matrix – Formath

type, public :: matrix

Constructor

public interface matrix

Construct a matrix

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

Create a new $n$ -by- $k$ matrix $A$ by passing the number of rows $n$ and the number of columns $k$

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	n	The number of rows in $m$
integer,	intent(in)			::	k	The number of cols in $m$

Return Value type(matrix)

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

Create a new $n$ -by- $k$ matrix $A$ by passing the number of rows $n$ and the number of columns $k$

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of rows in $m$
integer,	intent(in)	::	k	The number of cols in $m$
integer,	intent(in)	::	val

Return Value type(matrix)

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

Create a new $n$ -by- $k$ matrix $A$ by passing the number of rows $n$ and the number of columns $k$

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of rows in $m$
integer,	intent(in)	::	k	The number of cols in $m$
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 $n$ -by- $k$ matrix $A$ by passing the number of rows $n$ and the number of columns $k$

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of rows in $m$
integer,	intent(in)	::	k	The number of cols in $m$
real(kind=real64),	intent(in)	::	val

Return Value type(matrix)

private pure function matrix_ctr_matrix(m2) result(A)

Create a new $n$ -by- $k$ matrix $A$ by passing a rank2 integer array

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: m2

Return Value type(matrix)
private pure function matrix_ctr_int(array) result(A)

Create a new $n$ -by- $k$ matrix $A$ by passing a rank2 integer array

Arguments

Type Intent Optional Attributes Name

integer, intent(in), dimension(:,:) :: array

Return Value type(matrix)
private pure function matrix_ctr_r32(array) result(A)

Create a new $n$ -by- $k$ matrix $A$ by passing a rank2 integer array

Arguments

Type Intent Optional Attributes Name

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

Return Value type(matrix)
private pure function matrix_ctr_r64(array) result(A)

Create a new $n$ -by- $k$ matrix $A$ by passing a rank2 integer array

Arguments

Type Intent Optional Attributes Name

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

Return Value type(matrix)

Type	Intent	Optional	Attributes		Name
class(matrix),	intent(in)			::	m2

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		dimension(:,:)	::	array

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:,:)	::	array

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	array

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

Construct a $n$ -by- $k$ given a rank1 array of ints

Arguments

Type	Intent	Attributes		Name
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 $n$ -by- $k$ given a rank1 array of ints

Arguments

Type	Intent	Attributes		Name
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 $n$ -by- $k$ given a rank1 array of ints

Arguments

Type	Intent	Attributes		Name
real(kind=real64),	intent(in),	dimension(:)	::	array
integer,	intent(in)		::	n
integer,	intent(in)		::	k

Return Value type(matrix)

Type-Bound Procedures

generic, public :: new => new_, new_matrix_

Create a new matrix

private elemental subroutine new_matrix(self, n, k)

Wipe the contents of a matrix and allocate the proper amount of space

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self	Matrix object to wipe
integer,	intent(in)	::	n	Dimension of each constituent vector
integer,	intent(in)	::	k	Number of vectors

private elemental subroutine new_matrix_from_matrix(self, m2)

Wipe the contents of a matrix and allocate the proper amount of space

Arguments

Type	Intent	Optional	Attributes		Name
class(matrix),	intent(inout)			::	self	Matrix object to wipe
class(matrix),	intent(in)			::	m2	Matrix object to wipe

procedure, public :: clear => clear_matrix

Clear all of the elements of a matrix

private elemental subroutine clear_matrix(self)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

procedure, public :: print => print_matrix

Print the contents of a matrix

private subroutine print_matrix(self)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

procedure, public :: vec => access_vector_matrix

Get the kth vector in the matrix

private elemental function access_vector_matrix(self, v) result(vec)

Get a copy of the vth vector

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

integer, intent(in) :: v

Return Value type(vector)

procedure, public :: at => at_index_matrix

Get the element at the index (i, j)

private elemental function at_index_matrix(self, i, j) result(element)

Arguments

Type	Intent		Name
class(matrix),	intent(in)	::	self
integer,	intent(in)	::	i	ith element
integer,	intent(in)	::	j	jth vector

Return Value real(kind=real64)

procedure, public :: gram_schmidt => gram_schmidt_matrix

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

private elemental function gram_schmidt_matrix(self) result(ortho)

If there are more vectors than the dimension of the vector, only output n vectors

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

Return Value type(matrix)

procedure, public :: is_orthonormal => is_orthonormal_matrix

Check whether a matrix is orthonormal

private elemental function is_orthonormal_matrix(self) result(bool)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

Return Value logical

procedure, public :: as_array => matrix_as_array

Return a rank2 Fortran array

private pure function matrix_as_array(self) result(array)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

Return Value real(kind=real64), dimension(self%n, self%k)

procedure, public :: id => identity_matrix

private elemental function identity_matrix(self, n) result(I_n)

Return $I_n$

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

integer, optional value :: n

Return Value type(matrix)

procedure, public :: ncol => matrix_ncol

Return the number of cols of A

private elemental function matrix_ncol(self) result(icol)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

Return Value integer

procedure, public :: nrow => matrix_nrow

Return the number of rows of A

private elemental function matrix_nrow(self) result(irow)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

Return Value integer

generic, public :: create_hh => create_hh_

private elemental function matrix_create_householder_matrix(normal) result(m)

Arguments

Type Intent Optional Attributes Name

class(vector), intent(in) :: normal
A UNIT vector that is normal to a plane of rotation

Return Value type(matrix)

Type	Intent	Optional	Attributes		Name
class(vector),	intent(in)			::	normal	A UNIT vector that is normal to a plane of rotation

generic, public :: fill => fill_int_, fill_r32_, fill_r64_

private elemental subroutine matrix_fill_int(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

integer, intent(in) :: val
private elemental subroutine matrix_fill_r32(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

real(kind=real32), intent(in) :: val
private elemental subroutine matrix_fill_r64(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

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

generic, public :: set => set_int_, set_r32_, set_r64_

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

private elemental subroutine set_index_matrix_int(self, i, j, x)

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self
integer,	intent(in)	::	i	ith element
integer,	intent(in)	::	j	jth vector
integer,	intent(in)	::	x

private elemental subroutine set_index_matrix_r32(self, i, j, x)

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self
integer,	intent(in)	::	i	ith element
integer,	intent(in)	::	j	jth vector
real(kind=real32),	intent(in)	::	x

private elemental subroutine set_index_matrix_r64(self, i, j, x)

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self
integer,	intent(in)	::	i	ith element
integer,	intent(in)	::	j	jth vector
real(kind=real64),	intent(in)	::	x

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

private pure subroutine matrix_from_rank2_array_int(self, array)

Assign a matrix from a rank2 integer array

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

integer, intent(in), dimension(:,:) :: array

private pure subroutine matrix_from_rank2_array_r32(self, array)

Assign a matrix from a rank2 single precision real array

Arguments

Type	Intent	Optional	Attributes		Name
class(matrix),	intent(inout)			::	self
real(kind=real32),	intent(in),		dimension(:,:)	::	array

private pure subroutine matrix_from_rank2_array_r64(self, array)

Assign a matrix from a rank2 double precision array

Arguments

Type	Intent	Optional	Attributes		Name
class(matrix),	intent(inout)			::	self
real(kind=real64),	intent(in),		dimension(:,:)	::	array

private elemental subroutine matrix_from_matrix(self, m)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

class(matrix), intent(in) :: m

procedure, public :: get_row => matrix_get_row

private elemental function matrix_get_row(self, i) result(row_i)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

integer, intent(in) :: i
$i$ th row

Return Value type(vector)

procedure, public :: get_col => matrix_get_col

private elemental function matrix_get_col(self, j) result(col_j)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

integer, intent(in) :: j
$j$ th row

Return Value type(vector)

generic, public :: set_row => set_row_int_, set_row_r32_, set_row_r64_, set_row_vec_

private pure subroutine matrix_set_row_array_int(self, i, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	i	Row number
integer,	intent(in),	dimension(:)	::	array

private pure subroutine matrix_set_row_array_r32(self, i, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	i	Row number
real(kind=real32),	intent(in),	dimension(:)	::	array

private pure subroutine matrix_set_row_array_r64(self, i, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	i	Row number
real(kind=real64),	intent(in),	dimension(:)	::	array

private elemental subroutine matrix_set_row_vec(self, i, vec)

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self
integer,	intent(in)	::	i	Row number
class(vector),	intent(in)	::	vec

generic, public :: set_col => set_col_int_, set_col_r32_, set_col_r64_, set_col_vec_

private pure subroutine matrix_set_col_array_int(self, j, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	j	Column number
integer,	intent(in),	dimension(:)	::	array

private pure subroutine matrix_set_col_array_r32(self, j, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	j	Column number
real(kind=real32),	intent(in),	dimension(:)	::	array

private pure subroutine matrix_set_col_array_r64(self, j, array)

Arguments

Type	Intent	Attributes		Name
class(matrix),	intent(inout)		::	self
integer,	intent(in)		::	j	Column number
real(kind=real64),	intent(in),	dimension(:)	::	array

private elemental subroutine matrix_set_col_vec(self, j, vec)

Arguments

Type	Intent		Name
class(matrix),	intent(inout)	::	self
integer,	intent(in)	::	j	Column number
class(vector),	intent(in)	::	vec

generic, public :: operator(+) => add_matrix_

Operator interface to add two matrices

Note

As an operator, this procedure is a function which return a new matrix. use the functional operator equivalent, use [[]]

private elemental function matrix_add_matrix(self, m2) result(m3)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

class(matrix), intent(in) :: m2

Return Value type(matrix)

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

Operator interface to subtract a matrix

Note

As an operator, this procedure is a function which return a new matrix. use the functional operator equivalent, use [[]]

private elemental function matrix_minus_matrix(self, m2) result(m3)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

class(matrix), intent(in) :: m2

Return Value type(matrix)

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

Operator interface to multiply two matrices

Note

As an operator, this procedure is a function which return a new matrix. use the functional operator equivalent, use [[]]

private elemental function matrix_times_matrix(self, m2) result(m3)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

class(matrix), intent(in) :: m2

Return Value type(matrix)
private elemental function matrix_times_vector(self, v) result(v2)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

class(vector), intent(in) :: v

Return Value type(vector)

generic, public :: operator(.o.) => hadamard_

private elemental function matrix_hadamard_matrix(self, m2) result(m3)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

class(matrix), intent(in) :: m2

Return Value type(matrix)

generic, public :: operator()** => to_the_n_

private elemental function matrix_to_the_n(self, n) result(m2)

Raise a matrix to the nth power. Must be a square matrix

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(in) :: self

integer, intent(in) :: n

Return Value type(matrix)

generic, public :: plus => add_matrix_sub_

Subroutine interface to add two matrices

Note

This subroutine will alter the passed matrix. To use the functional operator equivalent, use $+$

private elemental subroutine matrix_add_matrix_sub(self, m2)

Subroutine interface to add two matrices
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Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

class(matrix), intent(in) :: m2

generic, public :: minus => minus_matrix_sub_

Subroutine interface to add two matrices

Note

This subroutine will alter the passed matrix. To use the functional operator equivalent, use $+$

private elemental subroutine matrix_minus_matrix_sub(self, m2)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

class(matrix), intent(in) :: m2

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

private elemental subroutine matrix_times_int_sub(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

integer, intent(in) :: val
private elemental subroutine matrix_times_r32_sub(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

real(kind=real32), intent(in) :: val
private elemental subroutine matrix_times_r64_sub(self, val)

Arguments

Type Intent Optional Attributes Name

class(matrix), intent(inout) :: self

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

matrix Derived Type

Contents

Constructor

Type-Bound Procedures

type, public :: matrix

Contents

Constructor

Type-Bound Procedures

Constructor

public interface matrix

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

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

private pure function matrix_ctr_matrix(m2) result(A)

Arguments

Return Value type(matrix)

private pure function matrix_ctr_int(array) result(A)

Arguments

Return Value type(matrix)

private pure function matrix_ctr_r32(array) result(A)

Arguments

Return Value type(matrix)

private pure function matrix_ctr_r64(array) result(A)

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

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

Arguments

Return Value type(matrix)

Type-Bound Procedures

generic, public :: new => new_, new_matrix_

private elemental subroutine new_matrix(self, n, k)

Arguments

private elemental subroutine new_matrix_from_matrix(self, m2)

Arguments

procedure, public :: clear => clear_matrix

private elemental subroutine clear_matrix(self)

Arguments

procedure, public :: print => print_matrix

private subroutine print_matrix(self)

Arguments

procedure, public :: vec => access_vector_matrix

private elemental function access_vector_matrix(self, v) result(vec)

Arguments

Return Value type(vector)

procedure, public :: at => at_index_matrix

private elemental function at_index_matrix(self, i, j) result(element)

Arguments

Return Value real(kind=real64)

procedure, public :: gram_schmidt => gram_schmidt_matrix

private elemental function gram_schmidt_matrix(self) result(ortho)

Arguments

Return Value type(matrix)

procedure, public :: is_orthonormal => is_orthonormal_matrix

private elemental function is_orthonormal_matrix(self) result(bool)

Arguments

Return Value logical

procedure, public :: as_array => matrix_as_array

private pure function matrix_as_array(self) result(array)

Arguments

Return Value real(kind=real64), dimension(self%n, self%k)

procedure, public :: id => identity_matrix

private elemental function identity_matrix(self, n) result(I_n)

Arguments

Return Value type(matrix)

procedure, public :: ncol => matrix_ncol