Annotation of rpl/lapack/lapack/dtftri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, 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, DIAG
! 13: INTEGER INFO, N
! 14: * ..
! 15: * .. Array Arguments ..
! 16: DOUBLE PRECISION A( 0: * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * DTFTRI computes the inverse of a triangular matrix A stored in RFP
! 23: * format.
! 24: *
! 25: * This is a Level 3 BLAS version of the algorithm.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * TRANSR (input) CHARACTER
! 31: * = 'N': The Normal TRANSR of RFP A is stored;
! 32: * = 'T': The Transpose TRANSR of RFP A is stored.
! 33: *
! 34: * UPLO (input) CHARACTER
! 35: * = 'U': A is upper triangular;
! 36: * = 'L': A is lower triangular.
! 37: *
! 38: * DIAG (input) CHARACTER
! 39: * = 'N': A is non-unit triangular;
! 40: * = 'U': A is unit triangular.
! 41: *
! 42: * N (input) INTEGER
! 43: * The order of the matrix A. N >= 0.
! 44: *
! 45: * A (input/output) DOUBLE PRECISION array, dimension (0:nt-1);
! 46: * nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
! 47: * Positive Definite matrix A in RFP format. RFP format is
! 48: * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
! 49: * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
! 50: * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
! 51: * the transpose of RFP A as defined when
! 52: * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
! 53: * follows: If UPLO = 'U' the RFP A contains the nt elements of
! 54: * upper packed A; If UPLO = 'L' the RFP A contains the nt
! 55: * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
! 56: * TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
! 57: * even and N is odd. See the Note below for more details.
! 58: *
! 59: * On exit, the (triangular) inverse of the original matrix, in
! 60: * the same storage format.
! 61: *
! 62: * INFO (output) INTEGER
! 63: * = 0: successful exit
! 64: * < 0: if INFO = -i, the i-th argument had an illegal value
! 65: * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 66: * matrix is singular and its inverse can not be computed.
! 67: *
! 68: * Further Details
! 69: * ===============
! 70: *
! 71: * We first consider Rectangular Full Packed (RFP) Format when N is
! 72: * even. We give an example where N = 6.
! 73: *
! 74: * AP is Upper AP is Lower
! 75: *
! 76: * 00 01 02 03 04 05 00
! 77: * 11 12 13 14 15 10 11
! 78: * 22 23 24 25 20 21 22
! 79: * 33 34 35 30 31 32 33
! 80: * 44 45 40 41 42 43 44
! 81: * 55 50 51 52 53 54 55
! 82: *
! 83: *
! 84: * Let TRANSR = 'N'. RFP holds AP as follows:
! 85: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 86: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 87: * the transpose of the first three columns of AP upper.
! 88: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 89: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 90: * the transpose of the last three columns of AP lower.
! 91: * This covers the case N even and TRANSR = 'N'.
! 92: *
! 93: * RFP A RFP A
! 94: *
! 95: * 03 04 05 33 43 53
! 96: * 13 14 15 00 44 54
! 97: * 23 24 25 10 11 55
! 98: * 33 34 35 20 21 22
! 99: * 00 44 45 30 31 32
! 100: * 01 11 55 40 41 42
! 101: * 02 12 22 50 51 52
! 102: *
! 103: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 104: * transpose of RFP A above. One therefore gets:
! 105: *
! 106: *
! 107: * RFP A RFP A
! 108: *
! 109: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 110: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 111: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 112: *
! 113: *
! 114: * We then consider Rectangular Full Packed (RFP) Format when N is
! 115: * odd. We give an example where N = 5.
! 116: *
! 117: * AP is Upper AP is Lower
! 118: *
! 119: * 00 01 02 03 04 00
! 120: * 11 12 13 14 10 11
! 121: * 22 23 24 20 21 22
! 122: * 33 34 30 31 32 33
! 123: * 44 40 41 42 43 44
! 124: *
! 125: *
! 126: * Let TRANSR = 'N'. RFP holds AP as follows:
! 127: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 128: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 129: * the transpose of the first two columns of AP upper.
! 130: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 131: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 132: * the transpose of the last two columns of AP lower.
! 133: * This covers the case N odd and TRANSR = 'N'.
! 134: *
! 135: * RFP A RFP A
! 136: *
! 137: * 02 03 04 00 33 43
! 138: * 12 13 14 10 11 44
! 139: * 22 23 24 20 21 22
! 140: * 00 33 34 30 31 32
! 141: * 01 11 44 40 41 42
! 142: *
! 143: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 144: * transpose of RFP A above. One therefore gets:
! 145: *
! 146: * RFP A RFP A
! 147: *
! 148: * 02 12 22 00 01 00 10 20 30 40 50
! 149: * 03 13 23 33 11 33 11 21 31 41 51
! 150: * 04 14 24 34 44 43 44 22 32 42 52
! 151: *
! 152: * =====================================================================
! 153: *
! 154: * .. Parameters ..
! 155: DOUBLE PRECISION ONE
! 156: PARAMETER ( ONE = 1.0D+0 )
! 157: * ..
! 158: * .. Local Scalars ..
! 159: LOGICAL LOWER, NISODD, NORMALTRANSR
! 160: INTEGER N1, N2, K
! 161: * ..
! 162: * .. External Functions ..
! 163: LOGICAL LSAME
! 164: EXTERNAL LSAME
! 165: * ..
! 166: * .. External Subroutines ..
! 167: EXTERNAL XERBLA, DTRMM, DTRTRI
! 168: * ..
! 169: * .. Intrinsic Functions ..
! 170: INTRINSIC MOD
! 171: * ..
! 172: * .. Executable Statements ..
! 173: *
! 174: * Test the input parameters.
! 175: *
! 176: INFO = 0
! 177: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 178: LOWER = LSAME( UPLO, 'L' )
! 179: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
! 180: INFO = -1
! 181: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 182: INFO = -2
! 183: ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
! 184: + THEN
! 185: INFO = -3
! 186: ELSE IF( N.LT.0 ) THEN
! 187: INFO = -4
! 188: END IF
! 189: IF( INFO.NE.0 ) THEN
! 190: CALL XERBLA( 'DTFTRI', -INFO )
! 191: RETURN
! 192: END IF
! 193: *
! 194: * Quick return if possible
! 195: *
! 196: IF( N.EQ.0 )
! 197: + RETURN
! 198: *
! 199: * If N is odd, set NISODD = .TRUE.
! 200: * If N is even, set K = N/2 and NISODD = .FALSE.
! 201: *
! 202: IF( MOD( N, 2 ).EQ.0 ) THEN
! 203: K = N / 2
! 204: NISODD = .FALSE.
! 205: ELSE
! 206: NISODD = .TRUE.
! 207: END IF
! 208: *
! 209: * Set N1 and N2 depending on LOWER
! 210: *
! 211: IF( LOWER ) THEN
! 212: N2 = N / 2
! 213: N1 = N - N2
! 214: ELSE
! 215: N1 = N / 2
! 216: N2 = N - N1
! 217: END IF
! 218: *
! 219: *
! 220: * start execution: there are eight cases
! 221: *
! 222: IF( NISODD ) THEN
! 223: *
! 224: * N is odd
! 225: *
! 226: IF( NORMALTRANSR ) THEN
! 227: *
! 228: * N is odd and TRANSR = 'N'
! 229: *
! 230: IF( LOWER ) THEN
! 231: *
! 232: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 233: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 234: * T1 -> a(0), T2 -> a(n), S -> a(n1)
! 235: *
! 236: CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
! 237: IF( INFO.GT.0 )
! 238: + RETURN
! 239: CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
! 240: + N, A( N1 ), N )
! 241: CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
! 242: IF( INFO.GT.0 )
! 243: + INFO = INFO + N1
! 244: IF( INFO.GT.0 )
! 245: + RETURN
! 246: CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
! 247: + A( N1 ), N )
! 248: *
! 249: ELSE
! 250: *
! 251: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 252: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 253: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
! 254: *
! 255: CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
! 256: IF( INFO.GT.0 )
! 257: + RETURN
! 258: CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
! 259: + N, A( 0 ), N )
! 260: CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
! 261: IF( INFO.GT.0 )
! 262: + INFO = INFO + N1
! 263: IF( INFO.GT.0 )
! 264: + RETURN
! 265: CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
! 266: + N, A( 0 ), N )
! 267: *
! 268: END IF
! 269: *
! 270: ELSE
! 271: *
! 272: * N is odd and TRANSR = 'T'
! 273: *
! 274: IF( LOWER ) THEN
! 275: *
! 276: * SRPA for LOWER, TRANSPOSE and N is odd
! 277: * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
! 278: *
! 279: CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
! 280: IF( INFO.GT.0 )
! 281: + RETURN
! 282: CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
! 283: + N1, A( N1*N1 ), N1 )
! 284: CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
! 285: IF( INFO.GT.0 )
! 286: + INFO = INFO + N1
! 287: IF( INFO.GT.0 )
! 288: + RETURN
! 289: CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
! 290: + N1, A( N1*N1 ), N1 )
! 291: *
! 292: ELSE
! 293: *
! 294: * SRPA for UPPER, TRANSPOSE and N is odd
! 295: * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
! 296: *
! 297: CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
! 298: IF( INFO.GT.0 )
! 299: + RETURN
! 300: CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
! 301: + A( N2*N2 ), N2, A( 0 ), N2 )
! 302: CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
! 303: IF( INFO.GT.0 )
! 304: + INFO = INFO + N1
! 305: IF( INFO.GT.0 )
! 306: + RETURN
! 307: CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
! 308: + A( N1*N2 ), N2, A( 0 ), N2 )
! 309: END IF
! 310: *
! 311: END IF
! 312: *
! 313: ELSE
! 314: *
! 315: * N is even
! 316: *
! 317: IF( NORMALTRANSR ) THEN
! 318: *
! 319: * N is even and TRANSR = 'N'
! 320: *
! 321: IF( LOWER ) THEN
! 322: *
! 323: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 324: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 325: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
! 326: *
! 327: CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
! 328: IF( INFO.GT.0 )
! 329: + RETURN
! 330: CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
! 331: + N+1, A( K+1 ), N+1 )
! 332: CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
! 333: IF( INFO.GT.0 )
! 334: + INFO = INFO + K
! 335: IF( INFO.GT.0 )
! 336: + RETURN
! 337: CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
! 338: + A( K+1 ), N+1 )
! 339: *
! 340: ELSE
! 341: *
! 342: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 343: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 344: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
! 345: *
! 346: CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
! 347: IF( INFO.GT.0 )
! 348: + RETURN
! 349: CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
! 350: + N+1, A( 0 ), N+1 )
! 351: CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
! 352: IF( INFO.GT.0 )
! 353: + INFO = INFO + K
! 354: IF( INFO.GT.0 )
! 355: + RETURN
! 356: CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
! 357: + A( 0 ), N+1 )
! 358: END IF
! 359: ELSE
! 360: *
! 361: * N is even and TRANSR = 'T'
! 362: *
! 363: IF( LOWER ) THEN
! 364: *
! 365: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
! 366: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
! 367: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
! 368: *
! 369: CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO )
! 370: IF( INFO.GT.0 )
! 371: + RETURN
! 372: CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
! 373: + A( K*( K+1 ) ), K )
! 374: CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
! 375: IF( INFO.GT.0 )
! 376: + INFO = INFO + K
! 377: IF( INFO.GT.0 )
! 378: + RETURN
! 379: CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
! 380: + A( K*( K+1 ) ), K )
! 381: ELSE
! 382: *
! 383: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
! 384: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
! 385: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
! 386: *
! 387: CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
! 388: IF( INFO.GT.0 )
! 389: + RETURN
! 390: CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
! 391: + A( K*( K+1 ) ), K, A( 0 ), K )
! 392: CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
! 393: IF( INFO.GT.0 )
! 394: + INFO = INFO + K
! 395: IF( INFO.GT.0 )
! 396: + RETURN
! 397: CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
! 398: + A( 0 ), K )
! 399: END IF
! 400: END IF
! 401: END IF
! 402: *
! 403: RETURN
! 404: *
! 405: * End of DTFTRI
! 406: *
! 407: END
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