Annotation of rpl/lapack/lapack/ztfttr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.1) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- April 2009 --
! 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: COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZTFTTR 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: * = 'C': ARF is in Conjugate-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 matrix A. N >= 0.
! 38: *
! 39: * ARF (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 40: * On entry, the upper or lower triangular matrix A stored in
! 41: * RFP format. For a further discussion see Notes below.
! 42: *
! 43: * A (output) COMPLEX*16 array, dimension ( LDA, N )
! 44: * On exit, the triangular matrix A. If UPLO = 'U', the
! 45: * leading N-by-N upper triangular part of the array A contains
! 46: * the upper triangular matrix, and the strictly lower
! 47: * triangular part of A is not referenced. If UPLO = 'L', the
! 48: * leading N-by-N lower triangular part of the array A contains
! 49: * the lower triangular matrix, and the strictly upper
! 50: * triangular part of A is not referenced.
! 51: *
! 52: * LDA (input) INTEGER
! 53: * The leading dimension of the array A. LDA >= max(1,N).
! 54: *
! 55: * INFO (output) INTEGER
! 56: * = 0: successful exit
! 57: * < 0: if INFO = -i, the i-th argument had an illegal value
! 58: *
! 59: * Further Details
! 60: * ===============
! 61: *
! 62: * We first consider Standard Packed Format when N is even.
! 63: * We give an example where N = 6.
! 64: *
! 65: * AP is Upper AP is Lower
! 66: *
! 67: * 00 01 02 03 04 05 00
! 68: * 11 12 13 14 15 10 11
! 69: * 22 23 24 25 20 21 22
! 70: * 33 34 35 30 31 32 33
! 71: * 44 45 40 41 42 43 44
! 72: * 55 50 51 52 53 54 55
! 73: *
! 74: *
! 75: * Let TRANSR = 'N'. RFP holds AP as follows:
! 76: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 77: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 78: * conjugate-transpose of the first three columns of AP upper.
! 79: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 80: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 81: * conjugate-transpose of the last three columns of AP lower.
! 82: * To denote conjugate we place -- above the element. This covers the
! 83: * case N even and TRANSR = 'N'.
! 84: *
! 85: * RFP A RFP A
! 86: *
! 87: * -- -- --
! 88: * 03 04 05 33 43 53
! 89: * -- --
! 90: * 13 14 15 00 44 54
! 91: * --
! 92: * 23 24 25 10 11 55
! 93: *
! 94: * 33 34 35 20 21 22
! 95: * --
! 96: * 00 44 45 30 31 32
! 97: * -- --
! 98: * 01 11 55 40 41 42
! 99: * -- -- --
! 100: * 02 12 22 50 51 52
! 101: *
! 102: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 103: * transpose of RFP A above. One therefore gets:
! 104: *
! 105: *
! 106: * RFP A RFP A
! 107: *
! 108: * -- -- -- -- -- -- -- -- -- --
! 109: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 110: * -- -- -- -- -- -- -- -- -- --
! 111: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 112: * -- -- -- -- -- -- -- -- -- --
! 113: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 114: *
! 115: *
! 116: * We next consider Standard Packed Format when N is odd.
! 117: * We give an example where N = 5.
! 118: *
! 119: * AP is Upper AP is Lower
! 120: *
! 121: * 00 01 02 03 04 00
! 122: * 11 12 13 14 10 11
! 123: * 22 23 24 20 21 22
! 124: * 33 34 30 31 32 33
! 125: * 44 40 41 42 43 44
! 126: *
! 127: *
! 128: * Let TRANSR = 'N'. RFP holds AP as follows:
! 129: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 130: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 131: * conjugate-transpose of the first two columns of AP upper.
! 132: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 133: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 134: * conjugate-transpose of the last two columns of AP lower.
! 135: * To denote conjugate we place -- above the element. This covers the
! 136: * case N odd and TRANSR = 'N'.
! 137: *
! 138: * RFP A RFP A
! 139: *
! 140: * -- --
! 141: * 02 03 04 00 33 43
! 142: * --
! 143: * 12 13 14 10 11 44
! 144: *
! 145: * 22 23 24 20 21 22
! 146: * --
! 147: * 00 33 34 30 31 32
! 148: * -- --
! 149: * 01 11 44 40 41 42
! 150: *
! 151: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 152: * transpose of RFP A above. One therefore gets:
! 153: *
! 154: *
! 155: * RFP A RFP A
! 156: *
! 157: * -- -- -- -- -- -- -- -- --
! 158: * 02 12 22 00 01 00 10 20 30 40 50
! 159: * -- -- -- -- -- -- -- -- --
! 160: * 03 13 23 33 11 33 11 21 31 41 51
! 161: * -- -- -- -- -- -- -- -- --
! 162: * 04 14 24 34 44 43 44 22 32 42 52
! 163: *
! 164: * =====================================================================
! 165: *
! 166: * .. Parameters ..
! 167: * ..
! 168: * .. Local Scalars ..
! 169: LOGICAL LOWER, NISODD, NORMALTRANSR
! 170: INTEGER N1, N2, K, NT, NX2, NP1X2
! 171: INTEGER I, J, L, IJ
! 172: * ..
! 173: * .. External Functions ..
! 174: LOGICAL LSAME
! 175: EXTERNAL LSAME
! 176: * ..
! 177: * .. External Subroutines ..
! 178: EXTERNAL XERBLA
! 179: * ..
! 180: * .. Intrinsic Functions ..
! 181: INTRINSIC DCONJG, MAX, MOD
! 182: * ..
! 183: * .. Executable Statements ..
! 184: *
! 185: * Test the input parameters.
! 186: *
! 187: INFO = 0
! 188: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 189: LOWER = LSAME( UPLO, 'L' )
! 190: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
! 191: INFO = -1
! 192: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 193: INFO = -2
! 194: ELSE IF( N.LT.0 ) THEN
! 195: INFO = -3
! 196: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 197: INFO = -6
! 198: END IF
! 199: IF( INFO.NE.0 ) THEN
! 200: CALL XERBLA( 'ZTFTTR', -INFO )
! 201: RETURN
! 202: END IF
! 203: *
! 204: * Quick return if possible
! 205: *
! 206: IF( N.LE.1 ) THEN
! 207: IF( N.EQ.1 ) THEN
! 208: IF( NORMALTRANSR ) THEN
! 209: A( 0, 0 ) = ARF( 0 )
! 210: ELSE
! 211: A( 0, 0 ) = DCONJG( ARF( 0 ) )
! 212: END IF
! 213: END IF
! 214: RETURN
! 215: END IF
! 216: *
! 217: * Size of array ARF(1:2,0:nt-1)
! 218: *
! 219: NT = N*( N+1 ) / 2
! 220: *
! 221: * set N1 and N2 depending on LOWER: for N even N1=N2=K
! 222: *
! 223: IF( LOWER ) THEN
! 224: N2 = N / 2
! 225: N1 = N - N2
! 226: ELSE
! 227: N1 = N / 2
! 228: N2 = N - N1
! 229: END IF
! 230: *
! 231: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
! 232: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
! 233: * N--by--(N+1)/2.
! 234: *
! 235: IF( MOD( N, 2 ).EQ.0 ) THEN
! 236: K = N / 2
! 237: NISODD = .FALSE.
! 238: IF( .NOT.LOWER )
! 239: + NP1X2 = N + N + 2
! 240: ELSE
! 241: NISODD = .TRUE.
! 242: IF( .NOT.LOWER )
! 243: + NX2 = N + N
! 244: END IF
! 245: *
! 246: IF( NISODD ) THEN
! 247: *
! 248: * N is odd
! 249: *
! 250: IF( NORMALTRANSR ) THEN
! 251: *
! 252: * N is odd and TRANSR = 'N'
! 253: *
! 254: IF( LOWER ) THEN
! 255: *
! 256: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 257: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 258: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
! 259: *
! 260: IJ = 0
! 261: DO J = 0, N2
! 262: DO I = N1, N2 + J
! 263: A( N2+J, I ) = DCONJG( ARF( IJ ) )
! 264: IJ = IJ + 1
! 265: END DO
! 266: DO I = J, N - 1
! 267: A( I, J ) = ARF( IJ )
! 268: IJ = IJ + 1
! 269: END DO
! 270: END DO
! 271: *
! 272: ELSE
! 273: *
! 274: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 275: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 276: * T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
! 277: *
! 278: IJ = NT - N
! 279: DO J = N - 1, N1, -1
! 280: DO I = 0, J
! 281: A( I, J ) = ARF( IJ )
! 282: IJ = IJ + 1
! 283: END DO
! 284: DO L = J - N1, N1 - 1
! 285: A( J-N1, L ) = DCONJG( ARF( IJ ) )
! 286: IJ = IJ + 1
! 287: END DO
! 288: IJ = IJ - NX2
! 289: END DO
! 290: *
! 291: END IF
! 292: *
! 293: ELSE
! 294: *
! 295: * N is odd and TRANSR = 'C'
! 296: *
! 297: IF( LOWER ) THEN
! 298: *
! 299: * SRPA for LOWER, TRANSPOSE and N is odd
! 300: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
! 301: * T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
! 302: *
! 303: IJ = 0
! 304: DO J = 0, N2 - 1
! 305: DO I = 0, J
! 306: A( J, I ) = DCONJG( ARF( IJ ) )
! 307: IJ = IJ + 1
! 308: END DO
! 309: DO I = N1 + J, N - 1
! 310: A( I, N1+J ) = ARF( IJ )
! 311: IJ = IJ + 1
! 312: END DO
! 313: END DO
! 314: DO J = N2, N - 1
! 315: DO I = 0, N1 - 1
! 316: A( J, I ) = DCONJG( ARF( IJ ) )
! 317: IJ = IJ + 1
! 318: END DO
! 319: END DO
! 320: *
! 321: ELSE
! 322: *
! 323: * SRPA for UPPER, TRANSPOSE and N is odd
! 324: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
! 325: * T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda = n2
! 326: *
! 327: IJ = 0
! 328: DO J = 0, N1
! 329: DO I = N1, N - 1
! 330: A( J, I ) = DCONJG( ARF( IJ ) )
! 331: IJ = IJ + 1
! 332: END DO
! 333: END DO
! 334: DO J = 0, N1 - 1
! 335: DO I = 0, J
! 336: A( I, J ) = ARF( IJ )
! 337: IJ = IJ + 1
! 338: END DO
! 339: DO L = N2 + J, N - 1
! 340: A( N2+J, L ) = DCONJG( ARF( IJ ) )
! 341: IJ = IJ + 1
! 342: END DO
! 343: END DO
! 344: *
! 345: END IF
! 346: *
! 347: END IF
! 348: *
! 349: ELSE
! 350: *
! 351: * N is even
! 352: *
! 353: IF( NORMALTRANSR ) THEN
! 354: *
! 355: * N is even and TRANSR = 'N'
! 356: *
! 357: IF( LOWER ) THEN
! 358: *
! 359: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 360: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 361: * T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
! 362: *
! 363: IJ = 0
! 364: DO J = 0, K - 1
! 365: DO I = K, K + J
! 366: A( K+J, I ) = DCONJG( ARF( IJ ) )
! 367: IJ = IJ + 1
! 368: END DO
! 369: DO I = J, N - 1
! 370: A( I, J ) = ARF( IJ )
! 371: IJ = IJ + 1
! 372: END DO
! 373: END DO
! 374: *
! 375: ELSE
! 376: *
! 377: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 378: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 379: * T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
! 380: *
! 381: IJ = NT - N - 1
! 382: DO J = N - 1, K, -1
! 383: DO I = 0, J
! 384: A( I, J ) = ARF( IJ )
! 385: IJ = IJ + 1
! 386: END DO
! 387: DO L = J - K, K - 1
! 388: A( J-K, L ) = DCONJG( ARF( IJ ) )
! 389: IJ = IJ + 1
! 390: END DO
! 391: IJ = IJ - NP1X2
! 392: END DO
! 393: *
! 394: END IF
! 395: *
! 396: ELSE
! 397: *
! 398: * N is even and TRANSR = 'C'
! 399: *
! 400: IF( LOWER ) THEN
! 401: *
! 402: * SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
! 403: * T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
! 404: * T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
! 405: *
! 406: IJ = 0
! 407: J = K
! 408: DO I = K, N - 1
! 409: A( I, J ) = ARF( IJ )
! 410: IJ = IJ + 1
! 411: END DO
! 412: DO J = 0, K - 2
! 413: DO I = 0, J
! 414: A( J, I ) = DCONJG( ARF( IJ ) )
! 415: IJ = IJ + 1
! 416: END DO
! 417: DO I = K + 1 + J, N - 1
! 418: A( I, K+1+J ) = ARF( IJ )
! 419: IJ = IJ + 1
! 420: END DO
! 421: END DO
! 422: DO J = K - 1, N - 1
! 423: DO I = 0, K - 1
! 424: A( J, I ) = DCONJG( ARF( IJ ) )
! 425: IJ = IJ + 1
! 426: END DO
! 427: END DO
! 428: *
! 429: ELSE
! 430: *
! 431: * SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
! 432: * T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
! 433: * T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
! 434: *
! 435: IJ = 0
! 436: DO J = 0, K
! 437: DO I = K, N - 1
! 438: A( J, I ) = DCONJG( ARF( IJ ) )
! 439: IJ = IJ + 1
! 440: END DO
! 441: END DO
! 442: DO J = 0, K - 2
! 443: DO I = 0, J
! 444: A( I, J ) = ARF( IJ )
! 445: IJ = IJ + 1
! 446: END DO
! 447: DO L = K + 1 + J, N - 1
! 448: A( K+1+J, L ) = DCONJG( ARF( IJ ) )
! 449: IJ = IJ + 1
! 450: END DO
! 451: END DO
! 452: *
! 453: * Note that here J = K-1
! 454: *
! 455: DO I = 0, J
! 456: A( I, J ) = ARF( IJ )
! 457: IJ = IJ + 1
! 458: END DO
! 459: *
! 460: END IF
! 461: *
! 462: END IF
! 463: *
! 464: END IF
! 465: *
! 466: RETURN
! 467: *
! 468: * End of ZTFTTR
! 469: *
! 470: END
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