![]() ![]() | ![]() |
Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZPFTRF( TRANSR, UPLO, 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: * .. 12: * .. Scalar Arguments .. 13: CHARACTER TRANSR, UPLO 14: INTEGER N, INFO 15: * .. 16: * .. Array Arguments .. 17: COMPLEX*16 A( 0: * ) 18: * 19: * Purpose 20: * ======= 21: * 22: * ZPFTRF computes the Cholesky factorization of a complex Hermitian 23: * positive definite matrix A. 24: * 25: * The factorization has the form 26: * A = U**H * U, if UPLO = 'U', or 27: * A = L * L**H, if UPLO = 'L', 28: * where U is an upper triangular matrix and L is lower triangular. 29: * 30: * This is the block version of the algorithm, calling Level 3 BLAS. 31: * 32: * Arguments 33: * ========= 34: * 35: * TRANSR (input) CHARACTER*1 36: * = 'N': The Normal TRANSR of RFP A is stored; 37: * = 'C': The Conjugate-transpose TRANSR of RFP A is stored. 38: * 39: * UPLO (input) CHARACTER*1 40: * = 'U': Upper triangle of RFP A is stored; 41: * = 'L': Lower triangle of RFP A is stored. 42: * 43: * N (input) INTEGER 44: * The order of the matrix A. N >= 0. 45: * 46: * A (input/output) COMPLEX array, dimension ( N*(N+1)/2 ); 47: * On entry, the Hermitian 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 = 'C' then RFP is 51: * the Conjugate-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 elements 55: * of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = 56: * 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N 57: * is odd. See the Note below for more details. 58: * 59: * On exit, if INFO = 0, the factor U or L from the Cholesky 60: * factorization RFP A = U**H*U or RFP A = L*L**H. 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, the leading minor of order i is not 66: * positive definite, and the factorization could not be 67: * completed. 68: * 69: * Further Notes on RFP Format: 70: * ============================ 71: * 72: * We first consider Standard Packed Format when N is even. 73: * We give an example where N = 6. 74: * 75: * AP is Upper AP is Lower 76: * 77: * 00 01 02 03 04 05 00 78: * 11 12 13 14 15 10 11 79: * 22 23 24 25 20 21 22 80: * 33 34 35 30 31 32 33 81: * 44 45 40 41 42 43 44 82: * 55 50 51 52 53 54 55 83: * 84: * 85: * Let TRANSR = 'N'. RFP holds AP as follows: 86: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 87: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of 88: * conjugate-transpose of the first three columns of AP upper. 89: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 90: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of 91: * conjugate-transpose of the last three columns of AP lower. 92: * To denote conjugate we place -- above the element. This covers the 93: * case N even and TRANSR = 'N'. 94: * 95: * RFP A RFP A 96: * 97: * -- -- -- 98: * 03 04 05 33 43 53 99: * -- -- 100: * 13 14 15 00 44 54 101: * -- 102: * 23 24 25 10 11 55 103: * 104: * 33 34 35 20 21 22 105: * -- 106: * 00 44 45 30 31 32 107: * -- -- 108: * 01 11 55 40 41 42 109: * -- -- -- 110: * 02 12 22 50 51 52 111: * 112: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 113: * transpose of RFP A above. One therefore gets: 114: * 115: * 116: * RFP A RFP A 117: * 118: * -- -- -- -- -- -- -- -- -- -- 119: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50 120: * -- -- -- -- -- -- -- -- -- -- 121: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51 122: * -- -- -- -- -- -- -- -- -- -- 123: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52 124: * 125: * 126: * We next consider Standard Packed Format when N is odd. 127: * We give an example where N = 5. 128: * 129: * AP is Upper AP is Lower 130: * 131: * 00 01 02 03 04 00 132: * 11 12 13 14 10 11 133: * 22 23 24 20 21 22 134: * 33 34 30 31 32 33 135: * 44 40 41 42 43 44 136: * 137: * 138: * Let TRANSR = 'N'. RFP holds AP as follows: 139: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 140: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of 141: * conjugate-transpose of the first two columns of AP upper. 142: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 143: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of 144: * conjugate-transpose of the last two columns of AP lower. 145: * To denote conjugate we place -- above the element. This covers the 146: * case N odd and TRANSR = 'N'. 147: * 148: * RFP A RFP A 149: * 150: * -- -- 151: * 02 03 04 00 33 43 152: * -- 153: * 12 13 14 10 11 44 154: * 155: * 22 23 24 20 21 22 156: * -- 157: * 00 33 34 30 31 32 158: * -- -- 159: * 01 11 44 40 41 42 160: * 161: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 162: * transpose of RFP A above. One therefore gets: 163: * 164: * 165: * RFP A RFP A 166: * 167: * -- -- -- -- -- -- -- -- -- 168: * 02 12 22 00 01 00 10 20 30 40 50 169: * -- -- -- -- -- -- -- -- -- 170: * 03 13 23 33 11 33 11 21 31 41 51 171: * -- -- -- -- -- -- -- -- -- 172: * 04 14 24 34 44 43 44 22 32 42 52 173: * 174: * ===================================================================== 175: * 176: * .. Parameters .. 177: DOUBLE PRECISION ONE 178: COMPLEX*16 CONE 179: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) ) 180: * .. 181: * .. Local Scalars .. 182: LOGICAL LOWER, NISODD, NORMALTRANSR 183: INTEGER N1, N2, K 184: * .. 185: * .. External Functions .. 186: LOGICAL LSAME 187: EXTERNAL LSAME 188: * .. 189: * .. External Subroutines .. 190: EXTERNAL XERBLA, ZHERK, ZPOTRF, ZTRSM 191: * .. 192: * .. Intrinsic Functions .. 193: INTRINSIC MOD 194: * .. 195: * .. Executable Statements .. 196: * 197: * Test the input parameters. 198: * 199: INFO = 0 200: NORMALTRANSR = LSAME( TRANSR, 'N' ) 201: LOWER = LSAME( UPLO, 'L' ) 202: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN 203: INFO = -1 204: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN 205: INFO = -2 206: ELSE IF( N.LT.0 ) THEN 207: INFO = -3 208: END IF 209: IF( INFO.NE.0 ) THEN 210: CALL XERBLA( 'ZPFTRF', -INFO ) 211: RETURN 212: END IF 213: * 214: * Quick return if possible 215: * 216: IF( N.EQ.0 ) 217: + RETURN 218: * 219: * If N is odd, set NISODD = .TRUE. 220: * If N is even, set K = N/2 and NISODD = .FALSE. 221: * 222: IF( MOD( N, 2 ).EQ.0 ) THEN 223: K = N / 2 224: NISODD = .FALSE. 225: ELSE 226: NISODD = .TRUE. 227: END IF 228: * 229: * Set N1 and N2 depending on LOWER 230: * 231: IF( LOWER ) THEN 232: N2 = N / 2 233: N1 = N - N2 234: ELSE 235: N1 = N / 2 236: N2 = N - N1 237: END IF 238: * 239: * start execution: there are eight cases 240: * 241: IF( NISODD ) THEN 242: * 243: * N is odd 244: * 245: IF( NORMALTRANSR ) THEN 246: * 247: * N is odd and TRANSR = 'N' 248: * 249: IF( LOWER ) THEN 250: * 251: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) 252: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) 253: * T1 -> a(0), T2 -> a(n), S -> a(n1) 254: * 255: CALL ZPOTRF( 'L', N1, A( 0 ), N, INFO ) 256: IF( INFO.GT.0 ) 257: + RETURN 258: CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE, A( 0 ), N, 259: + A( N1 ), N ) 260: CALL ZHERK( 'U', 'N', N2, N1, -ONE, A( N1 ), N, ONE, 261: + A( N ), N ) 262: CALL ZPOTRF( 'U', N2, A( N ), N, INFO ) 263: IF( INFO.GT.0 ) 264: + INFO = INFO + N1 265: * 266: ELSE 267: * 268: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) 269: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) 270: * T1 -> a(n2), T2 -> a(n1), S -> a(0) 271: * 272: CALL ZPOTRF( 'L', N1, A( N2 ), N, INFO ) 273: IF( INFO.GT.0 ) 274: + RETURN 275: CALL ZTRSM( 'L', 'L', 'N', 'N', N1, N2, CONE, A( N2 ), N, 276: + A( 0 ), N ) 277: CALL ZHERK( 'U', 'C', N2, N1, -ONE, A( 0 ), N, ONE, 278: + A( N1 ), N ) 279: CALL ZPOTRF( 'U', N2, A( N1 ), N, INFO ) 280: IF( INFO.GT.0 ) 281: + INFO = INFO + N1 282: * 283: END IF 284: * 285: ELSE 286: * 287: * N is odd and TRANSR = 'C' 288: * 289: IF( LOWER ) THEN 290: * 291: * SRPA for LOWER, TRANSPOSE and N is odd 292: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) 293: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 294: * 295: CALL ZPOTRF( 'U', N1, A( 0 ), N1, INFO ) 296: IF( INFO.GT.0 ) 297: + RETURN 298: CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE, A( 0 ), N1, 299: + A( N1*N1 ), N1 ) 300: CALL ZHERK( 'L', 'C', N2, N1, -ONE, A( N1*N1 ), N1, ONE, 301: + A( 1 ), N1 ) 302: CALL ZPOTRF( 'L', N2, A( 1 ), N1, INFO ) 303: IF( INFO.GT.0 ) 304: + INFO = INFO + N1 305: * 306: ELSE 307: * 308: * SRPA for UPPER, TRANSPOSE and N is odd 309: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) 310: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 311: * 312: CALL ZPOTRF( 'U', N1, A( N2*N2 ), N2, INFO ) 313: IF( INFO.GT.0 ) 314: + RETURN 315: CALL ZTRSM( 'R', 'U', 'N', 'N', N2, N1, CONE, A( N2*N2 ), 316: + N2, A( 0 ), N2 ) 317: CALL ZHERK( 'L', 'N', N2, N1, -ONE, A( 0 ), N2, ONE, 318: + A( N1*N2 ), N2 ) 319: CALL ZPOTRF( 'L', N2, A( N1*N2 ), N2, INFO ) 320: IF( INFO.GT.0 ) 321: + INFO = INFO + N1 322: * 323: END IF 324: * 325: END IF 326: * 327: ELSE 328: * 329: * N is even 330: * 331: IF( NORMALTRANSR ) THEN 332: * 333: * N is even and TRANSR = 'N' 334: * 335: IF( LOWER ) THEN 336: * 337: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) 338: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) 339: * T1 -> a(1), T2 -> a(0), S -> a(k+1) 340: * 341: CALL ZPOTRF( 'L', K, A( 1 ), N+1, INFO ) 342: IF( INFO.GT.0 ) 343: + RETURN 344: CALL ZTRSM( 'R', 'L', 'C', 'N', K, K, CONE, A( 1 ), N+1, 345: + A( K+1 ), N+1 ) 346: CALL ZHERK( 'U', 'N', K, K, -ONE, A( K+1 ), N+1, ONE, 347: + A( 0 ), N+1 ) 348: CALL ZPOTRF( 'U', K, A( 0 ), N+1, INFO ) 349: IF( INFO.GT.0 ) 350: + INFO = INFO + K 351: * 352: ELSE 353: * 354: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) 355: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) 356: * T1 -> a(k+1), T2 -> a(k), S -> a(0) 357: * 358: CALL ZPOTRF( 'L', K, A( K+1 ), N+1, INFO ) 359: IF( INFO.GT.0 ) 360: + RETURN 361: CALL ZTRSM( 'L', 'L', 'N', 'N', K, K, CONE, A( K+1 ), 362: + N+1, A( 0 ), N+1 ) 363: CALL ZHERK( 'U', 'C', K, K, -ONE, A( 0 ), N+1, ONE, 364: + A( K ), N+1 ) 365: CALL ZPOTRF( 'U', K, A( K ), N+1, INFO ) 366: IF( INFO.GT.0 ) 367: + INFO = INFO + K 368: * 369: END IF 370: * 371: ELSE 372: * 373: * N is even and TRANSR = 'C' 374: * 375: IF( LOWER ) THEN 376: * 377: * SRPA for LOWER, TRANSPOSE and N is even (see paper) 378: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) 379: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k 380: * 381: CALL ZPOTRF( 'U', K, A( 0+K ), K, INFO ) 382: IF( INFO.GT.0 ) 383: + RETURN 384: CALL ZTRSM( 'L', 'U', 'C', 'N', K, K, CONE, A( K ), N1, 385: + A( K*( K+1 ) ), K ) 386: CALL ZHERK( 'L', 'C', K, K, -ONE, A( K*( K+1 ) ), K, ONE, 387: + A( 0 ), K ) 388: CALL ZPOTRF( 'L', K, A( 0 ), K, INFO ) 389: IF( INFO.GT.0 ) 390: + INFO = INFO + K 391: * 392: ELSE 393: * 394: * SRPA for UPPER, TRANSPOSE and N is even (see paper) 395: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) 396: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k 397: * 398: CALL ZPOTRF( 'U', K, A( K*( K+1 ) ), K, INFO ) 399: IF( INFO.GT.0 ) 400: + RETURN 401: CALL ZTRSM( 'R', 'U', 'N', 'N', K, K, CONE, 402: + A( K*( K+1 ) ), K, A( 0 ), K ) 403: CALL ZHERK( 'L', 'N', K, K, -ONE, A( 0 ), K, ONE, 404: + A( K*K ), K ) 405: CALL ZPOTRF( 'L', K, A( K*K ), K, INFO ) 406: IF( INFO.GT.0 ) 407: + INFO = INFO + K 408: * 409: END IF 410: * 411: END IF 412: * 413: END IF 414: * 415: RETURN 416: * 417: * End of ZPFTRF 418: * 419: END