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