Annotation of rpl/lapack/lapack/dtfttr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.2) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- June 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
! 29: * = 'N': ARF is in Normal format;
! 30: * = 'T': ARF is in Transpose format.
! 31: *
! 32: * UPLO (input) CHARACTER
! 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
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