LAPACK 3.3.0

ztftri.f

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00001       SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.3.0)                                    --
00004 *
00005 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
00006 *     November 2010
00007 *
00008 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00009 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00010 *
00011 *     .. Scalar Arguments ..
00012       CHARACTER          TRANSR, UPLO, DIAG
00013       INTEGER            INFO, N
00014 *     ..
00015 *     .. Array Arguments ..
00016       COMPLEX*16         A( 0: * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  ZTFTRI computes the inverse of a triangular matrix A stored in RFP
00023 *  format.
00024 *
00025 *  This is a Level 3 BLAS version of the algorithm.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  TRANSR    (input) CHARACTER*1
00031 *          = 'N':  The Normal TRANSR of RFP A is stored;
00032 *          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
00033 *
00034 *  UPLO    (input) CHARACTER*1
00035 *          = 'U':  A is upper triangular;
00036 *          = 'L':  A is lower triangular.
00037 *
00038 *  DIAG    (input) CHARACTER*1
00039 *          = 'N':  A is non-unit triangular;
00040 *          = 'U':  A is unit triangular.
00041 *
00042 *  N       (input) INTEGER
00043 *          The order of the matrix A.  N >= 0.
00044 *
00045 *  A       (input/output) COMPLEX*16 array, dimension ( N*(N+1)/2 );
00046 *          On entry, the triangular matrix A in RFP format. RFP format
00047 *          is described by TRANSR, UPLO, and N as follows: If TRANSR =
00048 *          'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
00049 *          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
00050 *          the Conjugate-transpose of RFP A as defined when
00051 *          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
00052 *          follows: If UPLO = 'U' the RFP A contains the nt elements of
00053 *          upper packed A; If UPLO = 'L' the RFP A contains the nt
00054 *          elements of lower packed A. The LDA of RFP A is (N+1)/2 when
00055 *          TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
00056 *          even and N is odd. See the Note below for more details.
00057 *
00058 *          On exit, the (triangular) inverse of the original matrix, in
00059 *          the same storage format.
00060 *
00061 *  INFO    (output) INTEGER
00062 *          = 0: successful exit
00063 *          < 0: if INFO = -i, the i-th argument had an illegal value
00064 *          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
00065 *               matrix is singular and its inverse can not be computed.
00066 *
00067 *  Further Details
00068 *  ===============
00069 *
00070 *  We first consider Standard Packed Format when N is even.
00071 *  We give an example where N = 6.
00072 *
00073 *      AP is Upper             AP is Lower
00074 *
00075 *   00 01 02 03 04 05       00
00076 *      11 12 13 14 15       10 11
00077 *         22 23 24 25       20 21 22
00078 *            33 34 35       30 31 32 33
00079 *               44 45       40 41 42 43 44
00080 *                  55       50 51 52 53 54 55
00081 *
00082 *
00083 *  Let TRANSR = 'N'. RFP holds AP as follows:
00084 *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00085 *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00086 *  conjugate-transpose of the first three columns of AP upper.
00087 *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00088 *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00089 *  conjugate-transpose of the last three columns of AP lower.
00090 *  To denote conjugate we place -- above the element. This covers the
00091 *  case N even and TRANSR = 'N'.
00092 *
00093 *         RFP A                   RFP A
00094 *
00095 *                                -- -- --
00096 *        03 04 05                33 43 53
00097 *                                   -- --
00098 *        13 14 15                00 44 54
00099 *                                      --
00100 *        23 24 25                10 11 55
00101 *
00102 *        33 34 35                20 21 22
00103 *        --
00104 *        00 44 45                30 31 32
00105 *        -- --
00106 *        01 11 55                40 41 42
00107 *        -- -- --
00108 *        02 12 22                50 51 52
00109 *
00110 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00111 *  transpose of RFP A above. One therefore gets:
00112 *
00113 *
00114 *           RFP A                   RFP A
00115 *
00116 *     -- -- -- --                -- -- -- -- -- --
00117 *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00118 *     -- -- -- -- --                -- -- -- -- --
00119 *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00120 *     -- -- -- -- -- --                -- -- -- --
00121 *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00122 *
00123 *
00124 *  We next  consider Standard Packed Format when N is odd.
00125 *  We give an example where N = 5.
00126 *
00127 *     AP is Upper                 AP is Lower
00128 *
00129 *   00 01 02 03 04              00
00130 *      11 12 13 14              10 11
00131 *         22 23 24              20 21 22
00132 *            33 34              30 31 32 33
00133 *               44              40 41 42 43 44
00134 *
00135 *
00136 *  Let TRANSR = 'N'. RFP holds AP as follows:
00137 *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00138 *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00139 *  conjugate-transpose of the first two   columns of AP upper.
00140 *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00141 *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00142 *  conjugate-transpose of the last two   columns of AP lower.
00143 *  To denote conjugate we place -- above the element. This covers the
00144 *  case N odd  and TRANSR = 'N'.
00145 *
00146 *         RFP A                   RFP A
00147 *
00148 *                                   -- --
00149 *        02 03 04                00 33 43
00150 *                                      --
00151 *        12 13 14                10 11 44
00152 *
00153 *        22 23 24                20 21 22
00154 *        --
00155 *        00 33 34                30 31 32
00156 *        -- --
00157 *        01 11 44                40 41 42
00158 *
00159 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00160 *  transpose of RFP A above. One therefore gets:
00161 *
00162 *
00163 *           RFP A                   RFP A
00164 *
00165 *     -- -- --                   -- -- -- -- -- --
00166 *     02 12 22 00 01             00 10 20 30 40 50
00167 *     -- -- -- --                   -- -- -- -- --
00168 *     03 13 23 33 11             33 11 21 31 41 51
00169 *     -- -- -- -- --                   -- -- -- --
00170 *     04 14 24 34 44             43 44 22 32 42 52
00171 *
00172 *  =====================================================================
00173 *
00174 *     .. Parameters ..
00175       COMPLEX*16         CONE
00176       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00177 *     ..
00178 *     .. Local Scalars ..
00179       LOGICAL            LOWER, NISODD, NORMALTRANSR
00180       INTEGER            N1, N2, K
00181 *     ..
00182 *     .. External Functions ..
00183       LOGICAL            LSAME
00184       EXTERNAL           LSAME
00185 *     ..
00186 *     .. External Subroutines ..
00187       EXTERNAL           XERBLA, ZTRMM, ZTRTRI
00188 *     ..
00189 *     .. Intrinsic Functions ..
00190       INTRINSIC          MOD
00191 *     ..
00192 *     .. Executable Statements ..
00193 *
00194 *     Test the input parameters.
00195 *
00196       INFO = 0
00197       NORMALTRANSR = LSAME( TRANSR, 'N' )
00198       LOWER = LSAME( UPLO, 'L' )
00199       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00200          INFO = -1
00201       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00202          INFO = -2
00203       ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
00204      +         THEN
00205          INFO = -3
00206       ELSE IF( N.LT.0 ) THEN
00207          INFO = -4
00208       END IF
00209       IF( INFO.NE.0 ) THEN
00210          CALL XERBLA( 'ZTFTRI', -INFO )
00211          RETURN
00212       END IF
00213 *
00214 *     Quick return if possible
00215 *
00216       IF( N.EQ.0 )
00217      +   RETURN
00218 *
00219 *     If N is odd, set NISODD = .TRUE.
00220 *     If N is even, set K = N/2 and NISODD = .FALSE.
00221 *
00222       IF( MOD( N, 2 ).EQ.0 ) THEN
00223          K = N / 2
00224          NISODD = .FALSE.
00225       ELSE
00226          NISODD = .TRUE.
00227       END IF
00228 *
00229 *     Set N1 and N2 depending on LOWER
00230 *
00231       IF( LOWER ) THEN
00232          N2 = N / 2
00233          N1 = N - N2
00234       ELSE
00235          N1 = N / 2
00236          N2 = N - N1
00237       END IF
00238 *
00239 *
00240 *     start execution: there are eight cases
00241 *
00242       IF( NISODD ) THEN
00243 *
00244 *        N is odd
00245 *
00246          IF( NORMALTRANSR ) THEN
00247 *
00248 *           N is odd and TRANSR = 'N'
00249 *
00250             IF( LOWER ) THEN
00251 *
00252 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00253 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00254 *             T1 -> a(0), T2 -> a(n), S -> a(n1)
00255 *
00256                CALL ZTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
00257                IF( INFO.GT.0 )
00258      +            RETURN
00259                CALL ZTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
00260      +                     N, A( N1 ), N )
00261                CALL ZTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
00262                IF( INFO.GT.0 )
00263      +            INFO = INFO + N1
00264                IF( INFO.GT.0 )
00265      +            RETURN
00266                CALL ZTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
00267      +                     A( N1 ), N )
00268 *
00269             ELSE
00270 *
00271 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00272 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00273 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00274 *
00275                CALL ZTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
00276                IF( INFO.GT.0 )
00277      +            RETURN
00278                CALL ZTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
00279      +                     N, A( 0 ), N )
00280                CALL ZTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
00281                IF( INFO.GT.0 )
00282      +            INFO = INFO + N1
00283                IF( INFO.GT.0 )
00284      +            RETURN
00285                CALL ZTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
00286      +                     N, A( 0 ), N )
00287 *
00288             END IF
00289 *
00290          ELSE
00291 *
00292 *           N is odd and TRANSR = 'C'
00293 *
00294             IF( LOWER ) THEN
00295 *
00296 *              SRPA for LOWER, TRANSPOSE and N is odd
00297 *              T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
00298 *
00299                CALL ZTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
00300                IF( INFO.GT.0 )
00301      +            RETURN
00302                CALL ZTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
00303      +                     N1, A( N1*N1 ), N1 )
00304                CALL ZTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
00305                IF( INFO.GT.0 )
00306      +            INFO = INFO + N1
00307                IF( INFO.GT.0 )
00308      +            RETURN
00309                CALL ZTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
00310      +                     N1, A( N1*N1 ), N1 )
00311 *
00312             ELSE
00313 *
00314 *              SRPA for UPPER, TRANSPOSE and N is odd
00315 *              T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
00316 *
00317                CALL ZTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
00318                IF( INFO.GT.0 )
00319      +            RETURN
00320                CALL ZTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
00321      +                     A( N2*N2 ), N2, A( 0 ), N2 )
00322                CALL ZTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
00323                IF( INFO.GT.0 )
00324      +            INFO = INFO + N1
00325                IF( INFO.GT.0 )
00326      +            RETURN
00327                CALL ZTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
00328      +                     A( N1*N2 ), N2, A( 0 ), N2 )
00329             END IF
00330 *
00331          END IF
00332 *
00333       ELSE
00334 *
00335 *        N is even
00336 *
00337          IF( NORMALTRANSR ) THEN
00338 *
00339 *           N is even and TRANSR = 'N'
00340 *
00341             IF( LOWER ) THEN
00342 *
00343 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00344 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00345 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00346 *
00347                CALL ZTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
00348                IF( INFO.GT.0 )
00349      +            RETURN
00350                CALL ZTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
00351      +                     N+1, A( K+1 ), N+1 )
00352                CALL ZTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
00353                IF( INFO.GT.0 )
00354      +            INFO = INFO + K
00355                IF( INFO.GT.0 )
00356      +            RETURN
00357                CALL ZTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
00358      +                     A( K+1 ), N+1 )
00359 *
00360             ELSE
00361 *
00362 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00363 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00364 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00365 *
00366                CALL ZTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
00367                IF( INFO.GT.0 )
00368      +            RETURN
00369                CALL ZTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
00370      +                     N+1, A( 0 ), N+1 )
00371                CALL ZTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
00372                IF( INFO.GT.0 )
00373      +            INFO = INFO + K
00374                IF( INFO.GT.0 )
00375      +            RETURN
00376                CALL ZTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
00377      +                     A( 0 ), N+1 )
00378             END IF
00379          ELSE
00380 *
00381 *           N is even and TRANSR = 'C'
00382 *
00383             IF( LOWER ) THEN
00384 *
00385 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00386 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00387 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00388 *
00389                CALL ZTRTRI( 'U', DIAG, K, A( K ), K, INFO )
00390                IF( INFO.GT.0 )
00391      +            RETURN
00392                CALL ZTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
00393      +                     A( K*( K+1 ) ), K )
00394                CALL ZTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
00395                IF( INFO.GT.0 )
00396      +            INFO = INFO + K
00397                IF( INFO.GT.0 )
00398      +            RETURN
00399                CALL ZTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
00400      +                     A( K*( K+1 ) ), K )
00401             ELSE
00402 *
00403 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00404 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00405 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00406 *
00407                CALL ZTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
00408                IF( INFO.GT.0 )
00409      +            RETURN
00410                CALL ZTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
00411      +                     A( K*( K+1 ) ), K, A( 0 ), K )
00412                CALL ZTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
00413                IF( INFO.GT.0 )
00414      +            INFO = INFO + K
00415                IF( INFO.GT.0 )
00416      +            RETURN
00417                CALL ZTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
00418      +                     A( 0 ), K )
00419             END IF
00420          END IF
00421       END IF
00422 *
00423       RETURN
00424 *
00425 *     End of ZTFTRI
00426 *
00427       END
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