFP format is 48: * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' 49: * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is 50: * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is 51: * the transpose of RFP A as defined when 52: * TRANSR = 'N'. The contents of RFP A are defined by UPLO as 53: * follows: If UPLO = 'U' the RFP A contains the nt elements of 54: * upper packed A; If UPLO = 'L' the RFP A contains the nt 55: * elements of lower packed A. The LDA of RFP A is (N+1)/2 when 56: * TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is 57: * even and N is odd. See the Note below for more details. 58: * 59: * On exit, the (triangular) inverse of the original matrix, in 60: * the same storage format. 61: * 62: * INFO (output) INTEGER 63: * = 0: successful exit 64: * < 0: if INFO = -i, the i-th argument had an illegal value 65: * > 0: if INFO = i, A(i,i) is exactly zero. The triangular 66: * matrix is singular and its inverse can not be computed. 67: * 68: * Further Details 69: * =============== 70: * 71: * We first consider Rectangular Full Packed (RFP) Format when N is 72: * even. We give an example where N = 6. 73: * 74: * AP is Upper AP is Lower 75: * 76: * 00 01 02 03 04 05 00 77: * 11 12 13 14 15 10 11 78: * 22 23 24 25 20 21 22 79: * 33 34 35 30 31 32 33 80: * 44 45 40 41 42 43 44 81: * 55 50 51 52 53 54 55 82: * 83: * 84: * Let TRANSR = 'N'. RFP holds AP as follows: 85: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 86: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of 87: * the transpose of the first three columns of AP upper. 88: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 89: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of 90: * the transpose of the last three columns of AP lower. 91: * This covers the case N even and TRANSR = 'N'. 92: * 93: * RFP A RFP A 94: * 95: * 03 04 05 33 43 53 96: * 13 14 15 00 44 54 97: * 23 24 25 10 11 55 98: * 33 34 35 20 21 22 99: * 00 44 45 30 31 32 100: * 01 11 55 40 41 42 101: * 02 12 22 50 51 52 102: * 103: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 104: * transpose of RFP A above. One therefore gets: 105: * 106: * 107: * RFP A RFP A 108: * 109: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50 110: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51 111: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52 112: * 113: * 114: * We then consider Rectangular Full Packed (RFP) Format when N is 115: * odd. We give an example where N = 5. 116: * 117: * AP is Upper AP is Lower 118: * 119: * 00 01 02 03 04 00 120: * 11 12 13 14 10 11 121: * 22 23 24 20 21 22 122: * 33 34 30 31 32 33 123: * 44 40 41 42 43 44 124: * 125: * 126: * Let TRANSR = 'N'. RFP holds AP as follows: 127: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 128: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of 129: * the transpose of the first two columns of AP upper. 130: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 131: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of 132: * the transpose of the last two columns of AP lower. 133: * This covers the case N odd and TRANSR = 'N'. 134: * 135: * RFP A RFP A 136: * 137: * 02 03 04 00 33 43 138: * 12 13 14 10 11 44 139: * 22 23 24 20 21 22 140: * 00 33 34 30 31 32 141: * 01 11 44 40 41 42 142: * 143: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 144: * transpose of RFP A above. One therefore gets: 145: * 146: * RFP A RFP A 147: * 148: * 02 12 22 00 01 00 10 20 30 40 50 149: * 03 13 23 33 11 33 11 21 31 41 51 150: * 04 14 24 34 44 43 44 22 32 42 52 151: * 152: * ===================================================================== 153: * 154: * .. Parameters .. 155: DOUBLE PRECISION ONE 156: PARAMETER ( ONE = 1.0D+0 ) 157: * .. 158: * .. Local Scalars .. 159: LOGICAL LOWER, NISODD, NORMALTRANSR 160: INTEGER N1, N2, K 161: * .. 162: * .. External Functions .. 163: LOGICAL LSAME 164: EXTERNAL LSAME 165: * .. 166: * .. External Subroutines .. 167: EXTERNAL XERBLA, DTRMM, DTRTRI 168: * .. 169: * .. Intrinsic Functions .. 170: INTRINSIC MOD 171: * .. 172: * .. Executable Statements .. 173: * 174: * Test the input parameters. 175: * 176: INFO = 0 177: NORMALTRANSR = LSAME( TRANSR, 'N' ) 178: LOWER = LSAME( UPLO, 'L' ) 179: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN 180: INFO = -1 181: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN 182: INFO = -2 183: ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) ) 184: + THEN 185: INFO = -3 186: ELSE IF( N.LT.0 ) THEN 187: INFO = -4 188: END IF 189: IF( INFO.NE.0 ) THEN 190: CALL XERBLA( 'DTFTRI', -INFO ) 191: RETURN 192: END IF 193: * 194: * Quick return if possible 195: * 196: IF( N.EQ.0 ) 197: + RETURN 198: * 199: * If N is odd, set NISODD = .TRUE. 200: * If N is even, set K = N/2 and NISODD = .FALSE. 201: * 202: IF( MOD( N, 2 ).EQ.0 ) THEN 203: K = N / 2 204: NISODD = .FALSE. 205: ELSE 206: NISODD = .TRUE. 207: END IF 208: * 209: * Set N1 and N2 depending on LOWER 210: * 211: IF( LOWER ) THEN 212: N2 = N / 2 213: N1 = N - N2 214: ELSE 215: N1 = N / 2 216: N2 = N - N1 217: END IF 218: * 219: * 220: * start execution: there are eight cases 221: * 222: IF( NISODD ) THEN 223: * 224: * N is odd 225: * 226: IF( NORMALTRANSR ) THEN 227: * 228: * N is odd and TRANSR = 'N' 229: * 230: IF( LOWER ) THEN 231: * 232: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) 233: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) 234: * T1 -> a(0), T2 -> a(n), S -> a(n1) 235: * 236: CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO ) 237: IF( INFO.GT.0 ) 238: + RETURN 239: CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ), 240: + N, A( N1 ), N ) 241: CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO ) 242: IF( INFO.GT.0 ) 243: + INFO = INFO + N1 244: IF( INFO.GT.0 ) 245: + RETURN 246: CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N, 247: + A( N1 ), N ) 248: * 249: ELSE 250: * 251: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) 252: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) 253: * T1 -> a(n2), T2 -> a(n1), S -> a(0) 254: * 255: CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO ) 256: IF( INFO.GT.0 ) 257: + RETURN 258: CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ), 259: + N, A( 0 ), N ) 260: CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO ) 261: IF( INFO.GT.0 ) 262: + INFO = INFO + N1 263: IF( INFO.GT.0 ) 264: + RETURN 265: CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ), 266: + N, A( 0 ), N ) 267: * 268: END IF 269: * 270: ELSE 271: * 272: * N is odd and TRANSR = 'T' 273: * 274: IF( LOWER ) THEN 275: * 276: * SRPA for LOWER, TRANSPOSE and N is odd 277: * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1) 278: * 279: CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO ) 280: IF( INFO.GT.0 ) 281: + RETURN 282: CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ), 283: + N1, A( N1*N1 ), N1 ) 284: CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO ) 285: IF( INFO.GT.0 ) 286: + INFO = INFO + N1 287: IF( INFO.GT.0 ) 288: + RETURN 289: CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ), 290: + N1, A( N1*N1 ), N1 ) 291: * 292: ELSE 293: * 294: * SRPA for UPPER, TRANSPOSE and N is odd 295: * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0) 296: * 297: CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO ) 298: IF( INFO.GT.0 ) 299: + RETURN 300: CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE, 301: + A( N2*N2 ), N2, A( 0 ), N2 ) 302: CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO ) 303: IF( INFO.GT.0 ) 304: + INFO = INFO + N1 305: IF( INFO.GT.0 ) 306: + RETURN 307: CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE, 308: + A( N1*N2 ), N2, A( 0 ), N2 ) 309: END IF 310: * 311: END IF 312: * 313: ELSE 314: * 315: * N is even 316: * 317: IF( NORMALTRANSR ) THEN 318: * 319: * N is even and TRANSR = 'N' 320: * 321: IF( LOWER ) THEN 322: * 323: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) 324: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) 325: * T1 -> a(1), T2 -> a(0), S -> a(k+1) 326: * 327: CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO ) 328: IF( INFO.GT.0 ) 329: + RETURN 330: CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ), 331: + N+1, A( K+1 ), N+1 ) 332: CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO ) 333: IF( INFO.GT.0 ) 334: + INFO = INFO + K 335: IF( INFO.GT.0 ) 336: + RETURN 337: CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1, 338: + A( K+1 ), N+1 ) 339: * 340: ELSE 341: * 342: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) 343: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) 344: * T1 -> a(k+1), T2 -> a(k), S -> a(0) 345: * 346: CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO ) 347: IF( INFO.GT.0 ) 348: + RETURN 349: CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ), 350: + N+1, A( 0 ), N+1 ) 351: CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO ) 352: IF( INFO.GT.0 ) 353: + INFO = INFO + K 354: IF( INFO.GT.0 ) 355: + RETURN 356: CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1, 357: + A( 0 ), N+1 ) 358: END IF 359: ELSE 360: * 361: * N is even and TRANSR = 'T' 362: * 363: IF( LOWER ) THEN 364: * 365: * SRPA for LOWER, TRANSPOSE and N is even (see paper) 366: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) 367: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k 368: * 369: CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO ) 370: IF( INFO.GT.0 ) 371: + RETURN 372: CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K, 373: + A( K*( K+1 ) ), K ) 374: CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO ) 375: IF( INFO.GT.0 ) 376: + INFO = INFO + K 377: IF( INFO.GT.0 ) 378: + RETURN 379: CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K, 380: + A( K*( K+1 ) ), K ) 381: ELSE 382: * 383: * SRPA for UPPER, TRANSPOSE and N is even (see paper) 384: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) 385: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k 386: * 387: CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO ) 388: IF( INFO.GT.0 ) 389: + RETURN 390: CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE, 391: + A( K*( K+1 ) ), K, A( 0 ), K ) 392: CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO ) 393: IF( INFO.GT.0 ) 394: + INFO = INFO + K 395: IF( INFO.GT.0 ) 396: + RETURN 397: CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K, 398: + A( 0 ), K ) 399: END IF 400: END IF 401: END IF 402: * 403: RETURN 404: * 405: * End of DTFTRI 406: * 407: END