linalg::cholesky_rank1_downdate Interface Reference

Computes the rank 1 downdate to a Cholesky factored matrix (upper triangular). More...

Public Member Functions
	cholesky_rank1_downdate_dbl
	cholesky_rank1_downdate_cmplx

Detailed Description

Computes the rank 1 downdate to a Cholesky factored matrix (upper triangular).

Syntax

subroutine cholesky_rank1_downdate(real(real64) r(:,:), real(real64) u(:), optional real(real64) work(:), optional class(errors) err)
subroutine cholesky_rank1_downdate(complex(real64) r(:,:), complex(real64) u(:), optional complex(real64) work(:), optional class(errors) err)

Parameters

[in,out]	r	On input, the N-by-N upper triangular matrix R. On output, the updated matrix R1.
[in,out]	u	On input, the N-element update vector U. On output, the rotation sines used to transform R to R1.
[out]	work	An optional argument that if supplied prevents local memory allocation. If provided, the array must have at least N elements. Additionally, this workspace array is used to contain the rotation cosines used to transform R to R1.
[in,out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. LA_ARRAY_SIZE_ERROR: Occurs if any of the input array sizes are incorrect. LA_OUT_OF_MEMORY_ERROR: Occurs if local memory must be allocated, and there is insufficient memory available. LA_MATRIX_FORMAT_ERROR: Occurs if the downdated matrix is not positive definite. LA_SINGULAR_MATRIX_ERROR: Occurs if r is singular.

Notes

This routine utilizes the QRUPDATE routine DCH1DN (ZCH1DN in the complex case).

See Also

Source

Usage

The following example illustrates the use of the rank 1 Cholesky downdate, and compares the results to factoring the original rank 1 downdated matrix.

program example
    use iso_fortran_env, only : real64, int32
    use linalg_factor, only : cholesky_factor, cholesky_rank1_downdate
    use linalg, only : rank1_update
    implicit none
 
    ! Variables
    real(real64) :: a(3,3), u(3), ad(3,3)
    integer(int32) :: i
 
    ! Build the 3-by-3 matrix A.
    !     |  4.25   11.25   -15 |
    ! A = | 11.25   39.25   -46 |
    !     |  -15     -46    102 |
    a = reshape([4.25d0, 11.25d0, -15.0d0, 11.25d0, 39.25d0, -46.0d0, &
        -15.0d0, -46.0d0, 102.0d0], [3, 3])
 
    ! The downdate vector
    !     |  0.5 |
    ! u = | -1.5 |
    !     |   2  |
    u = [0.5d0, -1.5d0, 2.0d0]
 
    ! Compute the rank 1 downdate of A
    ad = a
    call rank1_update(-1.0d0, u, u, ad)
 
    ! Compute the Cholesky factorization of the original matrix
    call cholesky_factor(a)
 
    ! Apply the rank 1 downdate to the factored matrix
    call cholesky_rank1_downdate(a, u)
 
    ! Compute the Cholesky factorization of the downdate to the original matrix
    call cholesky_factor(ad)
 
    ! Display the matrices
    print '(A)', "Downdating the Factored Form:"
    do i = 1, size(a, 1)
        print *, a(i,:)
    end do
 
    print '(A)', "Downdating A Directly:"
    do i = 1, size(ad, 1)
        print *, ad(i,:)
    end do
end program

The above program produces the following output.

Downdating the Factored Form:
 2.0000000000000000        6.0000000000000000       -8.0000000000000000
 0.0000000000000000        1.0000000000000000        4.9999999999999973
 0.0000000000000000        0.0000000000000000        3.0000000000000049
Downdating A Directly:
 2.0000000000000000        6.0000000000000000       -8.0000000000000000
 0.0000000000000000        1.0000000000000000        5.0000000000000000
 0.0000000000000000        0.0000000000000000        3.0000000000000000

Definition at line 1893 of file linalg.f90.

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The documentation for this interface was generated from the following file:

• D:/Code/linalg/src/linalg.f90