Annotation of rpl/lapack/lapack/ztftri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, 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, DIAG
! 13: INTEGER INFO, N
! 14: * ..
! 15: * .. Array Arguments ..
! 16: COMPLEX*16 A( 0: * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZTFTRI 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: * = 'C': The Conjugate-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) COMPLEX*16 array, dimension ( N*(N+1)/2 );
! 46: * On entry, the triangular matrix A in RFP format. RFP format
! 47: * is described by TRANSR, UPLO, and N as follows: If TRANSR =
! 48: * 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
! 49: * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
! 50: * the Conjugate-transpose of RFP A as defined when
! 51: * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
! 52: * follows: If UPLO = 'U' the RFP A contains the nt elements of
! 53: * upper packed A; If UPLO = 'L' the RFP A contains the nt
! 54: * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
! 55: * TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
! 56: * even and N is odd. See the Note below for more details.
! 57: *
! 58: * On exit, the (triangular) inverse of the original matrix, in
! 59: * the same storage format.
! 60: *
! 61: * INFO (output) INTEGER
! 62: * = 0: successful exit
! 63: * < 0: if INFO = -i, the i-th argument had an illegal value
! 64: * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 65: * matrix is singular and its inverse can not be computed.
! 66: *
! 67: * Further Details
! 68: * ===============
! 69: *
! 70: * We first consider Standard Packed Format when N is even.
! 71: * We give an example where N = 6.
! 72: *
! 73: * AP is Upper AP is Lower
! 74: *
! 75: * 00 01 02 03 04 05 00
! 76: * 11 12 13 14 15 10 11
! 77: * 22 23 24 25 20 21 22
! 78: * 33 34 35 30 31 32 33
! 79: * 44 45 40 41 42 43 44
! 80: * 55 50 51 52 53 54 55
! 81: *
! 82: *
! 83: * Let TRANSR = 'N'. RFP holds AP as follows:
! 84: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 85: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 86: * conjugate-transpose of the first three columns of AP upper.
! 87: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 88: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 89: * conjugate-transpose of the last three columns of AP lower.
! 90: * To denote conjugate we place -- above the element. This covers the
! 91: * case N even and TRANSR = 'N'.
! 92: *
! 93: * RFP A RFP A
! 94: *
! 95: * -- -- --
! 96: * 03 04 05 33 43 53
! 97: * -- --
! 98: * 13 14 15 00 44 54
! 99: * --
! 100: * 23 24 25 10 11 55
! 101: *
! 102: * 33 34 35 20 21 22
! 103: * --
! 104: * 00 44 45 30 31 32
! 105: * -- --
! 106: * 01 11 55 40 41 42
! 107: * -- -- --
! 108: * 02 12 22 50 51 52
! 109: *
! 110: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 111: * transpose of RFP A above. One therefore gets:
! 112: *
! 113: *
! 114: * RFP A RFP A
! 115: *
! 116: * -- -- -- -- -- -- -- -- -- --
! 117: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 118: * -- -- -- -- -- -- -- -- -- --
! 119: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 120: * -- -- -- -- -- -- -- -- -- --
! 121: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 122: *
! 123: *
! 124: * We next consider Standard Packed Format when N is odd.
! 125: * We give an example where N = 5.
! 126: *
! 127: * AP is Upper AP is Lower
! 128: *
! 129: * 00 01 02 03 04 00
! 130: * 11 12 13 14 10 11
! 131: * 22 23 24 20 21 22
! 132: * 33 34 30 31 32 33
! 133: * 44 40 41 42 43 44
! 134: *
! 135: *
! 136: * Let TRANSR = 'N'. RFP holds AP as follows:
! 137: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 138: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 139: * conjugate-transpose of the first two columns of AP upper.
! 140: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 141: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 142: * conjugate-transpose of the last two columns of AP lower.
! 143: * To denote conjugate we place -- above the element. This covers the
! 144: * case N odd and TRANSR = 'N'.
! 145: *
! 146: * RFP A RFP A
! 147: *
! 148: * -- --
! 149: * 02 03 04 00 33 43
! 150: * --
! 151: * 12 13 14 10 11 44
! 152: *
! 153: * 22 23 24 20 21 22
! 154: * --
! 155: * 00 33 34 30 31 32
! 156: * -- --
! 157: * 01 11 44 40 41 42
! 158: *
! 159: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 160: * transpose of RFP A above. One therefore gets:
! 161: *
! 162: *
! 163: * RFP A RFP A
! 164: *
! 165: * -- -- -- -- -- -- -- -- --
! 166: * 02 12 22 00 01 00 10 20 30 40 50
! 167: * -- -- -- -- -- -- -- -- --
! 168: * 03 13 23 33 11 33 11 21 31 41 51
! 169: * -- -- -- -- -- -- -- -- --
! 170: * 04 14 24 34 44 43 44 22 32 42 52
! 171: *
! 172: * =====================================================================
! 173: *
! 174: * .. Parameters ..
! 175: COMPLEX*16 CONE
! 176: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 177: * ..
! 178: * .. Local Scalars ..
! 179: LOGICAL LOWER, NISODD, NORMALTRANSR
! 180: INTEGER N1, N2, K
! 181: * ..
! 182: * .. External Functions ..
! 183: LOGICAL LSAME
! 184: EXTERNAL LSAME
! 185: * ..
! 186: * .. External Subroutines ..
! 187: EXTERNAL XERBLA, ZTRMM, ZTRTRI
! 188: * ..
! 189: * .. Intrinsic Functions ..
! 190: INTRINSIC MOD
! 191: * ..
! 192: * .. Executable Statements ..
! 193: *
! 194: * Test the input parameters.
! 195: *
! 196: INFO = 0
! 197: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 198: LOWER = LSAME( UPLO, 'L' )
! 199: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
! 200: INFO = -1
! 201: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 202: INFO = -2
! 203: ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
! 204: + THEN
! 205: INFO = -3
! 206: ELSE IF( N.LT.0 ) THEN
! 207: INFO = -4
! 208: END IF
! 209: IF( INFO.NE.0 ) THEN
! 210: CALL XERBLA( 'ZTFTRI', -INFO )
! 211: RETURN
! 212: END IF
! 213: *
! 214: * Quick return if possible
! 215: *
! 216: IF( N.EQ.0 )
! 217: + RETURN
! 218: *
! 219: * If N is odd, set NISODD = .TRUE.
! 220: * If N is even, set K = N/2 and NISODD = .FALSE.
! 221: *
! 222: IF( MOD( N, 2 ).EQ.0 ) THEN
! 223: K = N / 2
! 224: NISODD = .FALSE.
! 225: ELSE
! 226: NISODD = .TRUE.
! 227: END IF
! 228: *
! 229: * Set N1 and N2 depending on LOWER
! 230: *
! 231: IF( LOWER ) THEN
! 232: N2 = N / 2
! 233: N1 = N - N2
! 234: ELSE
! 235: N1 = N / 2
! 236: N2 = N - N1
! 237: END IF
! 238: *
! 239: *
! 240: * start execution: there are eight cases
! 241: *
! 242: IF( NISODD ) THEN
! 243: *
! 244: * N is odd
! 245: *
! 246: IF( NORMALTRANSR ) THEN
! 247: *
! 248: * N is odd and TRANSR = 'N'
! 249: *
! 250: IF( LOWER ) THEN
! 251: *
! 252: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
! 253: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
! 254: * T1 -> a(0), T2 -> a(n), S -> a(n1)
! 255: *
! 256: CALL ZTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
! 257: IF( INFO.GT.0 )
! 258: + RETURN
! 259: CALL ZTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
! 260: + N, A( N1 ), N )
! 261: CALL ZTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
! 262: IF( INFO.GT.0 )
! 263: + INFO = INFO + N1
! 264: IF( INFO.GT.0 )
! 265: + RETURN
! 266: CALL ZTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
! 267: + A( N1 ), N )
! 268: *
! 269: ELSE
! 270: *
! 271: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
! 272: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
! 273: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
! 274: *
! 275: CALL ZTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
! 276: IF( INFO.GT.0 )
! 277: + RETURN
! 278: CALL ZTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
! 279: + N, A( 0 ), N )
! 280: CALL ZTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
! 281: IF( INFO.GT.0 )
! 282: + INFO = INFO + N1
! 283: IF( INFO.GT.0 )
! 284: + RETURN
! 285: CALL ZTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
! 286: + N, A( 0 ), N )
! 287: *
! 288: END IF
! 289: *
! 290: ELSE
! 291: *
! 292: * N is odd and TRANSR = 'C'
! 293: *
! 294: IF( LOWER ) THEN
! 295: *
! 296: * SRPA for LOWER, TRANSPOSE and N is odd
! 297: * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
! 298: *
! 299: CALL ZTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
! 300: IF( INFO.GT.0 )
! 301: + RETURN
! 302: CALL ZTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
! 303: + N1, A( N1*N1 ), N1 )
! 304: CALL ZTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
! 305: IF( INFO.GT.0 )
! 306: + INFO = INFO + N1
! 307: IF( INFO.GT.0 )
! 308: + RETURN
! 309: CALL ZTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
! 310: + N1, A( N1*N1 ), N1 )
! 311: *
! 312: ELSE
! 313: *
! 314: * SRPA for UPPER, TRANSPOSE and N is odd
! 315: * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
! 316: *
! 317: CALL ZTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
! 318: IF( INFO.GT.0 )
! 319: + RETURN
! 320: CALL ZTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
! 321: + A( N2*N2 ), N2, A( 0 ), N2 )
! 322: CALL ZTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
! 323: IF( INFO.GT.0 )
! 324: + INFO = INFO + N1
! 325: IF( INFO.GT.0 )
! 326: + RETURN
! 327: CALL ZTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
! 328: + A( N1*N2 ), N2, A( 0 ), N2 )
! 329: END IF
! 330: *
! 331: END IF
! 332: *
! 333: ELSE
! 334: *
! 335: * N is even
! 336: *
! 337: IF( NORMALTRANSR ) THEN
! 338: *
! 339: * N is even and TRANSR = 'N'
! 340: *
! 341: IF( LOWER ) THEN
! 342: *
! 343: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 344: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
! 345: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
! 346: *
! 347: CALL ZTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
! 348: IF( INFO.GT.0 )
! 349: + RETURN
! 350: CALL ZTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
! 351: + N+1, A( K+1 ), N+1 )
! 352: CALL ZTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
! 353: IF( INFO.GT.0 )
! 354: + INFO = INFO + K
! 355: IF( INFO.GT.0 )
! 356: + RETURN
! 357: CALL ZTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
! 358: + A( K+1 ), N+1 )
! 359: *
! 360: ELSE
! 361: *
! 362: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
! 363: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
! 364: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
! 365: *
! 366: CALL ZTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
! 367: IF( INFO.GT.0 )
! 368: + RETURN
! 369: CALL ZTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
! 370: + N+1, A( 0 ), N+1 )
! 371: CALL ZTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
! 372: IF( INFO.GT.0 )
! 373: + INFO = INFO + K
! 374: IF( INFO.GT.0 )
! 375: + RETURN
! 376: CALL ZTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
! 377: + A( 0 ), N+1 )
! 378: END IF
! 379: ELSE
! 380: *
! 381: * N is even and TRANSR = 'C'
! 382: *
! 383: IF( LOWER ) THEN
! 384: *
! 385: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
! 386: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
! 387: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
! 388: *
! 389: CALL ZTRTRI( 'U', DIAG, K, A( K ), K, INFO )
! 390: IF( INFO.GT.0 )
! 391: + RETURN
! 392: CALL ZTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
! 393: + A( K*( K+1 ) ), K )
! 394: CALL ZTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
! 395: IF( INFO.GT.0 )
! 396: + INFO = INFO + K
! 397: IF( INFO.GT.0 )
! 398: + RETURN
! 399: CALL ZTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
! 400: + A( K*( K+1 ) ), K )
! 401: ELSE
! 402: *
! 403: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
! 404: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
! 405: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
! 406: *
! 407: CALL ZTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
! 408: IF( INFO.GT.0 )
! 409: + RETURN
! 410: CALL ZTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
! 411: + A( K*( K+1 ) ), K, A( 0 ), K )
! 412: CALL ZTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
! 413: IF( INFO.GT.0 )
! 414: + INFO = INFO + K
! 415: IF( INFO.GT.0 )
! 416: + RETURN
! 417: CALL ZTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
! 418: + A( 0 ), K )
! 419: END IF
! 420: END IF
! 421: END IF
! 422: *
! 423: RETURN
! 424: *
! 425: * End of ZTFTRI
! 426: *
! 427: END
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