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version 1.6, 2011/07/22 07:38:09 version 1.7, 2011/11/21 20:43:01
Line 1 Line 1
       SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO )  *> \brief \b DPFTRF
   *
   *  =========== DOCUMENTATION ===========
 *  *
 *  -- LAPACK routine (version 3.3.1)                                    --  * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
 *  *
 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --  *> \htmlonly
 *  -- April 2011                                                      --  *> Download DPFTRF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftrf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftrf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftrf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          TRANSR, UPLO
   *       INTEGER            N, INFO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( 0: * )
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DPFTRF computes the Cholesky factorization of a real symmetric
   *> positive definite matrix A.
   *>
   *> The factorization has the form
   *>    A = U**T * U,  if UPLO = 'U', or
   *>    A = L  * L**T,  if UPLO = 'L',
   *> where U is an upper triangular matrix and L is lower triangular.
   *>
   *> This is the block version of the algorithm, calling Level 3 BLAS.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] TRANSR
   *> \verbatim
   *>          TRANSR is CHARACTER*1
   *>          = 'N':  The Normal TRANSR of RFP A is stored;
   *>          = 'T':  The Transpose TRANSR of RFP A is stored.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangle of RFP A is stored;
   *>          = 'L':  Lower triangle of RFP A is stored.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
   *>          On entry, the symmetric matrix A in RFP format. RFP format is
   *>          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
   *>          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
   *>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
   *>          the transpose of RFP A as defined when
   *>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
   *>          follows: If UPLO = 'U' the RFP A contains the NT elements of
   *>          upper packed A. If UPLO = 'L' the RFP A contains the elements
   *>          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
   *>          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N
   *>          is odd. See the Note below for more details.
   *>
   *>          On exit, if INFO = 0, the factor U or L from the Cholesky
   *>          factorization RFP A = U**T*U or RFP A = L*L**T.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = i, the leading minor of order i is not
   *>                positive definite, and the factorization could not be
   *>                completed.
   *> \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
   *>
   *  =====================================================================
         SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, 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
       INTEGER            N, INFO        INTEGER            N, INFO
Line 16 Line 210
 *     .. Array Arguments ..  *     .. Array Arguments ..
       DOUBLE PRECISION   A( 0: * )        DOUBLE PRECISION   A( 0: * )
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DPFTRF computes the Cholesky factorization of a real symmetric  
 *  positive definite matrix A.  
 *  
 *  The factorization has the form  
 *     A = U**T * U,  if UPLO = 'U', or  
 *     A = L  * L**T,  if UPLO = 'L',  
 *  where U is an upper triangular matrix and L is lower triangular.  
 *  
 *  This is the block version of the algorithm, calling Level 3 BLAS.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  TRANSR    (input) CHARACTER*1  
 *          = 'N':  The Normal TRANSR of RFP A is stored;  
 *          = 'T':  The Transpose TRANSR of RFP A is stored.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of RFP A is stored;  
 *          = 'L':  Lower triangle of RFP A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );  
 *          On entry, the symmetric matrix A in RFP format. RFP format is  
 *          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'  
 *          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is  
 *          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is  
 *          the transpose of RFP A as defined when  
 *          TRANSR = 'N'. The contents of RFP A are defined by UPLO as  
 *          follows: If UPLO = 'U' the RFP A contains the NT elements of  
 *          upper packed A. If UPLO = 'L' the RFP A contains the elements  
 *          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =  
 *          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N  
 *          is odd. See the Note below for more details.  
 *  
 *          On exit, if INFO = 0, the factor U or L from the Cholesky  
 *          factorization RFP A = U**T*U or RFP A = L*L**T.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = i, the leading minor of order i is not  
 *                positive definite, and the factorization could not be  
 *                completed.  
 *  
 *  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  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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