SRC/spftrf.f(3)

NAME
SRC/spftrf.f

SYNOPSIS

  Functions/Subroutines
subroutine spftrf (transr, uplo, n, a, info)
SPFTRF

Function/Subroutine Documentation

  subroutine spftrf (character transr, character uplo, integer n, real, dimension( 0: * ) a, integer info)

SPFTRF

Purpose:

    !>
    !> SPFTRF 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.
    !>

Parameters
    TRANSR

    !>          TRANSR is CHARACTER*1
    !>          = 'N':  The Normal TRANSR of RFP A is stored;
    !>          = 'T':  The Transpose TRANSR of RFP A is stored.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of RFP A is stored;
    !>          = 'L':  Lower triangle of RFP A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL 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

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, the leading principal minor of order i
    !>                is not positive, and the factorization could not be
    !>                completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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
    !>

Definition at line 197 of file spftrf.f.

Author

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