LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztfttr.f
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00001 *> \brief \b ZTFTTR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZTFTTR + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfttr.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfttr.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfttr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO
00025 *       INTEGER            INFO, N, LDA
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX*16         A( 0: LDA-1, 0: * ), ARF( 0: * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> ZTFTTR copies a triangular matrix A from rectangular full packed
00038 *> format (TF) to standard full format (TR).
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] TRANSR
00045 *> \verbatim
00046 *>          TRANSR is CHARACTER*1
00047 *>          = 'N':  ARF is in Normal format;
00048 *>          = 'C':  ARF is in Conjugate-transpose format;
00049 *> \endverbatim
00050 *>
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  A is upper triangular;
00055 *>          = 'L':  A is lower triangular.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] ARF
00065 *> \verbatim
00066 *>          ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
00067 *>          On entry, the upper or lower triangular matrix A stored in
00068 *>          RFP format. For a further discussion see Notes below.
00069 *> \endverbatim
00070 *>
00071 *> \param[out] A
00072 *> \verbatim
00073 *>          A is COMPLEX*16 array, dimension ( LDA, N )
00074 *>          On exit, the triangular matrix A.  If UPLO = 'U', the
00075 *>          leading N-by-N upper triangular part of the array A contains
00076 *>          the upper triangular matrix, and the strictly lower
00077 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00078 *>          leading N-by-N lower triangular part of the array A contains
00079 *>          the lower triangular matrix, and the strictly upper
00080 *>          triangular part of A is not referenced.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDA
00084 *> \verbatim
00085 *>          LDA is INTEGER
00086 *>          The leading dimension of the array A.  LDA >= max(1,N).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] INFO
00090 *> \verbatim
00091 *>          INFO is INTEGER
00092 *>          = 0:  successful exit
00093 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00094 *> \endverbatim
00095 *
00096 *  Authors:
00097 *  ========
00098 *
00099 *> \author Univ. of Tennessee 
00100 *> \author Univ. of California Berkeley 
00101 *> \author Univ. of Colorado Denver 
00102 *> \author NAG Ltd. 
00103 *
00104 *> \date November 2011
00105 *
00106 *> \ingroup complex16OTHERcomputational
00107 *
00108 *> \par Further Details:
00109 *  =====================
00110 *>
00111 *> \verbatim
00112 *>
00113 *>  We first consider Standard Packed Format when N is even.
00114 *>  We give an example where N = 6.
00115 *>
00116 *>      AP is Upper             AP is Lower
00117 *>
00118 *>   00 01 02 03 04 05       00
00119 *>      11 12 13 14 15       10 11
00120 *>         22 23 24 25       20 21 22
00121 *>            33 34 35       30 31 32 33
00122 *>               44 45       40 41 42 43 44
00123 *>                  55       50 51 52 53 54 55
00124 *>
00125 *>
00126 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00127 *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00128 *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00129 *>  conjugate-transpose of the first three columns of AP upper.
00130 *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00131 *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00132 *>  conjugate-transpose of the last three columns of AP lower.
00133 *>  To denote conjugate we place -- above the element. This covers the
00134 *>  case N even and TRANSR = 'N'.
00135 *>
00136 *>         RFP A                   RFP A
00137 *>
00138 *>                                -- -- --
00139 *>        03 04 05                33 43 53
00140 *>                                   -- --
00141 *>        13 14 15                00 44 54
00142 *>                                      --
00143 *>        23 24 25                10 11 55
00144 *>
00145 *>        33 34 35                20 21 22
00146 *>        --
00147 *>        00 44 45                30 31 32
00148 *>        -- --
00149 *>        01 11 55                40 41 42
00150 *>        -- -- --
00151 *>        02 12 22                50 51 52
00152 *>
00153 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00154 *>  transpose of RFP A above. One therefore gets:
00155 *>
00156 *>
00157 *>           RFP A                   RFP A
00158 *>
00159 *>     -- -- -- --                -- -- -- -- -- --
00160 *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00161 *>     -- -- -- -- --                -- -- -- -- --
00162 *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00163 *>     -- -- -- -- -- --                -- -- -- --
00164 *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00165 *>
00166 *>
00167 *>  We next  consider Standard Packed Format when N is odd.
00168 *>  We give an example where N = 5.
00169 *>
00170 *>     AP is Upper                 AP is Lower
00171 *>
00172 *>   00 01 02 03 04              00
00173 *>      11 12 13 14              10 11
00174 *>         22 23 24              20 21 22
00175 *>            33 34              30 31 32 33
00176 *>               44              40 41 42 43 44
00177 *>
00178 *>
00179 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00180 *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00181 *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00182 *>  conjugate-transpose of the first two   columns of AP upper.
00183 *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00184 *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00185 *>  conjugate-transpose of the last two   columns of AP lower.
00186 *>  To denote conjugate we place -- above the element. This covers the
00187 *>  case N odd  and TRANSR = 'N'.
00188 *>
00189 *>         RFP A                   RFP A
00190 *>
00191 *>                                   -- --
00192 *>        02 03 04                00 33 43
00193 *>                                      --
00194 *>        12 13 14                10 11 44
00195 *>
00196 *>        22 23 24                20 21 22
00197 *>        --
00198 *>        00 33 34                30 31 32
00199 *>        -- --
00200 *>        01 11 44                40 41 42
00201 *>
00202 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00203 *>  transpose of RFP A above. One therefore gets:
00204 *>
00205 *>
00206 *>           RFP A                   RFP A
00207 *>
00208 *>     -- -- --                   -- -- -- -- -- --
00209 *>     02 12 22 00 01             00 10 20 30 40 50
00210 *>     -- -- -- --                   -- -- -- -- --
00211 *>     03 13 23 33 11             33 11 21 31 41 51
00212 *>     -- -- -- -- --                   -- -- -- --
00213 *>     04 14 24 34 44             43 44 22 32 42 52
00214 *> \endverbatim
00215 *>
00216 *  =====================================================================
00217       SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
00218 *
00219 *  -- LAPACK computational routine (version 3.4.0) --
00220 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00221 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00222 *     November 2011
00223 *
00224 *     .. Scalar Arguments ..
00225       CHARACTER          TRANSR, UPLO
00226       INTEGER            INFO, N, LDA
00227 *     ..
00228 *     .. Array Arguments ..
00229       COMPLEX*16         A( 0: LDA-1, 0: * ), ARF( 0: * )
00230 *     ..
00231 *
00232 *  =====================================================================
00233 *
00234 *     .. Parameters ..
00235 *     ..
00236 *     .. Local Scalars ..
00237       LOGICAL            LOWER, NISODD, NORMALTRANSR
00238       INTEGER            N1, N2, K, NT, NX2, NP1X2
00239       INTEGER            I, J, L, IJ
00240 *     ..
00241 *     .. External Functions ..
00242       LOGICAL            LSAME
00243       EXTERNAL           LSAME
00244 *     ..
00245 *     .. External Subroutines ..
00246       EXTERNAL           XERBLA
00247 *     ..
00248 *     .. Intrinsic Functions ..
00249       INTRINSIC          DCONJG, MAX, MOD
00250 *     ..
00251 *     .. Executable Statements ..
00252 *
00253 *     Test the input parameters.
00254 *
00255       INFO = 0
00256       NORMALTRANSR = LSAME( TRANSR, 'N' )
00257       LOWER = LSAME( UPLO, 'L' )
00258       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00259          INFO = -1
00260       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00261          INFO = -2
00262       ELSE IF( N.LT.0 ) THEN
00263          INFO = -3
00264       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00265          INFO = -6
00266       END IF
00267       IF( INFO.NE.0 ) THEN
00268          CALL XERBLA( 'ZTFTTR', -INFO )
00269          RETURN
00270       END IF
00271 *
00272 *     Quick return if possible
00273 *
00274       IF( N.LE.1 ) THEN
00275          IF( N.EQ.1 ) THEN
00276             IF( NORMALTRANSR ) THEN
00277                A( 0, 0 ) = ARF( 0 )
00278             ELSE
00279                A( 0, 0 ) = DCONJG( ARF( 0 ) )
00280             END IF
00281          END IF
00282          RETURN
00283       END IF
00284 *
00285 *     Size of array ARF(1:2,0:nt-1)
00286 *
00287       NT = N*( N+1 ) / 2
00288 *
00289 *     set N1 and N2 depending on LOWER: for N even N1=N2=K
00290 *
00291       IF( LOWER ) THEN
00292          N2 = N / 2
00293          N1 = N - N2
00294       ELSE
00295          N1 = N / 2
00296          N2 = N - N1
00297       END IF
00298 *
00299 *     If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
00300 *     If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
00301 *     N--by--(N+1)/2.
00302 *
00303       IF( MOD( N, 2 ).EQ.0 ) THEN
00304          K = N / 2
00305          NISODD = .FALSE.
00306          IF( .NOT.LOWER )
00307      $      NP1X2 = N + N + 2
00308       ELSE
00309          NISODD = .TRUE.
00310          IF( .NOT.LOWER )
00311      $      NX2 = N + N
00312       END IF
00313 *
00314       IF( NISODD ) THEN
00315 *
00316 *        N is odd
00317 *
00318          IF( NORMALTRANSR ) THEN
00319 *
00320 *           N is odd and TRANSR = 'N'
00321 *
00322             IF( LOWER ) THEN
00323 *
00324 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00325 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00326 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
00327 *
00328                IJ = 0
00329                DO J = 0, N2
00330                   DO I = N1, N2 + J
00331                      A( N2+J, I ) = DCONJG( ARF( IJ ) )
00332                      IJ = IJ + 1
00333                   END DO
00334                   DO I = J, N - 1
00335                      A( I, J ) = ARF( IJ )
00336                      IJ = IJ + 1
00337                   END DO
00338                END DO
00339 *
00340             ELSE
00341 *
00342 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00343 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00344 *             T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
00345 *
00346                IJ = NT - N
00347                DO J = N - 1, N1, -1
00348                   DO I = 0, J
00349                      A( I, J ) = ARF( IJ )
00350                      IJ = IJ + 1
00351                   END DO
00352                   DO L = J - N1, N1 - 1
00353                      A( J-N1, L ) = DCONJG( ARF( IJ ) )
00354                      IJ = IJ + 1
00355                   END DO
00356                   IJ = IJ - NX2
00357                END DO
00358 *
00359             END IF
00360 *
00361          ELSE
00362 *
00363 *           N is odd and TRANSR = 'C'
00364 *
00365             IF( LOWER ) THEN
00366 *
00367 *              SRPA for LOWER, TRANSPOSE and N is odd
00368 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
00369 *              T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
00370 *
00371                IJ = 0
00372                DO J = 0, N2 - 1
00373                   DO I = 0, J
00374                      A( J, I ) = DCONJG( ARF( IJ ) )
00375                      IJ = IJ + 1
00376                   END DO
00377                   DO I = N1 + J, N - 1
00378                      A( I, N1+J ) = ARF( IJ )
00379                      IJ = IJ + 1
00380                   END DO
00381                END DO
00382                DO J = N2, N - 1
00383                   DO I = 0, N1 - 1
00384                      A( J, I ) = DCONJG( ARF( IJ ) )
00385                      IJ = IJ + 1
00386                   END DO
00387                END DO
00388 *
00389             ELSE
00390 *
00391 *              SRPA for UPPER, TRANSPOSE and N is odd
00392 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
00393 *              T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda = n2
00394 *
00395                IJ = 0
00396                DO J = 0, N1
00397                   DO I = N1, N - 1
00398                      A( J, I ) = DCONJG( ARF( IJ ) )
00399                      IJ = IJ + 1
00400                   END DO
00401                END DO
00402                DO J = 0, N1 - 1
00403                   DO I = 0, J
00404                      A( I, J ) = ARF( IJ )
00405                      IJ = IJ + 1
00406                   END DO
00407                   DO L = N2 + J, N - 1
00408                      A( N2+J, L ) = DCONJG( ARF( IJ ) )
00409                      IJ = IJ + 1
00410                   END DO
00411                END DO
00412 *
00413             END IF
00414 *
00415          END IF
00416 *
00417       ELSE
00418 *
00419 *        N is even
00420 *
00421          IF( NORMALTRANSR ) THEN
00422 *
00423 *           N is even and TRANSR = 'N'
00424 *
00425             IF( LOWER ) THEN
00426 *
00427 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00428 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00429 *              T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
00430 *
00431                IJ = 0
00432                DO J = 0, K - 1
00433                   DO I = K, K + J
00434                      A( K+J, I ) = DCONJG( ARF( IJ ) )
00435                      IJ = IJ + 1
00436                   END DO
00437                   DO I = J, N - 1
00438                      A( I, J ) = ARF( IJ )
00439                      IJ = IJ + 1
00440                   END DO
00441                END DO
00442 *
00443             ELSE
00444 *
00445 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00446 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00447 *              T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
00448 *
00449                IJ = NT - N - 1
00450                DO J = N - 1, K, -1
00451                   DO I = 0, J
00452                      A( I, J ) = ARF( IJ )
00453                      IJ = IJ + 1
00454                   END DO
00455                   DO L = J - K, K - 1
00456                      A( J-K, L ) = DCONJG( ARF( IJ ) )
00457                      IJ = IJ + 1
00458                   END DO
00459                   IJ = IJ - NP1X2
00460                END DO
00461 *
00462             END IF
00463 *
00464          ELSE
00465 *
00466 *           N is even and TRANSR = 'C'
00467 *
00468             IF( LOWER ) THEN
00469 *
00470 *              SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
00471 *              T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
00472 *              T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
00473 *
00474                IJ = 0
00475                J = K
00476                DO I = K, N - 1
00477                   A( I, J ) = ARF( IJ )
00478                   IJ = IJ + 1
00479                END DO
00480                DO J = 0, K - 2
00481                   DO I = 0, J
00482                      A( J, I ) = DCONJG( ARF( IJ ) )
00483                      IJ = IJ + 1
00484                   END DO
00485                   DO I = K + 1 + J, N - 1
00486                      A( I, K+1+J ) = ARF( IJ )
00487                      IJ = IJ + 1
00488                   END DO
00489                END DO
00490                DO J = K - 1, N - 1
00491                   DO I = 0, K - 1
00492                      A( J, I ) = DCONJG( ARF( IJ ) )
00493                      IJ = IJ + 1
00494                   END DO
00495                END DO
00496 *
00497             ELSE
00498 *
00499 *              SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
00500 *              T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
00501 *              T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
00502 *
00503                IJ = 0
00504                DO J = 0, K
00505                   DO I = K, N - 1
00506                      A( J, I ) = DCONJG( ARF( IJ ) )
00507                      IJ = IJ + 1
00508                   END DO
00509                END DO
00510                DO J = 0, K - 2
00511                   DO I = 0, J
00512                      A( I, J ) = ARF( IJ )
00513                      IJ = IJ + 1
00514                   END DO
00515                   DO L = K + 1 + J, N - 1
00516                      A( K+1+J, L ) = DCONJG( ARF( IJ ) )
00517                      IJ = IJ + 1
00518                   END DO
00519                END DO
00520 *
00521 *              Note that here J = K-1
00522 *
00523                DO I = 0, J
00524                   A( I, J ) = ARF( IJ )
00525                   IJ = IJ + 1
00526                END DO
00527 *
00528             END IF
00529 *
00530          END IF
00531 *
00532       END IF
00533 *
00534       RETURN
00535 *
00536 *     End of ZTFTTR
00537 *
00538       END
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