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version 1.6, 2011/07/22 07:38:12 version 1.7, 2011/11/21 20:43:05
Line 1 Line 1
       SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )  *> \brief \b DTFTTR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
 *  *
 *  -- LAPACK routine (version 3.3.1)                                    --  *> \htmlonly
   *> Download DTFTTR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfttr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfttr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfttr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          TRANSR, UPLO
   *       INTEGER            INFO, N, LDA
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( 0: LDA-1, 0: * ), ARF( 0: * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTFTTR copies a triangular matrix A from rectangular full packed
   *> format (TF) to standard full format (TR).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] TRANSR
   *> \verbatim
   *>          TRANSR is CHARACTER*1
   *>          = 'N':  ARF is in Normal format;
   *>          = 'T':  ARF is in Transpose format.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  A is upper triangular;
   *>          = 'L':  A is lower triangular.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrices ARF and A. N >= 0.
   *> \endverbatim
   *>
   *> \param[in] ARF
   *> \verbatim
   *>          ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2).
   *>          On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
   *>          matrix A in RFP format. See the "Notes" below for more
   *>          details.
   *> \endverbatim
   *>
   *> \param[out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          On exit, the triangular matrix A.  If UPLO = 'U', the
   *>          leading N-by-N upper triangular part of the array A contains
   *>          the upper triangular matrix, and the strictly lower
   *>          triangular part of A is not referenced.  If UPLO = 'L', the
   *>          leading N-by-N lower triangular part of the array A contains
   *>          the lower triangular matrix, and the strictly upper
   *>          triangular part of A is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  We first consider Rectangular Full Packed (RFP) Format when N is
   *>  even. We give an example where N = 6.
   *>
   *>      AP is Upper             AP is Lower
   *>
   *>   00 01 02 03 04 05       00
   *>      11 12 13 14 15       10 11
   *>         22 23 24 25       20 21 22
   *>            33 34 35       30 31 32 33
   *>               44 45       40 41 42 43 44
   *>                  55       50 51 52 53 54 55
   *>
   *>
   *>  Let TRANSR = 'N'. RFP holds AP as follows:
   *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
   *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
   *>  the transpose of the first three columns of AP upper.
   *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
   *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
   *>  the transpose of the last three columns of AP lower.
   *>  This covers the case N even and TRANSR = 'N'.
   *>
   *>         RFP A                   RFP A
   *>
   *>        03 04 05                33 43 53
   *>        13 14 15                00 44 54
   *>        23 24 25                10 11 55
   *>        33 34 35                20 21 22
   *>        00 44 45                30 31 32
   *>        01 11 55                40 41 42
   *>        02 12 22                50 51 52
   *>
   *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
   *>  transpose of RFP A above. One therefore gets:
   *>
   *>
   *>           RFP A                   RFP A
   *>
   *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
   *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
   *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
   *>
   *>
   *>  We then consider Rectangular Full Packed (RFP) Format when N is
   *>  odd. We give an example where N = 5.
   *>
   *>     AP is Upper                 AP is Lower
   *>
   *>   00 01 02 03 04              00
   *>      11 12 13 14              10 11
   *>         22 23 24              20 21 22
   *>            33 34              30 31 32 33
   *>               44              40 41 42 43 44
   *>
   *>
   *>  Let TRANSR = 'N'. RFP holds AP as follows:
   *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
   *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
   *>  the transpose of the first two columns of AP upper.
   *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
   *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
   *>  the transpose of the last two columns of AP lower.
   *>  This covers the case N odd and TRANSR = 'N'.
   *>
   *>         RFP A                   RFP A
   *>
   *>        02 03 04                00 33 43
   *>        12 13 14                10 11 44
   *>        22 23 24                20 21 22
   *>        00 33 34                30 31 32
   *>        01 11 44                40 41 42
   *>
   *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
   *>  transpose of RFP A above. One therefore gets:
   *>
   *>           RFP A                   RFP A
   *>
   *>     02 12 22 00 01             00 10 20 30 40 50
   *>     03 13 23 33 11             33 11 21 31 41 51
   *>     04 14 24 34 44             43 44 22 32 42 52
   *> \endverbatim
 *  *
 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --  *  =====================================================================
 *  -- April 2011                                                      --        SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
 *  *
   *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          TRANSR, UPLO        CHARACTER          TRANSR, UPLO
Line 16 Line 209
       DOUBLE PRECISION   A( 0: LDA-1, 0: * ), ARF( 0: * )        DOUBLE PRECISION   A( 0: LDA-1, 0: * ), ARF( 0: * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DTFTTR copies a triangular matrix A from rectangular full packed  
 *  format (TF) to standard full format (TR).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  TRANSR  (input) CHARACTER*1  
 *          = 'N':  ARF is in Normal format;  
 *          = 'T':  ARF is in Transpose format.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  A is upper triangular;  
 *          = 'L':  A is lower triangular.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices ARF and A. N >= 0.  
 *  
 *  ARF     (input) DOUBLE PRECISION array, dimension (N*(N+1)/2).  
 *          On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')  
 *          matrix A in RFP format. See the "Notes" below for more  
 *          details.  
 *  
 *  A       (output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On exit, the triangular matrix A.  If UPLO = 'U', the  
 *          leading N-by-N upper triangular part of the array A contains  
 *          the upper triangular matrix, and the strictly lower  
 *          triangular part of A is not referenced.  If UPLO = 'L', the  
 *          leading N-by-N lower triangular part of the array A contains  
 *          the lower triangular matrix, and the strictly upper  
 *          triangular part of A is not referenced.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  We first consider Rectangular Full Packed (RFP) Format when N is  
 *  even. We give an example where N = 6.  
 *  
 *      AP is Upper             AP is Lower  
 *  
 *   00 01 02 03 04 05       00  
 *      11 12 13 14 15       10 11  
 *         22 23 24 25       20 21 22  
 *            33 34 35       30 31 32 33  
 *               44 45       40 41 42 43 44  
 *                  55       50 51 52 53 54 55  
 *  
 *  
 *  Let TRANSR = 'N'. RFP holds AP as follows:  
 *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last  
 *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of  
 *  the transpose of the first three columns of AP upper.  
 *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first  
 *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of  
 *  the transpose of the last three columns of AP lower.  
 *  This covers the case N even and TRANSR = 'N'.  
 *  
 *         RFP A                   RFP A  
 *  
 *        03 04 05                33 43 53  
 *        13 14 15                00 44 54  
 *        23 24 25                10 11 55  
 *        33 34 35                20 21 22  
 *        00 44 45                30 31 32  
 *        01 11 55                40 41 42  
 *        02 12 22                50 51 52  
 *  
 *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the  
 *  transpose of RFP A above. One therefore gets:  
 *  
 *  
 *           RFP A                   RFP A  
 *  
 *     03 13 23 33 00 01 02    33 00 10 20 30 40 50  
 *     04 14 24 34 44 11 12    43 44 11 21 31 41 51  
 *     05 15 25 35 45 55 22    53 54 55 22 32 42 52  
 *  
 *  
 *  We then consider Rectangular Full Packed (RFP) Format when N is  
 *  odd. We give an example where N = 5.  
 *  
 *     AP is Upper                 AP is Lower  
 *  
 *   00 01 02 03 04              00  
 *      11 12 13 14              10 11  
 *         22 23 24              20 21 22  
 *            33 34              30 31 32 33  
 *               44              40 41 42 43 44  
 *  
 *  
 *  Let TRANSR = 'N'. RFP holds AP as follows:  
 *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last  
 *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of  
 *  the transpose of the first two columns of AP upper.  
 *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first  
 *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of  
 *  the transpose of the last two columns of AP lower.  
 *  This covers the case N odd and TRANSR = 'N'.  
 *  
 *         RFP A                   RFP A  
 *  
 *        02 03 04                00 33 43  
 *        12 13 14                10 11 44  
 *        22 23 24                20 21 22  
 *        00 33 34                30 31 32  
 *        01 11 44                40 41 42  
 *  
 *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the  
 *  transpose of RFP A above. One therefore gets:  
 *  
 *           RFP A                   RFP A  
 *  
 *     02 12 22 00 01             00 10 20 30 40 50  
 *     03 13 23 33 11             33 11 21 31 41 51  
 *     04 14 24 34 44             43 44 22 32 42 52  
 *  
 *  Reference  
 *  =========  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     ..  *     ..
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