linalg::solve_lq Interface Reference

Solves a system of M LQ-factored equations of N unknowns. N must be greater than or equal to M. More...

Public Member Functions
	solve_lq_mtx
	solve_lq_mtx_cmplx
	solve_lq_vec
	solve_lq_vec_cmplx

Detailed Description

Solves a system of M LQ-factored equations of N unknowns. N must be greater than or equal to M.

Syntax

subroutine solve_lq(real(real64) a(:,:), real(real64) tau(:), real(real64) b(:,:), optional real(real64) work(:), optional integer(int32) olwork, optional class(errors) err)
subroutine solve_lq(complex(real64) a(:,:), complex(real64) tau(:), complex(real64) b(:,:), optional complex(real64) work(:), optional integer(int32) olwork, optional class(errors) err)
subroutine solve_lq(real(real64) a(:,:), real(real64) tau(:), real(real64) b(:), optional real(real64) work(:), optional integer(int32) olwork, optional class(errors) err)
subroutine solve_lq(complex(real64) a(:,:), complex(real64) tau(:), complex(real64) b(:), optional complex(real64) work(:), optional integer(int32) olwork, optional class(errors) err)

Parameters

[in]	a	On input, the M-by-N LQ factored matrix as returned by lq_factor. On output, the contents of this matrix are restored. Notice, N must be greater than or equal to M.
[in]	tau	A MIN(M, N)-element array containing the scalar factors of the elementary reflectors as returned by lq_factor.
[in]	b	On input, an N-by-NRHS matrix where the first M rows contain the right-hand-side matrix. On output, the N-by-NRHS solution matrix X.
[out]	work	An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.
[out]	olwork	An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.
[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 arrays are not sized appropriately. LA_OUT_OF_MEMORY_ERROR: Occurs if local memory must be allocated, and there is insufficient memory available.

Usage

The following example illustrates the solution of a system of equations using LQ factorization.

program example
    use iso_fortran_env, only : real64, int32
    use linalg
    implicit none
 
    ! Local Variables
    real(real64) :: a(3,3), tau(3), b(3)
    integer(int32) :: i, pvt(3)
 
    ! Build the 3-by-3 matrix A.
    !     | 1   2   3 |
    ! A = | 4   5   6 |
    !     | 7   8   0 |
    a = reshape( &
        [1.0d0, 4.0d0, 7.0d0, 2.0d0, 5.0d0, 8.0d0, 3.0d0, 6.0d0, 0.0d0], &
        [3, 3])
 
    ! Build the right-hand-side vector B.
    !     | -1 |
    ! b = | -2 |
    !     | -3 |
    b = [-1.0d0, -2.0d0, -3.0d0]
 
    ! The solution is:
    !     |  1/3 |
    ! x = | -2/3 |
    !     |   0  |
 
    ! Compute the LQ factorization
    call lq_factor(a, tau)
 
    ! Compute the solution.  The results overwrite b.
    call solve_lq(a, tau, b)
 
    ! Display the results
    print '(A)', "LQ Solution: X = "
    print '(F8.4)', (b(i), i = 1, size(b))
end program

The above program produces the following output.

QR Solution: X =
0.3333
-0.6667
0.0000

See Also

• LAPACK Users Manual

Definition at line 3928 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