struct Geode::Matrix(T, M, N)

Overview

Generic matrix type. Provides a rectangular array of scalars of the same type.

T is the scalar type. M and N are positive integers indicating the number of rows and columns respectively. Indices i and j refer to the zero-based row and column index respectively. Unless noted otherwise, all operations are in row-major order.

Included Modules

Defined in:

geode/matrices/matrix.cr

Constructors

Class Method Summary

Instance Method Summary

Macro Summary

Instance methods inherited from module Geode::SquareMatrix(T, M, N)

determinant determinant, diagonal : CommonVector(T, N) diagonal, each_diagonal(& : T -> _) : Nil
each_diagonal : Iterator(T)
each_diagonal
, inv inv, inverse inverse, trace trace

Instance methods inherited from module Geode::CommonMatrix(T, M, N)

[](i : Int, j : Int) : T [], []?(i : Int, j : Int) : T? []?, column(j : Int) : CommonVector(T, M) column, column?(j : Int) : CommonVector(T, M)? column?, columns : Int columns, columns_at(*indices) : Tuple columns_at, each_column(& : CommonVector(T, M) -> _) each_column, each_column_with_index(offset = 0, & : CommonVector(T, M), Int32 -> _) each_column_with_index, each_indices(& : Int32, Int32 -> _) each_indices, each_row(& : CommonVector(T, N) -> _) each_row, each_row_with_index(offset = 0, & : CommonVector(T, N), Int32 -> _) each_row_with_index, each_with_indices(& : T, Int32, Int32 -> _) each_with_indices, inspect(io : IO) : Nil inspect, map(& : T -> U) : CommonMatrix forall U map, map_with_index(offset = 0, & : T, Int32 -> U) : CommonMatrix(U, M, N) forall U map_with_index, map_with_indices(& : T, Int32, Int32 -> U) : CommonMatrix(U, M, N) forall U map_with_indices, row(i : Int) : CommonVector(T, N) row, row?(i : Int) : CommonVector(T, N)? row?, rows : Int rows, rows_at(*indices) : Tuple rows_at, size size, square? square?, to_columns : Array to_columns, to_rows : Array to_rows, to_s(io : IO) : Nil to_s, unsafe_fetch(i : Int, j : Int) : T unsafe_fetch, unsafe_fetch_column(j : Int) : CommonVector(T, M) unsafe_fetch_column, unsafe_fetch_row(i : Int) : CommonVector(T, N) unsafe_fetch_row, zip_map(other : CommonMatrix(U, M, N), & : T, U -> V) : CommonMatrix(V, M, N) forall U, V zip_map

Instance methods inherited from module Geode::MatrixVectors(M, N)

&*(vector : CommonVector(U, P)) : CommonVector forall U, P &*, *(vector : CommonVector(U, P)) : CommonVector forall U, P *, column? column?, row? row?, to_vector : CommonVector to_vector

Instance methods inherited from module Geode::MatrixOperations(M, N)

&*(scalar : Number) : CommonMatrix &*, &+(other : CommonMatrix(T, M, N)) : CommonMatrix forall T &+, &-(other : CommonMatrix(T, M, N)) : CommonMatrix forall T &-, *(scalar : Number) : CommonMatrix *, +(other : CommonMatrix(T, M, N)) : CommonMatrix forall T +, -(other : CommonMatrix(T, M, N)) : CommonMatrix forall T
- : self
-
, /(scalar : Number) : CommonMatrix /, //(scalar : Number) : CommonMatrix //, abs : self abs, abs2 : self abs2, ceil : self ceil, clamp(min : CommonMatrix(T, M, N), max : CommonMatrix(T, M, N)) : CommonMatrix forall T
clamp(min, max) : CommonMatrix
clamp(range : Range(CommonMatrix(T, M, N), CommonMatrix(T, M, N))) : CommonMatrix forall T
clamp(range : Range) : CommonMatrix
clamp
, edge(edge : CommonMatrix(T, M, N)) : self forall T
edge(edge) : self
edge
, floor : self floor, fraction : self fraction, lerp(other : CommonMatrix(T, M, N), t : Number) : CommonMatrix forall T lerp, round(mode : Number::RoundingMode = :ties_even) : self
round(digits : Number, base = 10, *, mode : Number::RoundingMode = :ties_even) : self
round
, scale(matrix : CommonMatrix(T, M, N)) : CommonMatrix forall T scale, scale!(matrix : CommonMatrix(T, M, N)) : CommonMatrix forall T scale!, sign : self sign

Instance methods inherited from module Geode::MatrixIterators(T, M, N)

each_column : Iterator(CommonVector(T, M)) each_column, each_column_with_index(offset = 0) : Iterator(Tuple(CommonVector(T, M), Int32)) each_column_with_index, each_indices : Iterator(Tuple(Int32, Int32)) each_indices, each_row : Iterator(CommonVector(T, N)) each_row, each_row_with_index(offset = 0) : Iterator(Tuple(CommonVector(T, N), Int32)) each_row_with_index, each_with_indices : Iterator(Tuple(T, Int32, Int32)) each_with_indices

Instance methods inherited from module Geode::MatrixComparison(M, N)

==(other : CommonMatrix(T, M, N)) forall T ==, compare(other : CommonMatrix(T, M, N)) : CommonMatrix(Int32, M, N) forall T compare, eq?(other : CommonMatrix(T, M, N)) : CommonMatrix(Bool, M, N) forall T eq?, ge?(other : CommonMatrix(T, M, N)) : CommonMatrix(Bool, M, N) forall T ge?, gt?(other : CommonMatrix(T, M, N)) : CommonMatrix(Bool, M, N) forall T gt?, le?(other : CommonMatrix(T, M, N)) : CommonMatrix(Bool, M, N) forall T le?, lt?(other : CommonMatrix(T, M, N)) : CommonMatrix(Bool, M, N) forall T lt?, near_zero?(tolerance) near_zero?, zero? zero?

Constructor Detail

def self.identity : self #

Creates an identity matrix.

An identity matrix is a square matrix with ones along the diagonal and zeroes elsewhere. Raises a compilation error if M and N are not the same (producing a square matrix).

Matrix(Int32, 3, 3).identity
# => [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

[View source]
def self.new(matrix : CommonMatrix(T, M, N)) #

Copies contents from another matrix.


[View source]
def self.new(&) #

Creates a new matrix by iterating through each element.

Yields the indices (i and j) for the matrix element. The block should return the value to use for the corresponding element.

Matrix(Int32, 3, 3).new { |i, j| i * 10 + j }
# => [[0, 1, 2], [10, 11, 12], [20, 21, 22]]

[View source]
def self.new(rows : Indexable(Indexable(T))) #

Creates a new matrix from nested collections.

The size of rows must be equal to the type argument M. Each row of elements in rows must have a size equal to the type argument N.

Matrix(Int32, 3, 2).new([[10, 20], [30, 40], [50, 60]])
# => [[10, 20], [30, 40], [50, 60]]
Matrix(Int32, 3, 2).new({{10, 20}, {30, 40}, {50, 60}})
# => [[10, 20], [30, 40], [50, 60]]

[View source]
def self.new(elements : Indexable(T)) #

Creates a new matrix from a flat collection of elements.

The size of elements must be equal to M x N. Items in elements are consumed in row-major order.

Matrix(Int32, 3, 2).new([1, 2, 3, 4, 5, 6])
# => [[1, 2], [3, 4], [5, 6]]

[View source]
def self.new(scalar : T) : self #

Creates a new matrix with the diagonal elements set to a scalar value.

The main diagonal will be filled with scalar. All other elements will be zeroes. Raises a compilation error if M and N are not the same (producing a square matrix).

Matrix(Int32, 3, 3).new(5)
# => [[5, 0, 0], [0, 5, 0], [0, 0, 5]]

[View source]
def self.zero : self #

Creates a matrix filled with zeroes.

Matrix(Int32, 2, 2).zero
# => [[0, 0], [0, 0]]

[View source]

Class Method Detail

def self.[](*rows) #

Constructs a matrix with existing elements.

The type of the elements is specified by the type parameter. Each value is cast to the type T.

Matrix(Float32, 3, 3)[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
# => [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]

[View source]

Instance Method Detail

def &*(other : CommonMatrix(U, N, P)) : Matrix forall U, P #

Multiplies this matrix by another.

The other matrix's row count (M) must be equal to this matrix's column count (N). Produces a new matrix with the row count from this matrix and the column count from other. Matrices can be of any size and type as long as this condition is met.

Values will wrap instead of overflowing and raising an error.

m1 = Matrix[[1, 2, 3], [4, 5, 6]]
m2 = Matrix[[1, 2], [3, 4], [5, 6]]
m1 &* m2 # => [[28, 29], [49, 64]]

[View source]
def *(other : CommonMatrix(U, N, P)) : Matrix forall U, P #

Multiplies this matrix by another.

The other matrix's row count (M) must be equal to this matrix's column count (N). Produces a new matrix with the row count from this matrix and the column count from other. Matrices can be of any size and type as long as this condition is met.

m1 = Matrix[[1, 2, 3], [4, 5, 6]]
m2 = Matrix[[1, 2], [3, 4], [5, 6]]
m1 * m2 # => [[28, 29], [49, 64]]

[View source]
def map(& : T -> U) : Matrix forall U #

Returns a new matrix with elements mapped by the given block.

matrix = Matrix[[1, 2], [3, 4], [5, 6]]
matrix.map { |e| e * 2 } # => [[2, 4], [6, 8], [10, 12]]

[View source]
def sub(i : Int, j : Int) : CommonMatrix #

Returns a smaller matrix by removing a row and column.

The row indicated by i and the column indicated by j are removed in the resulting matrix. This method can only be called if the matrix has two or more rows and columns.

matrix = Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
matrix.sub(1, 1) # => [[1, 3], [7, 9]]

[View source]
def to_slice : Slice(T) #

Returns a slice that points to the elements in this matrix.


[View source]
def to_unsafe : Pointer(T) #

Returns a pointer to the data for this matrix.

The elements are tightly packed and ordered consecutively in memory.


[View source]
def transpose : Matrix(T, N, M) #

Returns a new matrix that is transposed from this one.

matrix = Matrix[[1, 2, 3], [4, 5, 6]]
matrix.transpose # => [[1, 4], [2, 5], [3, 6]]

[View source]
def unsafe_fetch(index : Int) #

Retrieves the scalar value of the component at the given index, without checking size boundaries.

End-users should never invoke this method directly. Instead, methods like #[] and #[]? should be used.

This method should only be directly invoked if the index is certain to be in bounds.


[View source]

Macro Detail

macro [](*rows) #

Constructs a matrix with existing elements.

The type of the components is derived from the type of each argument. The size of the vector is determined by the number of components.

Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
# => [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

[View source]