linalg::cholesky_rank1_update Interface Reference

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

Public Member Functions
	cholesky_rank1_update_dbl
	cholesky_rank1_update_cmplx

Detailed Description

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

Syntax

subroutine cholesky_rank1_update(real(real64) r(:,:), real(real64) u(:), optional real(real64) work(:), optional class(errors) err)
subroutine cholesky_rank1_update(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.

Notes

This routine utilizes the QRUPDATE routine DCH1UP (ZCH1UP in the complex case).

See Also

Source

Usage

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

program example
    use iso_fortran_env, only : real64, int32
    use linalg
    implicit none
 
    ! Variables
    real(real64) :: a(3,3), u(3), au(3,3)
    integer(int32) :: i
 
    ! Build the 3-by-3 positive-definite matrix A.
    !     | 4   12   -16 |
    ! A = | 12  37   -43 |
    !     |-16 -43    98 |
    a = reshape([4.0d0, 12.0d0, -16.0d0, 12.0d0, 37.0d0, -43.0d0, -16.0d0, &
        -43.0d0, 98.0d0], [3, 3])
 
    ! Build the update vector U
    u = [0.5d0, -1.5d0, 2.0d0]
 
    ! Compute the rank 1 update of A
    au = a
    call rank1_update(1.0d0, u, u, au)
 
    ! Compute the Cholesky factorization of the original matrix
    call cholesky_factor(a)
 
    ! Apply the rank 1 update to the factored matrix
    call cholesky_rank1_update(a, u)
 
    ! Compute the Cholesky factorization of the update of the original matrix
    call cholesky_factor(au)
 
    ! Display the matrices
    print '(A)', "Updating the Factored Form:"
    do i = 1, size(a, 1)
        print *, a(i,:)
    end do
 
    print '(A)', "Updating A Directly:"
    do i = 1, size(au, 1)
        print *, au(i,:)
    end do
end program

The above program produces the following output.

Updating the Factored Form:
 2.0615528128088303        5.4570515633174921       -7.2760687510899889
 0.0000000000000000        3.0774320845949008       -2.0452498947307731
 0.0000000000000000        0.0000000000000000        6.6989384530323566
Updating A Directly:
 2.0615528128088303        5.4570515633174921       -7.2760687510899889
 0.0000000000000000        3.0774320845949008       -2.0452498947307736
 0.0000000000000000        0.0000000000000000        6.6989384530323557

Definition at line 1786 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