Annotation of rpl/lapack/lapack/ztrttf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, 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: * ZTRTTF copies a triangular matrix A from standard full format (TR)
! 23: * to rectangular full packed format (TF) .
! 24: *
! 25: * Arguments
! 26: * =========
! 27: *
! 28: * TRANSR (input) CHARACTER
! 29: * = 'N': ARF in Normal mode is wanted;
! 30: * = 'C': ARF in Conjugate Transpose mode is wanted;
! 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: * A (input) COMPLEX*16 array, dimension ( LDA, N )
! 40: * On entry, the triangular matrix A. If UPLO = 'U', the
! 41: * leading N-by-N upper triangular part of the array A contains
! 42: * the upper triangular matrix, and the strictly lower
! 43: * triangular part of A is not referenced. If UPLO = 'L', the
! 44: * leading N-by-N lower triangular part of the array A contains
! 45: * the lower triangular matrix, and the strictly upper
! 46: * triangular part of A is not referenced.
! 47: *
! 48: * LDA (input) INTEGER
! 49: * The leading dimension of the matrix A. LDA >= max(1,N).
! 50: *
! 51: * ARF (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
! 52: * On exit, the upper or lower triangular matrix A stored in
! 53: * RFP format. For a further discussion see Notes below.
! 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 I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
! 171: * ..
! 172: * .. External Functions ..
! 173: LOGICAL LSAME
! 174: EXTERNAL LSAME
! 175: * ..
! 176: * .. External Subroutines ..
! 177: EXTERNAL XERBLA
! 178: * ..
! 179: * .. Intrinsic Functions ..
! 180: INTRINSIC DCONJG, MAX, MOD
! 181: * ..
! 182: * .. Executable Statements ..
! 183: *
! 184: * Test the input parameters.
! 185: *
! 186: INFO = 0
! 187: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 188: LOWER = LSAME( UPLO, 'L' )
! 189: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
! 190: INFO = -1
! 191: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 192: INFO = -2
! 193: ELSE IF( N.LT.0 ) THEN
! 194: INFO = -3
! 195: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 196: INFO = -5
! 197: END IF
! 198: IF( INFO.NE.0 ) THEN
! 199: CALL XERBLA( 'ZTRTTF', -INFO )
! 200: RETURN
! 201: END IF
! 202: *
! 203: * Quick return if possible
! 204: *
! 205: IF( N.LE.1 ) THEN
! 206: IF( N.EQ.1 ) THEN
! 207: IF( NORMALTRANSR ) THEN
! 208: ARF( 0 ) = A( 0, 0 )
! 209: ELSE
! 210: ARF( 0 ) = DCONJG( A( 0, 0 ) )
! 211: END IF
! 212: END IF
! 213: RETURN
! 214: END IF
! 215: *
! 216: * Size of array ARF(1:2,0:nt-1)
! 217: *
! 218: NT = N*( N+1 ) / 2
! 219: *
! 220: * set N1 and N2 depending on LOWER: for N even N1=N2=K
! 221: *
! 222: IF( LOWER ) THEN
! 223: N2 = N / 2
! 224: N1 = N - N2
! 225: ELSE
! 226: N1 = N / 2
! 227: N2 = N - N1
! 228: END IF
! 229: *
! 230: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
! 231: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
! 232: * N--by--(N+1)/2.
! 233: *
! 234: IF( MOD( N, 2 ).EQ.0 ) THEN
! 235: K = N / 2
! 236: NISODD = .FALSE.
! 237: IF( .NOT.LOWER )
! 238: + NP1X2 = N + N + 2
! 239: ELSE
! 240: NISODD = .TRUE.
! 241: IF( .NOT.LOWER )
! 242: + NX2 = N + N
! 243: END IF
! 244: *
! 245: IF( NISODD ) THEN
! 246: *
! 247: * N is odd
! 248: *
! 249: IF( NORMALTRANSR ) THEN
! 250: *
! 251: * N is odd and TRANSR = 'N'
! 252: *
! 253: IF( LOWER ) THEN
! 254: *
! 255: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 256: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 257: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
! 258: *
! 259: IJ = 0
! 260: DO J = 0, N2
! 261: DO I = N1, N2 + J
! 262: ARF( IJ ) = DCONJG( A( N2+J, I ) )
! 263: IJ = IJ + 1
! 264: END DO
! 265: DO I = J, N - 1
! 266: ARF( IJ ) = A( I, J )
! 267: IJ = IJ + 1
! 268: END DO
! 269: END DO
! 270: *
! 271: ELSE
! 272: *
! 273: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 274: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 275: * T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
! 276: *
! 277: IJ = NT - N
! 278: DO J = N - 1, N1, -1
! 279: DO I = 0, J
! 280: ARF( IJ ) = A( I, J )
! 281: IJ = IJ + 1
! 282: END DO
! 283: DO L = J - N1, N1 - 1
! 284: ARF( IJ ) = DCONJG( A( J-N1, L ) )
! 285: IJ = IJ + 1
! 286: END DO
! 287: IJ = IJ - NX2
! 288: END DO
! 289: *
! 290: END IF
! 291: *
! 292: ELSE
! 293: *
! 294: * N is odd and TRANSR = 'C'
! 295: *
! 296: IF( LOWER ) THEN
! 297: *
! 298: * SRPA for LOWER, TRANSPOSE and N is odd
! 299: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
! 300: * T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
! 301: *
! 302: IJ = 0
! 303: DO J = 0, N2 - 1
! 304: DO I = 0, J
! 305: ARF( IJ ) = DCONJG( A( J, I ) )
! 306: IJ = IJ + 1
! 307: END DO
! 308: DO I = N1 + J, N - 1
! 309: ARF( IJ ) = A( I, N1+J )
! 310: IJ = IJ + 1
! 311: END DO
! 312: END DO
! 313: DO J = N2, N - 1
! 314: DO I = 0, N1 - 1
! 315: ARF( IJ ) = DCONJG( A( J, I ) )
! 316: IJ = IJ + 1
! 317: END DO
! 318: END DO
! 319: *
! 320: ELSE
! 321: *
! 322: * SRPA for UPPER, TRANSPOSE and N is odd
! 323: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
! 324: * T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
! 325: *
! 326: IJ = 0
! 327: DO J = 0, N1
! 328: DO I = N1, N - 1
! 329: ARF( IJ ) = DCONJG( A( J, I ) )
! 330: IJ = IJ + 1
! 331: END DO
! 332: END DO
! 333: DO J = 0, N1 - 1
! 334: DO I = 0, J
! 335: ARF( IJ ) = A( I, J )
! 336: IJ = IJ + 1
! 337: END DO
! 338: DO L = N2 + J, N - 1
! 339: ARF( IJ ) = DCONJG( A( N2+J, L ) )
! 340: IJ = IJ + 1
! 341: END DO
! 342: END DO
! 343: *
! 344: END IF
! 345: *
! 346: END IF
! 347: *
! 348: ELSE
! 349: *
! 350: * N is even
! 351: *
! 352: IF( NORMALTRANSR ) THEN
! 353: *
! 354: * N is even and TRANSR = 'N'
! 355: *
! 356: IF( LOWER ) THEN
! 357: *
! 358: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 359: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 360: * T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
! 361: *
! 362: IJ = 0
! 363: DO J = 0, K - 1
! 364: DO I = K, K + J
! 365: ARF( IJ ) = DCONJG( A( K+J, I ) )
! 366: IJ = IJ + 1
! 367: END DO
! 368: DO I = J, N - 1
! 369: ARF( IJ ) = A( I, J )
! 370: IJ = IJ + 1
! 371: END DO
! 372: END DO
! 373: *
! 374: ELSE
! 375: *
! 376: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 377: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 378: * T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
! 379: *
! 380: IJ = NT - N - 1
! 381: DO J = N - 1, K, -1
! 382: DO I = 0, J
! 383: ARF( IJ ) = A( I, J )
! 384: IJ = IJ + 1
! 385: END DO
! 386: DO L = J - K, K - 1
! 387: ARF( IJ ) = DCONJG( A( J-K, L ) )
! 388: IJ = IJ + 1
! 389: END DO
! 390: IJ = IJ - NP1X2
! 391: END DO
! 392: *
! 393: END IF
! 394: *
! 395: ELSE
! 396: *
! 397: * N is even and TRANSR = 'C'
! 398: *
! 399: IF( LOWER ) THEN
! 400: *
! 401: * SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
! 402: * T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
! 403: * T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
! 404: *
! 405: IJ = 0
! 406: J = K
! 407: DO I = K, N - 1
! 408: ARF( IJ ) = A( I, J )
! 409: IJ = IJ + 1
! 410: END DO
! 411: DO J = 0, K - 2
! 412: DO I = 0, J
! 413: ARF( IJ ) = DCONJG( A( J, I ) )
! 414: IJ = IJ + 1
! 415: END DO
! 416: DO I = K + 1 + J, N - 1
! 417: ARF( IJ ) = A( I, K+1+J )
! 418: IJ = IJ + 1
! 419: END DO
! 420: END DO
! 421: DO J = K - 1, N - 1
! 422: DO I = 0, K - 1
! 423: ARF( IJ ) = DCONJG( A( J, I ) )
! 424: IJ = IJ + 1
! 425: END DO
! 426: END DO
! 427: *
! 428: ELSE
! 429: *
! 430: * SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
! 431: * T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
! 432: * T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
! 433: *
! 434: IJ = 0
! 435: DO J = 0, K
! 436: DO I = K, N - 1
! 437: ARF( IJ ) = DCONJG( A( J, I ) )
! 438: IJ = IJ + 1
! 439: END DO
! 440: END DO
! 441: DO J = 0, K - 2
! 442: DO I = 0, J
! 443: ARF( IJ ) = A( I, J )
! 444: IJ = IJ + 1
! 445: END DO
! 446: DO L = K + 1 + J, N - 1
! 447: ARF( IJ ) = DCONJG( A( K+1+J, L ) )
! 448: IJ = IJ + 1
! 449: END DO
! 450: END DO
! 451: *
! 452: * Note that here J = K-1
! 453: *
! 454: DO I = 0, J
! 455: ARF( IJ ) = A( I, J )
! 456: IJ = IJ + 1
! 457: END DO
! 458: *
! 459: END IF
! 460: *
! 461: END IF
! 462: *
! 463: END IF
! 464: *
! 465: RETURN
! 466: *
! 467: * End of ZTRTTF
! 468: *
! 469: END
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