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