Annotation of rpl/lapack/lapack/dtfttp.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, 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: * ..
! 12: * .. Scalar Arguments ..
! 13: CHARACTER TRANSR, UPLO
! 14: INTEGER INFO, N
! 15: * ..
! 16: * .. Array Arguments ..
! 17: DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
! 18: * ..
! 19: *
! 20: * Purpose
! 21: * =======
! 22: *
! 23: * DTFTTP copies a triangular matrix A from rectangular full packed
! 24: * format (TF) to standard packed format (TP).
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * TRANSR (input) CHARACTER
! 30: * = 'N': ARF is in Normal format;
! 31: * = 'T': ARF is in Transpose format;
! 32: *
! 33: * UPLO (input) CHARACTER
! 34: * = 'U': A is upper triangular;
! 35: * = 'L': A is lower triangular.
! 36: *
! 37: * N (input) INTEGER
! 38: * The order of the matrix A. N >= 0.
! 39: *
! 40: * ARF (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
! 41: * On entry, the upper or lower triangular matrix A stored in
! 42: * RFP format. For a further discussion see Notes below.
! 43: *
! 44: * AP (output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
! 45: * On exit, the upper or lower triangular matrix A, packed
! 46: * columnwise in a linear array. The j-th column of A is stored
! 47: * in the array AP as follows:
! 48: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 49: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 50: *
! 51: * INFO (output) INTEGER
! 52: * = 0: successful exit
! 53: * < 0: if INFO = -i, the i-th argument had an illegal value
! 54: *
! 55: * Further Details
! 56: * ===============
! 57: *
! 58: * We first consider Rectangular Full Packed (RFP) Format when N is
! 59: * even. We give an example where N = 6.
! 60: *
! 61: * AP is Upper AP is Lower
! 62: *
! 63: * 00 01 02 03 04 05 00
! 64: * 11 12 13 14 15 10 11
! 65: * 22 23 24 25 20 21 22
! 66: * 33 34 35 30 31 32 33
! 67: * 44 45 40 41 42 43 44
! 68: * 55 50 51 52 53 54 55
! 69: *
! 70: *
! 71: * Let TRANSR = 'N'. RFP holds AP as follows:
! 72: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 73: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 74: * the transpose of the first three columns of AP upper.
! 75: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 76: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 77: * the transpose of the last three columns of AP lower.
! 78: * This covers the case N even and TRANSR = 'N'.
! 79: *
! 80: * RFP A RFP A
! 81: *
! 82: * 03 04 05 33 43 53
! 83: * 13 14 15 00 44 54
! 84: * 23 24 25 10 11 55
! 85: * 33 34 35 20 21 22
! 86: * 00 44 45 30 31 32
! 87: * 01 11 55 40 41 42
! 88: * 02 12 22 50 51 52
! 89: *
! 90: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 91: * transpose of RFP A above. One therefore gets:
! 92: *
! 93: *
! 94: * RFP A RFP A
! 95: *
! 96: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 97: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 98: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 99: *
! 100: *
! 101: * We then consider Rectangular Full Packed (RFP) Format when N is
! 102: * odd. We give an example where N = 5.
! 103: *
! 104: * AP is Upper AP is Lower
! 105: *
! 106: * 00 01 02 03 04 00
! 107: * 11 12 13 14 10 11
! 108: * 22 23 24 20 21 22
! 109: * 33 34 30 31 32 33
! 110: * 44 40 41 42 43 44
! 111: *
! 112: *
! 113: * Let TRANSR = 'N'. RFP holds AP as follows:
! 114: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 115: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 116: * the transpose of the first two columns of AP upper.
! 117: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 118: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 119: * the transpose of the last two columns of AP lower.
! 120: * This covers the case N odd and TRANSR = 'N'.
! 121: *
! 122: * RFP A RFP A
! 123: *
! 124: * 02 03 04 00 33 43
! 125: * 12 13 14 10 11 44
! 126: * 22 23 24 20 21 22
! 127: * 00 33 34 30 31 32
! 128: * 01 11 44 40 41 42
! 129: *
! 130: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 131: * transpose of RFP A above. One therefore gets:
! 132: *
! 133: * RFP A RFP A
! 134: *
! 135: * 02 12 22 00 01 00 10 20 30 40 50
! 136: * 03 13 23 33 11 33 11 21 31 41 51
! 137: * 04 14 24 34 44 43 44 22 32 42 52
! 138: *
! 139: * =====================================================================
! 140: *
! 141: * .. Parameters ..
! 142: * ..
! 143: * .. Local Scalars ..
! 144: LOGICAL LOWER, NISODD, NORMALTRANSR
! 145: INTEGER N1, N2, K, NT
! 146: INTEGER I, J, IJ
! 147: INTEGER IJP, JP, LDA, JS
! 148: * ..
! 149: * .. External Functions ..
! 150: LOGICAL LSAME
! 151: EXTERNAL LSAME
! 152: * ..
! 153: * .. External Subroutines ..
! 154: EXTERNAL XERBLA
! 155: * ..
! 156: * .. Executable Statements ..
! 157: *
! 158: * Test the input parameters.
! 159: *
! 160: INFO = 0
! 161: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 162: LOWER = LSAME( UPLO, 'L' )
! 163: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
! 164: INFO = -1
! 165: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 166: INFO = -2
! 167: ELSE IF( N.LT.0 ) THEN
! 168: INFO = -3
! 169: END IF
! 170: IF( INFO.NE.0 ) THEN
! 171: CALL XERBLA( 'DTFTTP', -INFO )
! 172: RETURN
! 173: END IF
! 174: *
! 175: * Quick return if possible
! 176: *
! 177: IF( N.EQ.0 )
! 178: + RETURN
! 179: *
! 180: IF( N.EQ.1 ) THEN
! 181: IF( NORMALTRANSR ) THEN
! 182: AP( 0 ) = ARF( 0 )
! 183: ELSE
! 184: AP( 0 ) = ARF( 0 )
! 185: END IF
! 186: RETURN
! 187: END IF
! 188: *
! 189: * Size of array ARF(0:NT-1)
! 190: *
! 191: NT = N*( N+1 ) / 2
! 192: *
! 193: * Set N1 and N2 depending on LOWER
! 194: *
! 195: IF( LOWER ) THEN
! 196: N2 = N / 2
! 197: N1 = N - N2
! 198: ELSE
! 199: N1 = N / 2
! 200: N2 = N - N1
! 201: END IF
! 202: *
! 203: * If N is odd, set NISODD = .TRUE.
! 204: * If N is even, set K = N/2 and NISODD = .FALSE.
! 205: *
! 206: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
! 207: * where noe = 0 if n is even, noe = 1 if n is odd
! 208: *
! 209: IF( MOD( N, 2 ).EQ.0 ) THEN
! 210: K = N / 2
! 211: NISODD = .FALSE.
! 212: LDA = N + 1
! 213: ELSE
! 214: NISODD = .TRUE.
! 215: LDA = N
! 216: END IF
! 217: *
! 218: * ARF^C has lda rows and n+1-noe cols
! 219: *
! 220: IF( .NOT.NORMALTRANSR )
! 221: + LDA = ( N+1 ) / 2
! 222: *
! 223: * start execution: there are eight cases
! 224: *
! 225: IF( NISODD ) THEN
! 226: *
! 227: * N is odd
! 228: *
! 229: IF( NORMALTRANSR ) THEN
! 230: *
! 231: * N is odd and TRANSR = 'N'
! 232: *
! 233: IF( LOWER ) THEN
! 234: *
! 235: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 236: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 237: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
! 238: *
! 239: IJP = 0
! 240: JP = 0
! 241: DO J = 0, N2
! 242: DO I = J, N - 1
! 243: IJ = I + JP
! 244: AP( IJP ) = ARF( IJ )
! 245: IJP = IJP + 1
! 246: END DO
! 247: JP = JP + LDA
! 248: END DO
! 249: DO I = 0, N2 - 1
! 250: DO J = 1 + I, N2
! 251: IJ = I + J*LDA
! 252: AP( IJP ) = ARF( IJ )
! 253: IJP = IJP + 1
! 254: END DO
! 255: END DO
! 256: *
! 257: ELSE
! 258: *
! 259: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 260: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 261: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
! 262: *
! 263: IJP = 0
! 264: DO J = 0, N1 - 1
! 265: IJ = N2 + J
! 266: DO I = 0, J
! 267: AP( IJP ) = ARF( IJ )
! 268: IJP = IJP + 1
! 269: IJ = IJ + LDA
! 270: END DO
! 271: END DO
! 272: JS = 0
! 273: DO J = N1, N - 1
! 274: IJ = JS
! 275: DO IJ = JS, JS + J
! 276: AP( IJP ) = ARF( IJ )
! 277: IJP = IJP + 1
! 278: END DO
! 279: JS = JS + LDA
! 280: END DO
! 281: *
! 282: END IF
! 283: *
! 284: ELSE
! 285: *
! 286: * N is odd and TRANSR = 'T'
! 287: *
! 288: IF( LOWER ) THEN
! 289: *
! 290: * SRPA for LOWER, TRANSPOSE and N is odd
! 291: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
! 292: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
! 293: *
! 294: IJP = 0
! 295: DO I = 0, N2
! 296: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
! 297: AP( IJP ) = ARF( IJ )
! 298: IJP = IJP + 1
! 299: END DO
! 300: END DO
! 301: JS = 1
! 302: DO J = 0, N2 - 1
! 303: DO IJ = JS, JS + N2 - J - 1
! 304: AP( IJP ) = ARF( IJ )
! 305: IJP = IJP + 1
! 306: END DO
! 307: JS = JS + LDA + 1
! 308: END DO
! 309: *
! 310: ELSE
! 311: *
! 312: * SRPA for UPPER, TRANSPOSE and N is odd
! 313: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
! 314: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
! 315: *
! 316: IJP = 0
! 317: JS = N2*LDA
! 318: DO J = 0, N1 - 1
! 319: DO IJ = JS, JS + J
! 320: AP( IJP ) = ARF( IJ )
! 321: IJP = IJP + 1
! 322: END DO
! 323: JS = JS + LDA
! 324: END DO
! 325: DO I = 0, N1
! 326: DO IJ = I, I + ( N1+I )*LDA, LDA
! 327: AP( IJP ) = ARF( IJ )
! 328: IJP = IJP + 1
! 329: END DO
! 330: END DO
! 331: *
! 332: END IF
! 333: *
! 334: END IF
! 335: *
! 336: ELSE
! 337: *
! 338: * N is even
! 339: *
! 340: IF( NORMALTRANSR ) THEN
! 341: *
! 342: * N is even and TRANSR = 'N'
! 343: *
! 344: IF( LOWER ) THEN
! 345: *
! 346: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 347: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 348: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
! 349: *
! 350: IJP = 0
! 351: JP = 0
! 352: DO J = 0, K - 1
! 353: DO I = J, N - 1
! 354: IJ = 1 + I + JP
! 355: AP( IJP ) = ARF( IJ )
! 356: IJP = IJP + 1
! 357: END DO
! 358: JP = JP + LDA
! 359: END DO
! 360: DO I = 0, K - 1
! 361: DO J = I, K - 1
! 362: IJ = I + J*LDA
! 363: AP( IJP ) = ARF( IJ )
! 364: IJP = IJP + 1
! 365: END DO
! 366: END DO
! 367: *
! 368: ELSE
! 369: *
! 370: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 371: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 372: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
! 373: *
! 374: IJP = 0
! 375: DO J = 0, K - 1
! 376: IJ = K + 1 + J
! 377: DO I = 0, J
! 378: AP( IJP ) = ARF( IJ )
! 379: IJP = IJP + 1
! 380: IJ = IJ + LDA
! 381: END DO
! 382: END DO
! 383: JS = 0
! 384: DO J = K, N - 1
! 385: IJ = JS
! 386: DO IJ = JS, JS + J
! 387: AP( IJP ) = ARF( IJ )
! 388: IJP = IJP + 1
! 389: END DO
! 390: JS = JS + LDA
! 391: END DO
! 392: *
! 393: END IF
! 394: *
! 395: ELSE
! 396: *
! 397: * N is even and TRANSR = 'T'
! 398: *
! 399: IF( LOWER ) THEN
! 400: *
! 401: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
! 402: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
! 403: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
! 404: *
! 405: IJP = 0
! 406: DO I = 0, K - 1
! 407: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
! 408: AP( IJP ) = ARF( IJ )
! 409: IJP = IJP + 1
! 410: END DO
! 411: END DO
! 412: JS = 0
! 413: DO J = 0, K - 1
! 414: DO IJ = JS, JS + K - J - 1
! 415: AP( IJP ) = ARF( IJ )
! 416: IJP = IJP + 1
! 417: END DO
! 418: JS = JS + LDA + 1
! 419: END DO
! 420: *
! 421: ELSE
! 422: *
! 423: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
! 424: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
! 425: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
! 426: *
! 427: IJP = 0
! 428: JS = ( K+1 )*LDA
! 429: DO J = 0, K - 1
! 430: DO IJ = JS, JS + J
! 431: AP( IJP ) = ARF( IJ )
! 432: IJP = IJP + 1
! 433: END DO
! 434: JS = JS + LDA
! 435: END DO
! 436: DO I = 0, K - 1
! 437: DO IJ = I, I + ( K+I )*LDA, LDA
! 438: AP( IJP ) = ARF( IJ )
! 439: IJP = IJP + 1
! 440: END DO
! 441: END DO
! 442: *
! 443: END IF
! 444: *
! 445: END IF
! 446: *
! 447: END IF
! 448: *
! 449: RETURN
! 450: *
! 451: * End of DTFTTP
! 452: *
! 453: END
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