NAFPack_matricielle

Module for Tensor operations in NAFPack

Uses

- NAFPack_constant
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Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.
Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Functions

public function dot(a, b) result(result)

function that calculates the dot product of two real 3-dimensional vectors $\vec{a}$ and $\vec{b}$ $\vec{a} \cdot \vec{b}$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in),		DIMENSION(:)	::	a
real(kind=dp),	intent(in),		DIMENSION(:)	::	b

Return Value real(kind=dp)

public function cross(a, b) result(result)

function that calculates the cross product between two real 3-dimensional vectors $\vec{a}$ and $\vec{b}$ $\vec{a} \times \vec{b}$ ¹

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),			DIMENSION(3)	::	a
real(kind=dp),			DIMENSION(3)	::	b

Return Value real(kind=dp), DIMENSION(3)

public function norm_2(a) result(result)

function that calculates the Euclidean norm (L2 norm) of a vector $\vec{a}$ , where $\vec{a} \in \mathbb{R}^n$ $||\vec{a}||_2 = \sqrt{\sum_{i=1}^{n} a_i^2} \quad \text{ with } \quad \sum_{i=1}^{n} a_i^2 = \vec{a} \cdot \vec{a}$ where $n$ is the dimension of the real vector $\vec{a}$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),			DIMENSION(:)	::	a

Return Value real(kind=dp)

public function norm_2_complex(a) result(result)

function that calculates the Euclidean norm (L2 norm or modulus) of a vector $\vec{a}$ , where $\vec{a} \in \mathbb{C}^n$ $||\vec{a}||_2 = \sqrt{\sum_{i=1}^{n} |a_i|^2} \quad \text{ with } \quad \sum_{i=1}^{n} |a_i|^2 = \vec{a} \cdot \overline{\vec{a}}$ where $n$ is the dimension of the complex vector $\vec{a}$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),			DIMENSION(:)	::	a

Return Value real(kind=dp)

public function normalise(a) result(result)

function that normalises a real vector a to make it a unit vector, where $\vec{a} \in \mathbb{R}^n$ $\hat{a} = \frac{\vec{a}}{||\vec{a}||_2}$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),			DIMENSION(:)	::	a

Return Value real(kind=dp), DIMENSION(SIZE(a))

public function normalise_complexe(a) result(result)

function that normalises a complex vector a to make it a unit vector, where $\vec{a} \in \mathbb{C}^n$ $\hat{a} = \frac{\vec{a}}{||\vec{a}||_2}$

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),			DIMENSION(:)	::	a

Return Value complex(kind=dp), DIMENSION(SIZE(a))

public function Trace(A) result(result)

function that calculates the trace of a square matrix $A$ $\text{Tr}(A) = \sum_{i=1}^{n} A(i,i)$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in),		DIMENSION(:, :)	::	A

Return Value real(kind=dp)

public function Diagonally_Dominant_Matrix(A) result(diagonally_dominant)

function which checks if A is diagonally dominant $\forall i, |A(i,i)| \geq \sum_{j \neq i} |A(i,j)|$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in),		DIMENSION(:, :)	::	A

Return Value logical

public function Identity_n(N, use_concurrent) result(Identity)

function that returns the identity matrix for a given size N $I_N = \begin{pmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{pmatrix}$

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	N
logical,	intent(in),	optional		::	use_concurrent

Return Value real(kind=dp), DIMENSION(N, N)

public function Diag(A) result(D)

function that extracts the diagonal of a matrix $D = \begin{pmatrix} A(1,1) & 0 & \cdots & 0 \\ 0 & A(2,2) & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & A(n,n) \end{pmatrix}$ where $D$ is a vector containing the diagonal elements of the matrix $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in),		DIMENSION(:,:)	::	A

Return Value real(kind=dp), DIMENSION(SIZE(A,1))

public function rotation_matrix(A, rotation) result(G)

Function to create a rotation matrix

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in),		DIMENSION(:, :)	::	A
integer,	intent(in),		DIMENSION(2)	::	rotation

NAFPack_matricielle Module

Contents

Functions

Uses

Used by

Functions

public function dot(a, b) result(result)

Arguments

Return Value real(kind=dp)

public function cross(a, b) result(result)

Arguments

Return Value real(kind=dp), DIMENSION(3)

public function norm_2(a) result(result)

Arguments

Return Value real(kind=dp)

public function norm_2_complex(a) result(result)

Arguments

Return Value real(kind=dp)

public function normalise(a) result(result)

Arguments

Return Value real(kind=dp), DIMENSION(SIZE(a))

public function normalise_complexe(a) result(result)

Arguments

Return Value complex(kind=dp), DIMENSION(SIZE(a))

public function Trace(A) result(result)

Arguments

Return Value real(kind=dp)

public function Diagonally_Dominant_Matrix(A) result(diagonally_dominant)

Arguments

Return Value logical

public function Identity_n(N, use_concurrent) result(Identity)

Arguments

Return Value real(kind=dp), DIMENSION(N, N)

public function Diag(A) result(D)

Arguments

Return Value real(kind=dp), DIMENSION(SIZE(A,1))

public function rotation_matrix(A, rotation) result(G)

Arguments

Return Value real(kind=dp), DIMENSION(SIZE(A, 1),SIZE(A, 2))