--- 
:name: dpftrf
:md5sum: 3fc77e15efea7d6ef9bac22a903fe147
:category: :subroutine
:arguments: 
- transr: 
    :type: char
    :intent: input
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - n*(n+1)/2
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DPFTRF computes the Cholesky factorization of a real symmetric\n\
  *  positive definite matrix A.\n\
  *\n\
  *  The factorization has the form\n\
  *     A = U**T * U,  if UPLO = 'U', or\n\
  *     A = L  * L**T,  if UPLO = 'L',\n\
  *  where U is an upper triangular matrix and L is lower triangular.\n\
  *\n\
  *  This is the block version of the algorithm, calling Level 3 BLAS.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  TRANSR    (input) CHARACTER*1\n\
  *          = 'N':  The Normal TRANSR of RFP A is stored;\n\
  *          = 'T':  The Transpose TRANSR of RFP A is stored.\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of RFP A is stored;\n\
  *          = 'L':  Lower triangle of RFP A is stored.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );\n\
  *          On entry, the symmetric matrix A in RFP format. RFP format is\n\
  *          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'\n\
  *          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is\n\
  *          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is\n\
  *          the transpose of RFP A as defined when\n\
  *          TRANSR = 'N'. The contents of RFP A are defined by UPLO as\n\
  *          follows: If UPLO = 'U' the RFP A contains the NT elements of\n\
  *          upper packed A. If UPLO = 'L' the RFP A contains the elements\n\
  *          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =\n\
  *          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N\n\
  *          is odd. See the Note below for more details.\n\
  *\n\
  *          On exit, if INFO = 0, the factor U or L from the Cholesky\n\
  *          factorization RFP A = U**T*U or RFP A = L*L**T.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *          > 0:  if INFO = i, the leading minor of order i is not\n\
  *                positive definite, and the factorization could not be\n\
  *                completed.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  We first consider Rectangular Full Packed (RFP) Format when N is\n\
  *  even. We give an example where N = 6.\n\
  *\n\
  *      AP is Upper             AP is Lower\n\
  *\n\
  *   00 01 02 03 04 05       00\n\
  *      11 12 13 14 15       10 11\n\
  *         22 23 24 25       20 21 22\n\
  *            33 34 35       30 31 32 33\n\
  *               44 45       40 41 42 43 44\n\
  *                  55       50 51 52 53 54 55\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of\n\
  *  the transpose of the first three columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of\n\
  *  the transpose of the last three columns of AP lower.\n\
  *  This covers the case N even and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        03 04 05                33 43 53\n\
  *        13 14 15                00 44 54\n\
  *        23 24 25                10 11 55\n\
  *        33 34 35                20 21 22\n\
  *        00 44 45                30 31 32\n\
  *        01 11 55                40 41 42\n\
  *        02 12 22                50 51 52\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     03 13 23 33 00 01 02    33 00 10 20 30 40 50\n\
  *     04 14 24 34 44 11 12    43 44 11 21 31 41 51\n\
  *     05 15 25 35 45 55 22    53 54 55 22 32 42 52\n\
  *\n\
  *\n\
  *  We then consider Rectangular Full Packed (RFP) Format when N is\n\
  *  odd. We give an example where N = 5.\n\
  *\n\
  *     AP is Upper                 AP is Lower\n\
  *\n\
  *   00 01 02 03 04              00\n\
  *      11 12 13 14              10 11\n\
  *         22 23 24              20 21 22\n\
  *            33 34              30 31 32 33\n\
  *               44              40 41 42 43 44\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of\n\
  *  the transpose of the first two columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of\n\
  *  the transpose of the last two columns of AP lower.\n\
  *  This covers the case N odd and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        02 03 04                00 33 43\n\
  *        12 13 14                10 11 44\n\
  *        22 23 24                20 21 22\n\
  *        00 33 34                30 31 32\n\
  *        01 11 44                40 41 42\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     02 12 22 00 01             00 10 20 30 40 50\n\
  *     03 13 23 33 11             33 11 21 31 41 51\n\
  *     04 14 24 34 44             43 44 22 32 42 52\n\
  *\n\
  *  =====================================================================\n\
  *\n"
