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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, 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 13: INTEGER INFO, N, LDA 14: * .. 15: * .. Array Arguments .. 16: DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * DTFTTR copies a triangular matrix A from rectangular full packed 23: * format (TF) to standard full format (TR). 24: * 25: * Arguments 26: * ========= 27: * 28: * TRANSR (input) CHARACTER*1 29: * = 'N': ARF is in Normal format; 30: * = 'T': ARF is in Transpose format. 31: * 32: * UPLO (input) CHARACTER*1 33: * = 'U': A is upper triangular; 34: * = 'L': A is lower triangular. 35: * 36: * N (input) INTEGER 37: * The order of the matrices ARF and A. N >= 0. 38: * 39: * ARF (input) DOUBLE PRECISION array, dimension (N*(N+1)/2). 40: * On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') 41: * matrix A in RFP format. See the "Notes" below for more 42: * details. 43: * 44: * A (output) DOUBLE PRECISION array, dimension (LDA,N) 45: * On exit, the triangular matrix A. If UPLO = 'U', the 46: * leading N-by-N upper triangular part of the array A contains 47: * the upper triangular matrix, and the strictly lower 48: * triangular part of A is not referenced. If UPLO = 'L', the 49: * leading N-by-N lower triangular part of the array A contains 50: * the lower triangular matrix, and the strictly upper 51: * triangular part of A is not referenced. 52: * 53: * LDA (input) INTEGER 54: * The leading dimension of the array A. LDA >= 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: * Further Details 61: * =============== 62: * 63: * We first consider Rectangular Full Packed (RFP) Format when N is 64: * even. We give an example where N = 6. 65: * 66: * AP is Upper AP is Lower 67: * 68: * 00 01 02 03 04 05 00 69: * 11 12 13 14 15 10 11 70: * 22 23 24 25 20 21 22 71: * 33 34 35 30 31 32 33 72: * 44 45 40 41 42 43 44 73: * 55 50 51 52 53 54 55 74: * 75: * 76: * Let TRANSR = 'N'. RFP holds AP as follows: 77: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 78: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of 79: * the transpose of the first three columns of AP upper. 80: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 81: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of 82: * the transpose of the last three columns of AP lower. 83: * This covers the case N even and TRANSR = 'N'. 84: * 85: * RFP A RFP A 86: * 87: * 03 04 05 33 43 53 88: * 13 14 15 00 44 54 89: * 23 24 25 10 11 55 90: * 33 34 35 20 21 22 91: * 00 44 45 30 31 32 92: * 01 11 55 40 41 42 93: * 02 12 22 50 51 52 94: * 95: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 96: * transpose of RFP A above. One therefore gets: 97: * 98: * 99: * RFP A RFP A 100: * 101: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50 102: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51 103: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52 104: * 105: * 106: * We then consider Rectangular Full Packed (RFP) Format when N is 107: * odd. We give an example where N = 5. 108: * 109: * AP is Upper AP is Lower 110: * 111: * 00 01 02 03 04 00 112: * 11 12 13 14 10 11 113: * 22 23 24 20 21 22 114: * 33 34 30 31 32 33 115: * 44 40 41 42 43 44 116: * 117: * 118: * Let TRANSR = 'N'. RFP holds AP as follows: 119: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 120: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of 121: * the transpose of the first two columns of AP upper. 122: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 123: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of 124: * the transpose of the last two columns of AP lower. 125: * This covers the case N odd and TRANSR = 'N'. 126: * 127: * RFP A RFP A 128: * 129: * 02 03 04 00 33 43 130: * 12 13 14 10 11 44 131: * 22 23 24 20 21 22 132: * 00 33 34 30 31 32 133: * 01 11 44 40 41 42 134: * 135: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 136: * transpose of RFP A above. One therefore gets: 137: * 138: * RFP A RFP A 139: * 140: * 02 12 22 00 01 00 10 20 30 40 50 141: * 03 13 23 33 11 33 11 21 31 41 51 142: * 04 14 24 34 44 43 44 22 32 42 52 143: * 144: * Reference 145: * ========= 146: * 147: * ===================================================================== 148: * 149: * .. 150: * .. Local Scalars .. 151: LOGICAL LOWER, NISODD, NORMALTRANSR 152: INTEGER N1, N2, K, NT, NX2, NP1X2 153: INTEGER I, J, L, IJ 154: * .. 155: * .. External Functions .. 156: LOGICAL LSAME 157: EXTERNAL LSAME 158: * .. 159: * .. External Subroutines .. 160: EXTERNAL XERBLA 161: * .. 162: * .. Intrinsic Functions .. 163: INTRINSIC MAX, MOD 164: * .. 165: * .. Executable Statements .. 166: * 167: * Test the input parameters. 168: * 169: INFO = 0 170: NORMALTRANSR = LSAME( TRANSR, 'N' ) 171: LOWER = LSAME( UPLO, 'L' ) 172: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN 173: INFO = -1 174: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN 175: INFO = -2 176: ELSE IF( N.LT.0 ) THEN 177: INFO = -3 178: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 179: INFO = -6 180: END IF 181: IF( INFO.NE.0 ) THEN 182: CALL XERBLA( 'DTFTTR', -INFO ) 183: RETURN 184: END IF 185: * 186: * Quick return if possible 187: * 188: IF( N.LE.1 ) THEN 189: IF( N.EQ.1 ) THEN 190: A( 0, 0 ) = ARF( 0 ) 191: END IF 192: RETURN 193: END IF 194: * 195: * Size of array ARF(0:nt-1) 196: * 197: NT = N*( N+1 ) / 2 198: * 199: * set N1 and N2 depending on LOWER: for N even N1=N2=K 200: * 201: IF( LOWER ) THEN 202: N2 = N / 2 203: N1 = N - N2 204: ELSE 205: N1 = N / 2 206: N2 = N - N1 207: END IF 208: * 209: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2. 210: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is 211: * N--by--(N+1)/2. 212: * 213: IF( MOD( N, 2 ).EQ.0 ) THEN 214: K = N / 2 215: NISODD = .FALSE. 216: IF( .NOT.LOWER ) 217: + NP1X2 = N + N + 2 218: ELSE 219: NISODD = .TRUE. 220: IF( .NOT.LOWER ) 221: + NX2 = N + N 222: END IF 223: * 224: IF( NISODD ) THEN 225: * 226: * N is odd 227: * 228: IF( NORMALTRANSR ) THEN 229: * 230: * N is odd and TRANSR = 'N' 231: * 232: IF( LOWER ) THEN 233: * 234: * N is odd, TRANSR = 'N', and UPLO = 'L' 235: * 236: IJ = 0 237: DO J = 0, N2 238: DO I = N1, N2 + J 239: A( N2+J, I ) = ARF( IJ ) 240: IJ = IJ + 1 241: END DO 242: DO I = J, N - 1 243: A( I, J ) = ARF( IJ ) 244: IJ = IJ + 1 245: END DO 246: END DO 247: * 248: ELSE 249: * 250: * N is odd, TRANSR = 'N', and UPLO = 'U' 251: * 252: IJ = NT - N 253: DO J = N - 1, N1, -1 254: DO I = 0, J 255: A( I, J ) = ARF( IJ ) 256: IJ = IJ + 1 257: END DO 258: DO L = J - N1, N1 - 1 259: A( J-N1, L ) = ARF( IJ ) 260: IJ = IJ + 1 261: END DO 262: IJ = IJ - NX2 263: END DO 264: * 265: END IF 266: * 267: ELSE 268: * 269: * N is odd and TRANSR = 'T' 270: * 271: IF( LOWER ) THEN 272: * 273: * N is odd, TRANSR = 'T', and UPLO = 'L' 274: * 275: IJ = 0 276: DO J = 0, N2 - 1 277: DO I = 0, J 278: A( J, I ) = ARF( IJ ) 279: IJ = IJ + 1 280: END DO 281: DO I = N1 + J, N - 1 282: A( I, N1+J ) = ARF( IJ ) 283: IJ = IJ + 1 284: END DO 285: END DO 286: DO J = N2, N - 1 287: DO I = 0, N1 - 1 288: A( J, I ) = ARF( IJ ) 289: IJ = IJ + 1 290: END DO 291: END DO 292: * 293: ELSE 294: * 295: * N is odd, TRANSR = 'T', and UPLO = 'U' 296: * 297: IJ = 0 298: DO J = 0, N1 299: DO I = N1, N - 1 300: A( J, I ) = ARF( IJ ) 301: IJ = IJ + 1 302: END DO 303: END DO 304: DO J = 0, N1 - 1 305: DO I = 0, J 306: A( I, J ) = ARF( IJ ) 307: IJ = IJ + 1 308: END DO 309: DO L = N2 + J, N - 1 310: A( N2+J, L ) = ARF( IJ ) 311: IJ = IJ + 1 312: END DO 313: END DO 314: * 315: END IF 316: * 317: END IF 318: * 319: ELSE 320: * 321: * N is even 322: * 323: IF( NORMALTRANSR ) THEN 324: * 325: * N is even and TRANSR = 'N' 326: * 327: IF( LOWER ) THEN 328: * 329: * N is even, TRANSR = 'N', and UPLO = 'L' 330: * 331: IJ = 0 332: DO J = 0, K - 1 333: DO I = K, K + J 334: A( K+J, I ) = ARF( IJ ) 335: IJ = IJ + 1 336: END DO 337: DO I = J, N - 1 338: A( I, J ) = ARF( IJ ) 339: IJ = IJ + 1 340: END DO 341: END DO 342: * 343: ELSE 344: * 345: * N is even, TRANSR = 'N', and UPLO = 'U' 346: * 347: IJ = NT - N - 1 348: DO J = N - 1, K, -1 349: DO I = 0, J 350: A( I, J ) = ARF( IJ ) 351: IJ = IJ + 1 352: END DO 353: DO L = J - K, K - 1 354: A( J-K, L ) = ARF( IJ ) 355: IJ = IJ + 1 356: END DO 357: IJ = IJ - NP1X2 358: END DO 359: * 360: END IF 361: * 362: ELSE 363: * 364: * N is even and TRANSR = 'T' 365: * 366: IF( LOWER ) THEN 367: * 368: * N is even, TRANSR = 'T', and UPLO = 'L' 369: * 370: IJ = 0 371: J = K 372: DO I = K, N - 1 373: A( I, J ) = ARF( IJ ) 374: IJ = IJ + 1 375: END DO 376: DO J = 0, K - 2 377: DO I = 0, J 378: A( J, I ) = ARF( IJ ) 379: IJ = IJ + 1 380: END DO 381: DO I = K + 1 + J, N - 1 382: A( I, K+1+J ) = ARF( IJ ) 383: IJ = IJ + 1 384: END DO 385: END DO 386: DO J = K - 1, N - 1 387: DO I = 0, K - 1 388: A( J, I ) = ARF( IJ ) 389: IJ = IJ + 1 390: END DO 391: END DO 392: * 393: ELSE 394: * 395: * N is even, TRANSR = 'T', and UPLO = 'U' 396: * 397: IJ = 0 398: DO J = 0, K 399: DO I = K, N - 1 400: A( J, I ) = ARF( IJ ) 401: IJ = IJ + 1 402: END DO 403: END DO 404: DO J = 0, K - 2 405: DO I = 0, J 406: A( I, J ) = ARF( IJ ) 407: IJ = IJ + 1 408: END DO 409: DO L = K + 1 + J, N - 1 410: A( K+1+J, L ) = ARF( IJ ) 411: IJ = IJ + 1 412: END DO 413: END DO 414: * Note that here, on exit of the loop, J = K-1 415: DO I = 0, J 416: A( I, J ) = ARF( IJ ) 417: IJ = IJ + 1 418: END DO 419: * 420: END IF 421: * 422: END IF 423: * 424: END IF 425: * 426: RETURN 427: * 428: * End of DTFTTR 429: * 430: END