LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ctrttf.f
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00001 *> \brief \b CTRTTF
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CTRTTF + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctrttf.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctrttf.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctrttf.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO
00025 *       INTEGER            INFO, N, LDA
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            A( 0: LDA-1, 0: * ), ARF( 0: * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CTRTTF copies a triangular matrix A from standard full format (TR)
00038 *> to rectangular full packed format (TF) .
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] TRANSR
00045 *> \verbatim
00046 *>          TRANSR is CHARACTER*1
00047 *>          = 'N':  ARF in Normal mode is wanted;
00048 *>          = 'C':  ARF in Conjugate Transpose mode is wanted;
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] A
00065 *> \verbatim
00066 *>          A is COMPLEX array, dimension ( LDA, N )
00067 *>          On entry, the triangular matrix A.  If UPLO = 'U', the
00068 *>          leading N-by-N upper triangular part of the array A contains
00069 *>          the upper triangular matrix, and the strictly lower
00070 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00071 *>          leading N-by-N lower triangular part of the array A contains
00072 *>          the lower triangular matrix, and the strictly upper
00073 *>          triangular part of A is not referenced.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] LDA
00077 *> \verbatim
00078 *>          LDA is INTEGER
00079 *>          The leading dimension of the matrix A.  LDA >= max(1,N).
00080 *> \endverbatim
00081 *>
00082 *> \param[out] ARF
00083 *> \verbatim
00084 *>          ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
00085 *>          On exit, the upper or lower triangular matrix A stored in
00086 *>          RFP format. For a further discussion see Notes below.
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 complexOTHERcomputational
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 CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, 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            A( 0: LDA-1, 0: * ), ARF( 0: * )
00230 *     ..
00231 *
00232 *  =====================================================================
00233 *
00234 *     .. Parameters ..
00235 *     ..
00236 *     .. Local Scalars ..
00237       LOGICAL            LOWER, NISODD, NORMALTRANSR
00238       INTEGER            I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
00239 *     ..
00240 *     .. External Functions ..
00241       LOGICAL            LSAME
00242       EXTERNAL           LSAME
00243 *     ..
00244 *     .. External Subroutines ..
00245       EXTERNAL           XERBLA
00246 *     ..
00247 *     .. Intrinsic Functions ..
00248       INTRINSIC          CONJG, MAX, MOD
00249 *     ..
00250 *     .. Executable Statements ..
00251 *
00252 *     Test the input parameters.
00253 *
00254       INFO = 0
00255       NORMALTRANSR = LSAME( TRANSR, 'N' )
00256       LOWER = LSAME( UPLO, 'L' )
00257       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00258          INFO = -1
00259       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00260          INFO = -2
00261       ELSE IF( N.LT.0 ) THEN
00262          INFO = -3
00263       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00264          INFO = -5
00265       END IF
00266       IF( INFO.NE.0 ) THEN
00267          CALL XERBLA( 'CTRTTF', -INFO )
00268          RETURN
00269       END IF
00270 *
00271 *     Quick return if possible
00272 *
00273       IF( N.LE.1 ) THEN
00274          IF( N.EQ.1 ) THEN
00275             IF( NORMALTRANSR ) THEN
00276                ARF( 0 ) = A( 0, 0 )
00277             ELSE
00278                ARF( 0 ) = CONJG( A( 0, 0 ) )
00279             END IF
00280          END IF
00281          RETURN
00282       END IF
00283 *
00284 *     Size of array ARF(1:2,0:nt-1)
00285 *
00286       NT = N*( N+1 ) / 2
00287 *
00288 *     set N1 and N2 depending on LOWER: for N even N1=N2=K
00289 *
00290       IF( LOWER ) THEN
00291          N2 = N / 2
00292          N1 = N - N2
00293       ELSE
00294          N1 = N / 2
00295          N2 = N - N1
00296       END IF
00297 *
00298 *     If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
00299 *     If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
00300 *     N--by--(N+1)/2.
00301 *
00302       IF( MOD( N, 2 ).EQ.0 ) THEN
00303          K = N / 2
00304          NISODD = .FALSE.
00305          IF( .NOT.LOWER )
00306      $      NP1X2 = N + N + 2
00307       ELSE
00308          NISODD = .TRUE.
00309          IF( .NOT.LOWER )
00310      $      NX2 = N + N
00311       END IF
00312 *
00313       IF( NISODD ) THEN
00314 *
00315 *        N is odd
00316 *
00317          IF( NORMALTRANSR ) THEN
00318 *
00319 *           N is odd and TRANSR = 'N'
00320 *
00321             IF( LOWER ) THEN
00322 *
00323 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00324 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00325 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
00326 *
00327                IJ = 0
00328                DO J = 0, N2
00329                   DO I = N1, N2 + J
00330                      ARF( IJ ) = CONJG( A( N2+J, I ) )
00331                      IJ = IJ + 1
00332                   END DO
00333                   DO I = J, N - 1
00334                      ARF( IJ ) = A( I, J )
00335                      IJ = IJ + 1
00336                   END DO
00337                END DO
00338 *
00339             ELSE
00340 *
00341 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00342 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00343 *             T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
00344 *
00345                IJ = NT - N
00346                DO J = N - 1, N1, -1
00347                   DO I = 0, J
00348                      ARF( IJ ) = A( I, J )
00349                      IJ = IJ + 1
00350                   END DO
00351                   DO L = J - N1, N1 - 1
00352                      ARF( IJ ) = CONJG( A( J-N1, L ) )
00353                      IJ = IJ + 1
00354                   END DO
00355                   IJ = IJ - NX2
00356                END DO
00357 *
00358             END IF
00359 *
00360          ELSE
00361 *
00362 *           N is odd and TRANSR = 'C'
00363 *
00364             IF( LOWER ) THEN
00365 *
00366 *              SRPA for LOWER, TRANSPOSE and N is odd
00367 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
00368 *              T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
00369 *
00370                IJ = 0
00371                DO J = 0, N2 - 1
00372                   DO I = 0, J
00373                      ARF( IJ ) = CONJG( A( J, I ) )
00374                      IJ = IJ + 1
00375                   END DO
00376                   DO I = N1 + J, N - 1
00377                      ARF( IJ ) = A( I, N1+J )
00378                      IJ = IJ + 1
00379                   END DO
00380                END DO
00381                DO J = N2, N - 1
00382                   DO I = 0, N1 - 1
00383                      ARF( IJ ) = CONJG( A( J, I ) )
00384                      IJ = IJ + 1
00385                   END DO
00386                END DO
00387 *
00388             ELSE
00389 *
00390 *              SRPA for UPPER, TRANSPOSE and N is odd
00391 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
00392 *              T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
00393 *
00394                IJ = 0
00395                DO J = 0, N1
00396                   DO I = N1, N - 1
00397                      ARF( IJ ) = CONJG( A( J, I ) )
00398                      IJ = IJ + 1
00399                   END DO
00400                END DO
00401                DO J = 0, N1 - 1
00402                   DO I = 0, J
00403                      ARF( IJ ) = A( I, J )
00404                      IJ = IJ + 1
00405                   END DO
00406                   DO L = N2 + J, N - 1
00407                      ARF( IJ ) = CONJG( A( N2+J, L ) )
00408                      IJ = IJ + 1
00409                   END DO
00410                END DO
00411 *
00412             END IF
00413 *
00414          END IF
00415 *
00416       ELSE
00417 *
00418 *        N is even
00419 *
00420          IF( NORMALTRANSR ) THEN
00421 *
00422 *           N is even and TRANSR = 'N'
00423 *
00424             IF( LOWER ) THEN
00425 *
00426 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00427 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00428 *              T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
00429 *
00430                IJ = 0
00431                DO J = 0, K - 1
00432                   DO I = K, K + J
00433                      ARF( IJ ) = CONJG( A( K+J, I ) )
00434                      IJ = IJ + 1
00435                   END DO
00436                   DO I = J, N - 1
00437                      ARF( IJ ) = A( I, J )
00438                      IJ = IJ + 1
00439                   END DO
00440                END DO
00441 *
00442             ELSE
00443 *
00444 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00445 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00446 *              T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
00447 *
00448                IJ = NT - N - 1
00449                DO J = N - 1, K, -1
00450                   DO I = 0, J
00451                      ARF( IJ ) = A( I, J )
00452                      IJ = IJ + 1
00453                   END DO
00454                   DO L = J - K, K - 1
00455                      ARF( IJ ) = CONJG( A( J-K, L ) )
00456                      IJ = IJ + 1
00457                   END DO
00458                   IJ = IJ - NP1X2
00459                END DO
00460 *
00461             END IF
00462 *
00463          ELSE
00464 *
00465 *           N is even and TRANSR = 'C'
00466 *
00467             IF( LOWER ) THEN
00468 *
00469 *              SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
00470 *              T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
00471 *              T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
00472 *
00473                IJ = 0
00474                J = K
00475                DO I = K, N - 1
00476                   ARF( IJ ) = A( I, J )
00477                   IJ = IJ + 1
00478                END DO
00479                DO J = 0, K - 2
00480                   DO I = 0, J
00481                      ARF( IJ ) = CONJG( A( J, I ) )
00482                      IJ = IJ + 1
00483                   END DO
00484                   DO I = K + 1 + J, N - 1
00485                      ARF( IJ ) = A( I, K+1+J )
00486                      IJ = IJ + 1
00487                   END DO
00488                END DO
00489                DO J = K - 1, N - 1
00490                   DO I = 0, K - 1
00491                      ARF( IJ ) = CONJG( A( J, I ) )
00492                      IJ = IJ + 1
00493                   END DO
00494                END DO
00495 *
00496             ELSE
00497 *
00498 *              SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
00499 *              T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
00500 *              T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
00501 *
00502                IJ = 0
00503                DO J = 0, K
00504                   DO I = K, N - 1
00505                      ARF( IJ ) = CONJG( A( J, I ) )
00506                      IJ = IJ + 1
00507                   END DO
00508                END DO
00509                DO J = 0, K - 2
00510                   DO I = 0, J
00511                      ARF( IJ ) = A( I, J )
00512                      IJ = IJ + 1
00513                   END DO
00514                   DO L = K + 1 + J, N - 1
00515                      ARF( IJ ) = CONJG( A( K+1+J, L ) )
00516                      IJ = IJ + 1
00517                   END DO
00518                END DO
00519 *
00520 *              Note that here J = K-1
00521 *
00522                DO I = 0, J
00523                   ARF( IJ ) = A( I, J )
00524                   IJ = IJ + 1
00525                END DO
00526 *
00527             END IF
00528 *
00529          END IF
00530 *
00531       END IF
00532 *
00533       RETURN
00534 *
00535 *     End of CTRTTF
00536 *
00537       END
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