matrix_m Module

  1. matrix.f90
  2. matrix_m

A matrix is a wrapper class for a rank 1 array of vector objects.
Matrices can be used to represent a variety of mathematical structures. This class is primarily used to bind a selection of Linear Algebra algorithms to a matrix object. Matrices can be instantiated by assignment of a rank2 array of any type, but the underlying data will be stored with double precision.

Matrix multiplication will be consistent with the mathematical operation (matmul), and element wise multiplication shall be represented by the hadamard product (OPERATOR .o.)

type(matrix) :: m, ortho_basis

m = reshape([1, 2, 3, 4], [2, 2]) ! Create a 2x2 matrix
print*, "M: "
call m%print()

ortho_basis = m%gram_schmidt() ! Compute an orthonormal basis using the Gram-Schmidt method

print"(A)", "Ortho:"
call ortho_basis%print()!!

output:

test


Uses


Contents

Interfaces

Derived Types


Interfaces

public interface matrix

Construct a matrix

  • private elemental function matrix_ctr_nk(n, k) result(A)

    Create a new -by- matrix by passing the number of rows and the number of columns

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in) :: n

    The number of rows in

    integer, intent(in) :: k

    The number of cols in

    Return Value type(matrix)

  • private elemental function matrix_ctr_nk_int(n, k, val) result(A)

    Create a new -by- matrix by passing the number of rows and the number of columns

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in) :: n

    The number of rows in

    integer, intent(in) :: k

    The number of cols in

    integer, intent(in) :: val

    Return Value type(matrix)

  • private elemental function matrix_ctr_nk_r32(n, k, val) result(A)

    Create a new -by- matrix by passing the number of rows and the number of columns

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in) :: n

    The number of rows in

    integer, intent(in) :: k

    The number of cols in

    real(kind=real32), intent(in) :: val

    Return Value type(matrix)

  • private elemental function matrix_ctr_nk_r64(n, k, val) result(A)

    Create a new -by- matrix by passing the number of rows and the number of columns

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in) :: n

    The number of rows in

    integer, intent(in) :: k

    The number of cols in

    real(kind=real64), intent(in) :: val

    Return Value type(matrix)

  • private pure function matrix_ctr_matrix(m2) result(A)

    Create a new -by- matrix by passing a rank2 integer array

    Arguments

    Type IntentOptional AttributesName
    class(matrix), intent(in) :: m2

    Return Value type(matrix)

  • private pure function matrix_ctr_int(array) result(A)

    Create a new -by- matrix by passing a rank2 integer array

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in), dimension(:,:):: array

    Return Value type(matrix)

  • private pure function matrix_ctr_r32(array) result(A)

    Create a new -by- matrix by passing a rank2 integer array

    Arguments

    Type IntentOptional AttributesName
    real(kind=real32), intent(in), dimension(:,:):: array

    Return Value type(matrix)

  • private pure function matrix_ctr_r64(array) result(A)

    Create a new -by- matrix by passing a rank2 integer array

    Arguments

    Type IntentOptional AttributesName
    real(kind=real64), intent(in), dimension(:,:):: array

    Return Value type(matrix)

  • private pure function matrix_ctr_rank1_int(array, n, k) result(A)

    Construct a -by- given a rank1 array of ints

    Arguments

    Type IntentOptional AttributesName
    integer, intent(in), dimension(:):: array
    integer, intent(in) :: n
    integer, intent(in) :: k

    Return Value type(matrix)

  • private pure function matrix_ctr_rank1_r32(array, n, k) result(A)

    Construct a -by- given a rank1 array of ints

    Arguments

    Type IntentOptional AttributesName
    real(kind=real32), intent(in), dimension(:):: array
    integer, intent(in) :: n
    integer, intent(in) :: k

    Return Value type(matrix)

  • private pure function matrix_ctr_rank1_r64(array, n, k) result(A)

    Construct a -by- given a rank1 array of ints

    Arguments

    Type IntentOptional AttributesName
    real(kind=real64), intent(in), dimension(:):: array
    integer, intent(in) :: n
    integer, intent(in) :: k

    Return Value type(matrix)


Derived Types

type, public :: matrix

Constructor

Construct a matrix

private elemental function matrix_ctr_nk(n, k)

Create a new -by- matrix by passing the number of rows and the number of columns

private elemental function matrix_ctr_nk_int(n, k, val)

Create a new -by- matrix by passing the number of rows and the number of columns

private elemental function matrix_ctr_nk_r32(n, k, val)

Create a new -by- matrix by passing the number of rows and the number of columns

private elemental function matrix_ctr_nk_r64(n, k, val)

Create a new -by- matrix by passing the number of rows and the number of columns

private pure function matrix_ctr_matrix(m2)

Create a new -by- matrix by passing a rank2 integer array

private pure function matrix_ctr_int(array)

Create a new -by- matrix by passing a rank2 integer array

private pure function matrix_ctr_r32(array)

Create a new -by- matrix by passing a rank2 integer array

private pure function matrix_ctr_r64(array)

Create a new -by- matrix by passing a rank2 integer array

private pure function matrix_ctr_rank1_int(array, n, k)

Construct a -by- given a rank1 array of ints

private pure function matrix_ctr_rank1_r32(array, n, k)

Construct a -by- given a rank1 array of ints

private pure function matrix_ctr_rank1_r64(array, n, k)

Construct a -by- given a rank1 array of ints

Type-Bound Procedures

generic, public :: new => new_, new_matrix_

Create a new matrix

procedure, public :: clear => clear_matrix

Clear all of the elements of a matrix

procedure, public :: print => print_matrix

Print the contents of a matrix

procedure, public :: vec => access_vector_matrix

Get the kth vector in the matrix

procedure, public :: at => at_index_matrix

Get the element at the index (i, j)

procedure, public :: gram_schmidt => gram_schmidt_matrix

Compute an otrthonormal basis for the vector space spanned by the columns of a matrix

procedure, public :: is_orthonormal => is_orthonormal_matrix

Check whether a matrix is orthonormal

procedure, public :: as_array => matrix_as_array

Return a rank2 Fortran array

procedure, public :: id => identity_matrix
procedure, public :: ncol => matrix_ncol

Return the number of cols of A

procedure, public :: nrow => matrix_nrow

Return the number of rows of A

generic, public :: create_hh => create_hh_
generic, public :: fill => fill_int_, fill_r32_, fill_r64_
generic, public :: set => set_int_, set_r32_, set_r64_

Set the value of (a_{i,j})

generic, public :: assignment(=) => from_array_int_, from_array_r32_, from_array_r64_, from_matrix

Assign the contents of a matrix from a rank2 Fortran array

procedure, public :: get_row => matrix_get_row
procedure, public :: get_col => matrix_get_col
generic, public :: set_row => set_row_int_, set_row_r32_, set_row_r64_, set_row_vec_
generic, public :: set_col => set_col_int_, set_col_r32_, set_col_r64_, set_col_vec_
generic, public :: operator(+) => add_matrix_

Operator interface to add two matrices

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generic, public :: operator(-) => minus_matrix_

Operator interface to subtract a matrix

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generic, public :: operator(*) => times_matrix_, times_vector_

Operator interface to multiply two matrices

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generic, public :: operator(.o.) => hadamard_
generic, public :: operator(**) => to_the_n_
generic, public :: plus => add_matrix_sub_

Subroutine interface to add two matrices

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generic, public :: minus => minus_matrix_sub_

Subroutine interface to add two matrices

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generic, public :: times => times_int_sub_, times_r32_sub_, times_r64_sub_