matrix.sc

Module with functions for manipulating matrices and vectors.

Functions:

colSums

determinant

leftTransposedMultiplication

rightTransposedMultiplication

diagMatrixMultiplication

dotProduct

matrixMultiplication

colSums

Function for summarizing the columns of a matrix.

Detailed Description

D - all protection domains

Supported types - bool / uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

mat	- a matrix of supported type

returns a vector with the sums of each column in the input matrix

None

Function Overloads

D uint colSums(D bool[[2]] mat)

D uint8 colSums(D uint8[[2]] mat)

D uint16 colSums(D uint16[[2]] mat)

D uint32 colSums(D uint32[[2]] mat)

D uint colSums(D uint[[2]] mat)

D int8 colSums(D int8[[2]] mat)

D int16 colSums(D int16[[2]] mat)

D int32 colSums(D int32[[2]] mat)

D int colSums(D int[[2]] mat)

D float32 colSums(D float32[[2]] mat)

D float64 colSums(D float64[[2]] mat)

determinant

Function for finding the determinant of a matrix.

Detailed Description

Supported types - float32 / float64

Parameters

mat	- a matrix of supported type

returns the determinant of the input matrix

None

Function Overloads

float32 determinant(float32[[2]] mat)

float64 determinant(float64[[2]] mat)

D float64 determinant(D float32[[2]] mat)

D - all protection domains

naive determinant implementation

D float64 determinant(D float64[[2]] mat)

D - all protection domains

naive determinant implementation

leftTransposedMultiplication

Function for multiplying X^T by X.

Detailed Description

D - any protection domain

Supported types uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

- matrix

returns transposed x multiplied by x

None

Function Overloads

D uint8 leftTransposedMultiplication(D uint8[[2]] x)

D uint16 leftTransposedMultiplication(D uint16[[2]] x)

D uint32 leftTransposedMultiplication(D uint32[[2]] x)

D uint64 leftTransposedMultiplication(D uint64[[2]] x)

D int8 leftTransposedMultiplication(D int8[[2]] x)

D int16 leftTransposedMultiplication(D int16[[2]] x)

D int32 leftTransposedMultiplication(D int32[[2]] x)

D int64 leftTransposedMultiplication(D int64[[2]] x)

D float32 leftTransposedMultiplication(D float32[[2]] x)

D float64 leftTransposedMultiplication(D float64[[2]] x)

rightTransposedMultiplication

Function for multiplying X by X^T.

Detailed Description

D - any protection domain

Supported types uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

- matrix

returns x multiplied by transposed x

None

Function Overloads

D uint8 rightTransposedMultiplication(D uint8[[2]] x)

D uint16 rightTransposedMultiplication(D uint16[[2]] x)

D uint32 rightTransposedMultiplication(D uint32[[2]] x)

D uint64 rightTransposedMultiplication(D uint64[[2]] x)

D int8 rightTransposedMultiplication(D int8[[2]] x)

D int16 rightTransposedMultiplication(D int16[[2]] x)

D int32 rightTransposedMultiplication(D int32[[2]] x)

D int64 rightTransposedMultiplication(D int64[[2]] x)

D float32 rightTransposedMultiplication(D float32[[2]] x)

D float64 rightTransposedMultiplication(D float64[[2]] x)

rowSums

Function for summing the rows of a matrix.

Detailed Description

D - all protection domains

Supported types - bool / uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

mat	- a matrix of supported type

returns a vector with the sums of each row in the input matrix

None

Function Overloads

D uint rowSums(D bool[[2]] mat)

D uint8 rowSums(D uint8[[2]] mat)

D uint16 rowSums(D uint16[[2]] mat)

D uint32 rowSums(D uint32[[2]] mat)

D uint rowSums(D uint[[2]] mat)

D int8 rowSums(D int8[[2]] mat)

D int16 rowSums(D int16[[2]] mat)

D int32 rowSums(D int32[[2]] mat)

D int rowSums(D int[[2]] mat)

D float32 rowSums(D float32[[2]] mat)

D float64 rowSums(D float64[[2]] mat)

transpose

Function for transposing matrices.

Detailed Description

D - all protection domains

T - any data type

Function Overloads

D T transpose(D T[[2]] mat)

Parameters

mat	- a 2-dimensional matrix

returns the transposed version of the input matrix

None

D T transpose(D T[[3]] arr)

Parameters

arr	- a 3-dimensional array

Transposes across the last two dimensions

returns a 2-dimensional array transposed across the last two dimension

None

unitMatrix

Function for creating a unit matrix.

Detailed Description

D - all protection domains

Parameters

n	- number of rows/columns in the matrix

a unit matrix of size n

Function Overloads

D bool unitMatrix(uint n)

unitVector

Function for finding the unit vector of the input vector.

Detailed Description

Only for public domain (at this point only public sqrt is in scope).

Supported types - float32 / float64

Function Overloads

float32 unitVector(float32[[1]] x)

Parameters

x	- vector of supported type

returns the unit vector for the input vector

float64 unitVector(float64[[1]] x)

Parameters

x	- vector of supported type

returns the unit vector for the input vector

float32 unitVector(float32[[2]] x)

Parameters

x	- matrix of supported type

returns a matrix with the unit vector of each row in the input matrix

float64 unitVector(float64[[2]] x)

Parameters

x	- matrix of supported type

returns a matrix with the unit vector of each row in the input matrix

vecLength

Function for finding the length of a vector.

Detailed Description

Only for public domain (at this point only public sqrt is in scope).

Supported types - float32 / float64

Function Overloads

float32 vecLength(float32[[1]] x)

Parameters

x	- vector of supported type

returns the length of the vector

float64 vecLength(float64[[1]] x)

Parameters

x	- vector of supported type

returns the length of the vector

float32 vecLength(float32[[2]] x)

Parameters

x	- matrix of supported type

returns a vector with length of each row in the matrix

float64 vecLength(float64[[2]] x)

Parameters

x	- matrix of supported type

returns a vector with length of each row in the matrix

crossProduct

Function for finding the cross product of two vectors/matrices.

Functions:

crossProduct[[1]]

crossProduct[[2]]

D - all protection domains

Supported types - int8 / int16 / int32 / int / float32 / float64

crossProduct[[1]]

Function for finding the cross product of two vectors.

Detailed Description

D - all protection domains

Supported types - int8 / int16 / int32 / int / float32 / float64

Parameters

x, y	- vectors of supported type

returns a vector with the cross product of the two input vectors

None

Function Overloads

D int8 crossProduct(D int8[[1]] x, D int8[[1]] y)

D int16 crossProduct(D int16[[1]] x, D int16[[1]] y)

D int32 crossProduct(D int32[[1]] x, D int32[[1]] y)

D int crossProduct(D int[[1]] x, D int[[1]] y)

D float32 crossProduct(D float32[[1]] x, D float32[[1]] y)

D float64 crossProduct(D float64[[1]] x, D float64[[1]] y)

crossProduct[[2]]

Function for finding the cross product of two matrices.

Detailed Description

D - all protection domains

Supported types - int8 / int16 / int32 / int / float32 / float64

Parameters

x, y	- matrices of supported type

returns a matrix with the cross product of each row of the two input matrices

None

Function Overloads

D int8 crossProduct(D int8[[2]] x, D int8[[2]] y)

D int16 crossProduct(D int16[[2]] x, D int16[[2]] y)

D int32 crossProduct(D int32[[2]] x, D int32[[2]] y)

D int crossProduct(D int[[2]] x, D int[[2]] y)

D float32 crossProduct(D float32[[2]] x, D float32[[2]] y)

D float64 crossProduct(D float64[[2]] x, D float64[[2]] y)

diagMatrixMultiplication

Function for multiplying two diagonal matrices.

Functions:

diagMatrixMultiplication[[2]]

diagMatrixMultiplication[[3]]

D - any protection domain

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

diagMatrixMultiplication[[2]]

Function for multiplying two diagonal matrices.

Detailed Description

D - any protection domain

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

NB! This matrix multiplication is very conditional. Before using, make sure that your matrices are in the right format. y must be diagonal

Parameters

x, y	- 2-dimensional matrices of supported type and shape

returns the matrix of x*y

None

Function Overloads

D uint8 diagMatrixMultiplication(D uint8[[2]] x, D uint8[[2]] y)

D uint16 diagMatrixMultiplication(D uint16[[2]] x, D uint16[[2]] y)

D uint32 diagMatrixMultiplication(D uint32[[2]] x, D uint32[[2]] y)

D uint diagMatrixMultiplication(D uint[[2]] x, D uint[[2]] y)

D int8 diagMatrixMultiplication(D int8[[2]] x, D int8[[2]] y)

D int16 diagMatrixMultiplication(D int16[[2]] x, D int16[[2]] y)

D int32 diagMatrixMultiplication(D int32[[2]] x, D int32[[2]] y)

D int diagMatrixMultiplication(D int[[2]] x, D int[[2]] y)

D float32 diagMatrixMultiplication(D float32[[2]] x, D float32[[2]] y)

D float64 diagMatrixMultiplication(D float64[[2]] x, D float64[[2]] y)

diagMatrixMultiplication[[3]]

Function for multiplying two diagonal matrices.

Detailed Description

D - any protection domain

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

NB! This matrix multiplication is very conditional. Before using, make sure that your matrices are in the right format. y must be diagonal

Parameters

x, y	- 3-dimensional matrices of supported type and shape

We multiply across the last two dimensions and return a vector of product matrices

None

Function Overloads

D uint8 diagMatrixMultiplication(D uint8[[3]] x, D uint8[[3]] y)

D uint16 diagMatrixMultiplication(D uint16[[3]] x, D uint16[[3]] y)

D uint32 diagMatrixMultiplication(D uint32[[3]] x, D uint32[[3]] y)

D uint diagMatrixMultiplication(D uint[[3]] x, D uint[[3]] y)

D int8 diagMatrixMultiplication(D int8[[3]] x, D int8[[3]] y)

D int16 diagMatrixMultiplication(D int16[[3]] x, D int16[[3]] y)

D int32 diagMatrixMultiplication(D int32[[3]] x, D int32[[3]] y)

D int diagMatrixMultiplication(D int[[3]] x, D int[[3]] y)

D float32 diagMatrixMultiplication(D float32[[3]] x, D float32[[3]] y)

D float64 diagMatrixMultiplication(D float64[[3]] x, D float64[[3]] y)

dotProduct

Function for finding the dot product of two vectors/matrices.

Functions:

dotProduct[[1]]

dotProduct[[2]]

D - all protection domains

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

dotProduct[[1]]

Function for finding the dot product of two vectors.

Detailed Description

D - all protection domains

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

x, y	- input vectors

returns a scalar with the dot product of the two input vectors

None

Function Overloads

D uint8 dotProduct(D uint8[[1]] x, D uint8[[1]] y)

D uint16 dotProduct(D uint16[[1]] x, D uint16[[1]] y)

D uint32 dotProduct(D uint32[[1]] x, D uint32[[1]] y)

D uint dotProduct(D uint[[1]] x, D uint[[1]] y)

D int8 dotProduct(D int8[[1]] x, D int8[[1]] y)

D int16 dotProduct(D int16[[1]] x, D int16[[1]] y)

D int32 dotProduct(D int32[[1]] x, D int32[[1]] y)

D int dotProduct(D int[[1]] x, D int[[1]] y)

D float32 dotProduct(D float32[[1]] x, D float32[[1]] y)

D float64 dotProduct(D float64[[1]] x, D float64[[1]] y)

dotProduct[[2]]

Function for finding the dot product of two matrices.

Detailed Description

D - all protection domains

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

Parameters

x, y	- matrices of supported type

returns a vector with the dot product of each row of the two input matrices

None

Function Overloads

D uint8 dotProduct(D uint8[[2]] x, D uint8[[2]] y)

D uint16 dotProduct(D uint16[[2]] x, D uint16[[2]] y)

D uint32 dotProduct(D uint32[[2]] x, D uint32[[2]] y)

D uint dotProduct(D uint[[2]] x, D uint[[2]] y)

D int8 dotProduct(D int8[[2]] x, D int8[[2]] y)

D int16 dotProduct(D int16[[2]] x, D int16[[2]] y)

D int32 dotProduct(D int32[[2]] x, D int32[[2]] y)

D int dotProduct(D int[[2]] x, D int[[2]] y)

D float32 dotProduct(D float32[[2]] x, D float32[[2]] y)

D float64 dotProduct(D float64[[2]] x, D float64[[2]] y)

matrixMultiplication

Function for multiplying two matrices.

Functions:

matrixMultiplication[[2]]

matrixMultiplication[[3]]

D - any protection domain

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

matrixMultiplication[[2]]

Function for multiplying two matrices.

Detailed Description

D - all protection domains

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

no. of columns of x must equal no. of rows of y

Parameters

x, y	- matrices of supported type and shape

returns the matrix of x*y

None

Function Overloads

D uint8 matrixMultiplication(D uint8[[2]] x, D uint8[[2]] y)

D uint16 matrixMultiplication(D uint16[[2]] x, D uint16[[2]] y)

D uint32 matrixMultiplication(D uint32[[2]] x, D uint32[[2]] y)

D uint matrixMultiplication(D uint[[2]] x, D uint[[2]] y)

D int8 matrixMultiplication(D int8[[2]] x, D int8[[2]] y)

D int16 matrixMultiplication(D int16[[2]] x, D int16[[2]] y)

D int32 matrixMultiplication(D int32[[2]] x, D int32[[2]] y)

D int matrixMultiplication(D int[[2]] x, D int[[2]] y)

D float32 matrixMultiplication(D float32[[2]] x, D float32[[2]] y)

D float64 matrixMultiplication(D float64[[2]] x, D float64[[2]] y)

matrixMultiplication[[3]]

Function for multiplying two matrices.

Detailed Description

D - any protection domain

Supported types - uint8 / uint16 / uint32 / uint / int8 / int16 / int32 / int / float32 / float64

no. of columns of x must equal no. of rows of y. Also, there should be an equal no. of matrices in both structures

Parameters

x, y	- 3-dimensional matrices of supported type and shape

We multiply across the last two dimensions and return a vector of product matrices

None

Function Overloads

D uint8 matrixMultiplication(D uint8[[3]] x, D uint8[[3]] y)

D uint16 matrixMultiplication(D uint16[[3]] x, D uint16[[3]] y)

D uint32 matrixMultiplication(D uint32[[3]] x, D uint32[[3]] y)

D uint matrixMultiplication(D uint[[3]] x, D uint[[3]] y)

D int8 matrixMultiplication(D int8[[3]] x, D int8[[3]] y)

D int16 matrixMultiplication(D int16[[3]] x, D int16[[3]] y)

D int32 matrixMultiplication(D int32[[3]] x, D int32[[3]] y)

D int matrixMultiplication(D int[[3]] x, D int[[3]] y)

D float32 matrixMultiplication(D float32[[3]] x, D float32[[3]] y)

D float64 matrixMultiplication(D float64[[3]] x, D float64[[3]] y)