LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ctftri.f
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00001 *> \brief \b CTFTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CTFTRI + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctftri.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctftri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctftri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO, DIAG
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            A( 0: * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CTFTRI computes the inverse of a triangular matrix A stored in RFP
00038 *> format.
00039 *>
00040 *> This is a Level 3 BLAS version of the algorithm.
00041 *> \endverbatim
00042 *
00043 *  Arguments:
00044 *  ==========
00045 *
00046 *> \param[in] TRANSR
00047 *> \verbatim
00048 *>          TRANSR is CHARACTER*1
00049 *>          = 'N':  The Normal TRANSR of RFP A is stored;
00050 *>          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] UPLO
00054 *> \verbatim
00055 *>          UPLO is CHARACTER*1
00056 *>          = 'U':  A is upper triangular;
00057 *>          = 'L':  A is lower triangular.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] DIAG
00061 *> \verbatim
00062 *>          DIAG is CHARACTER*1
00063 *>          = 'N':  A is non-unit triangular;
00064 *>          = 'U':  A is unit triangular.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] N
00068 *> \verbatim
00069 *>          N is INTEGER
00070 *>          The order of the matrix A.  N >= 0.
00071 *> \endverbatim
00072 *>
00073 *> \param[in,out] A
00074 *> \verbatim
00075 *>          A is COMPLEX array, dimension ( N*(N+1)/2 );
00076 *>          On entry, the triangular matrix A in RFP format. RFP format
00077 *>          is described by TRANSR, UPLO, and N as follows: If TRANSR =
00078 *>          'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
00079 *>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
00080 *>          the Conjugate-transpose of RFP A as defined when
00081 *>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
00082 *>          follows: If UPLO = 'U' the RFP A contains the nt elements of
00083 *>          upper packed A; If UPLO = 'L' the RFP A contains the nt
00084 *>          elements of lower packed A. The LDA of RFP A is (N+1)/2 when
00085 *>          TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
00086 *>          even and N is odd. See the Note below for more details.
00087 *>
00088 *>          On exit, the (triangular) inverse of the original matrix, in
00089 *>          the same storage format.
00090 *> \endverbatim
00091 *>
00092 *> \param[out] INFO
00093 *> \verbatim
00094 *>          INFO is INTEGER
00095 *>          = 0: successful exit
00096 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00097 *>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
00098 *>               matrix is singular and its inverse can not be computed.
00099 *> \endverbatim
00100 *
00101 *  Authors:
00102 *  ========
00103 *
00104 *> \author Univ. of Tennessee 
00105 *> \author Univ. of California Berkeley 
00106 *> \author Univ. of Colorado Denver 
00107 *> \author NAG Ltd. 
00108 *
00109 *> \date November 2011
00110 *
00111 *> \ingroup complexOTHERcomputational
00112 *
00113 *> \par Further Details:
00114 *  =====================
00115 *>
00116 *> \verbatim
00117 *>
00118 *>  We first consider Standard Packed Format when N is even.
00119 *>  We give an example where N = 6.
00120 *>
00121 *>      AP is Upper             AP is Lower
00122 *>
00123 *>   00 01 02 03 04 05       00
00124 *>      11 12 13 14 15       10 11
00125 *>         22 23 24 25       20 21 22
00126 *>            33 34 35       30 31 32 33
00127 *>               44 45       40 41 42 43 44
00128 *>                  55       50 51 52 53 54 55
00129 *>
00130 *>
00131 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00132 *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00133 *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00134 *>  conjugate-transpose of the first three columns of AP upper.
00135 *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00136 *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00137 *>  conjugate-transpose of the last three columns of AP lower.
00138 *>  To denote conjugate we place -- above the element. This covers the
00139 *>  case N even and TRANSR = 'N'.
00140 *>
00141 *>         RFP A                   RFP A
00142 *>
00143 *>                                -- -- --
00144 *>        03 04 05                33 43 53
00145 *>                                   -- --
00146 *>        13 14 15                00 44 54
00147 *>                                      --
00148 *>        23 24 25                10 11 55
00149 *>
00150 *>        33 34 35                20 21 22
00151 *>        --
00152 *>        00 44 45                30 31 32
00153 *>        -- --
00154 *>        01 11 55                40 41 42
00155 *>        -- -- --
00156 *>        02 12 22                50 51 52
00157 *>
00158 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00159 *>  transpose of RFP A above. One therefore gets:
00160 *>
00161 *>
00162 *>           RFP A                   RFP A
00163 *>
00164 *>     -- -- -- --                -- -- -- -- -- --
00165 *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00166 *>     -- -- -- -- --                -- -- -- -- --
00167 *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00168 *>     -- -- -- -- -- --                -- -- -- --
00169 *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00170 *>
00171 *>
00172 *>  We next  consider Standard Packed Format when N is odd.
00173 *>  We give an example where N = 5.
00174 *>
00175 *>     AP is Upper                 AP is Lower
00176 *>
00177 *>   00 01 02 03 04              00
00178 *>      11 12 13 14              10 11
00179 *>         22 23 24              20 21 22
00180 *>            33 34              30 31 32 33
00181 *>               44              40 41 42 43 44
00182 *>
00183 *>
00184 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00185 *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00186 *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00187 *>  conjugate-transpose of the first two   columns of AP upper.
00188 *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00189 *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00190 *>  conjugate-transpose of the last two   columns of AP lower.
00191 *>  To denote conjugate we place -- above the element. This covers the
00192 *>  case N odd  and TRANSR = 'N'.
00193 *>
00194 *>         RFP A                   RFP A
00195 *>
00196 *>                                   -- --
00197 *>        02 03 04                00 33 43
00198 *>                                      --
00199 *>        12 13 14                10 11 44
00200 *>
00201 *>        22 23 24                20 21 22
00202 *>        --
00203 *>        00 33 34                30 31 32
00204 *>        -- --
00205 *>        01 11 44                40 41 42
00206 *>
00207 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00208 *>  transpose of RFP A above. One therefore gets:
00209 *>
00210 *>
00211 *>           RFP A                   RFP A
00212 *>
00213 *>     -- -- --                   -- -- -- -- -- --
00214 *>     02 12 22 00 01             00 10 20 30 40 50
00215 *>     -- -- -- --                   -- -- -- -- --
00216 *>     03 13 23 33 11             33 11 21 31 41 51
00217 *>     -- -- -- -- --                   -- -- -- --
00218 *>     04 14 24 34 44             43 44 22 32 42 52
00219 *> \endverbatim
00220 *>
00221 *  =====================================================================
00222       SUBROUTINE CTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
00223 *
00224 *  -- LAPACK computational routine (version 3.4.0) --
00225 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00226 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00227 *     November 2011
00228 *
00229 *     .. Scalar Arguments ..
00230       CHARACTER          TRANSR, UPLO, DIAG
00231       INTEGER            INFO, N
00232 *     ..
00233 *     .. Array Arguments ..
00234       COMPLEX            A( 0: * )
00235 *     ..
00236 *
00237 *  =====================================================================
00238 *
00239 *     .. Parameters ..
00240       COMPLEX            CONE
00241       PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
00242 *     ..
00243 *     .. Local Scalars ..
00244       LOGICAL            LOWER, NISODD, NORMALTRANSR
00245       INTEGER            N1, N2, K
00246 *     ..
00247 *     .. External Functions ..
00248       LOGICAL            LSAME
00249       EXTERNAL           LSAME
00250 *     ..
00251 *     .. External Subroutines ..
00252       EXTERNAL           XERBLA, CTRMM, CTRTRI
00253 *     ..
00254 *     .. Intrinsic Functions ..
00255       INTRINSIC          MOD
00256 *     ..
00257 *     .. Executable Statements ..
00258 *
00259 *     Test the input parameters.
00260 *
00261       INFO = 0
00262       NORMALTRANSR = LSAME( TRANSR, 'N' )
00263       LOWER = LSAME( UPLO, 'L' )
00264       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00265          INFO = -1
00266       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00267          INFO = -2
00268       ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
00269      $         THEN
00270          INFO = -3
00271       ELSE IF( N.LT.0 ) THEN
00272          INFO = -4
00273       END IF
00274       IF( INFO.NE.0 ) THEN
00275          CALL XERBLA( 'CTFTRI', -INFO )
00276          RETURN
00277       END IF
00278 *
00279 *     Quick return if possible
00280 *
00281       IF( N.EQ.0 )
00282      $   RETURN
00283 *
00284 *     If N is odd, set NISODD = .TRUE.
00285 *     If N is even, set K = N/2 and NISODD = .FALSE.
00286 *
00287       IF( MOD( N, 2 ).EQ.0 ) THEN
00288          K = N / 2
00289          NISODD = .FALSE.
00290       ELSE
00291          NISODD = .TRUE.
00292       END IF
00293 *
00294 *     Set N1 and N2 depending on LOWER
00295 *
00296       IF( LOWER ) THEN
00297          N2 = N / 2
00298          N1 = N - N2
00299       ELSE
00300          N1 = N / 2
00301          N2 = N - N1
00302       END IF
00303 *
00304 *
00305 *     start execution: there are eight cases
00306 *
00307       IF( NISODD ) THEN
00308 *
00309 *        N is odd
00310 *
00311          IF( NORMALTRANSR ) THEN
00312 *
00313 *           N is odd and TRANSR = 'N'
00314 *
00315             IF( LOWER ) THEN
00316 *
00317 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00318 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00319 *             T1 -> a(0), T2 -> a(n), S -> a(n1)
00320 *
00321                CALL CTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
00322                IF( INFO.GT.0 )
00323      $            RETURN
00324                CALL CTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
00325      $                     N, A( N1 ), N )
00326                CALL CTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
00327                IF( INFO.GT.0 )
00328      $            INFO = INFO + N1
00329                IF( INFO.GT.0 )
00330      $            RETURN
00331                CALL CTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
00332      $                     A( N1 ), N )
00333 *
00334             ELSE
00335 *
00336 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00337 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00338 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00339 *
00340                CALL CTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
00341                IF( INFO.GT.0 )
00342      $            RETURN
00343                CALL CTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
00344      $                     N, A( 0 ), N )
00345                CALL CTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
00346                IF( INFO.GT.0 )
00347      $            INFO = INFO + N1
00348                IF( INFO.GT.0 )
00349      $            RETURN
00350                CALL CTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
00351      $                     N, A( 0 ), N )
00352 *
00353             END IF
00354 *
00355          ELSE
00356 *
00357 *           N is odd and TRANSR = 'C'
00358 *
00359             IF( LOWER ) THEN
00360 *
00361 *              SRPA for LOWER, TRANSPOSE and N is odd
00362 *              T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
00363 *
00364                CALL CTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
00365                IF( INFO.GT.0 )
00366      $            RETURN
00367                CALL CTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
00368      $                     N1, A( N1*N1 ), N1 )
00369                CALL CTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
00370                IF( INFO.GT.0 )
00371      $            INFO = INFO + N1
00372                IF( INFO.GT.0 )
00373      $            RETURN
00374                CALL CTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
00375      $                     N1, A( N1*N1 ), N1 )
00376 *
00377             ELSE
00378 *
00379 *              SRPA for UPPER, TRANSPOSE and N is odd
00380 *              T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
00381 *
00382                CALL CTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
00383                IF( INFO.GT.0 )
00384      $            RETURN
00385                CALL CTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
00386      $                     A( N2*N2 ), N2, A( 0 ), N2 )
00387                CALL CTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
00388                IF( INFO.GT.0 )
00389      $            INFO = INFO + N1
00390                IF( INFO.GT.0 )
00391      $            RETURN
00392                CALL CTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
00393      $                     A( N1*N2 ), N2, A( 0 ), N2 )
00394             END IF
00395 *
00396          END IF
00397 *
00398       ELSE
00399 *
00400 *        N is even
00401 *
00402          IF( NORMALTRANSR ) THEN
00403 *
00404 *           N is even and TRANSR = 'N'
00405 *
00406             IF( LOWER ) THEN
00407 *
00408 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00409 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00410 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00411 *
00412                CALL CTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
00413                IF( INFO.GT.0 )
00414      $            RETURN
00415                CALL CTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
00416      $                     N+1, A( K+1 ), N+1 )
00417                CALL CTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
00418                IF( INFO.GT.0 )
00419      $            INFO = INFO + K
00420                IF( INFO.GT.0 )
00421      $            RETURN
00422                CALL CTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
00423      $                     A( K+1 ), N+1 )
00424 *
00425             ELSE
00426 *
00427 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00428 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00429 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00430 *
00431                CALL CTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
00432                IF( INFO.GT.0 )
00433      $            RETURN
00434                CALL CTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
00435      $                     N+1, A( 0 ), N+1 )
00436                CALL CTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
00437                IF( INFO.GT.0 )
00438      $            INFO = INFO + K
00439                IF( INFO.GT.0 )
00440      $            RETURN
00441                CALL CTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
00442      $                     A( 0 ), N+1 )
00443             END IF
00444          ELSE
00445 *
00446 *           N is even and TRANSR = 'C'
00447 *
00448             IF( LOWER ) THEN
00449 *
00450 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00451 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00452 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00453 *
00454                CALL CTRTRI( 'U', DIAG, K, A( K ), K, INFO )
00455                IF( INFO.GT.0 )
00456      $            RETURN
00457                CALL CTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
00458      $                     A( K*( K+1 ) ), K )
00459                CALL CTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
00460                IF( INFO.GT.0 )
00461      $            INFO = INFO + K
00462                IF( INFO.GT.0 )
00463      $            RETURN
00464                CALL CTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
00465      $                     A( K*( K+1 ) ), K )
00466             ELSE
00467 *
00468 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00469 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00470 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00471 *
00472                CALL CTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
00473                IF( INFO.GT.0 )
00474      $            RETURN
00475                CALL CTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
00476      $                     A( K*( K+1 ) ), K, A( 0 ), K )
00477                CALL CTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
00478                IF( INFO.GT.0 )
00479      $            INFO = INFO + K
00480                IF( INFO.GT.0 )
00481      $            RETURN
00482                CALL CTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
00483      $                     A( 0 ), K )
00484             END IF
00485          END IF
00486       END IF
00487 *
00488       RETURN
00489 *
00490 *     End of CTFTRI
00491 *
00492       END
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