401 lines
8.2 KiB
Go
401 lines
8.2 KiB
Go
package matrix
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import (
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"bytes"
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"errors"
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"math"
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)
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const (
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// DefaultEpsilon represents the minimum precision for matrix math operations.
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DefaultEpsilon = 0.000001
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)
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var (
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// ErrDimensionMismatch is a typical error.
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ErrDimensionMismatch = errors.New("dimension mismatch")
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)
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// New returns a new matrix.
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func New(rows, cols int, values ...float64) *Matrix {
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if len(values) == 0 {
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return &Matrix{
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stride: cols,
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epsilon: DefaultEpsilon,
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elements: make([]float64, rows*cols),
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}
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}
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elems := make([]float64, rows*cols)
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copy(elems, values)
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return &Matrix{
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stride: cols,
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epsilon: DefaultEpsilon,
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elements: elems,
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}
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}
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// Identity returns the identity matrix of a given order.
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func Identity(order int) *Matrix {
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m := New(order, order)
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for i := 0; i < order; i++ {
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m.Set(i, i, 1)
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}
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return m
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}
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// Zero returns a matrix of a given size zeroed.
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func Zero(rows, cols int) *Matrix {
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return New(rows, cols)
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}
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// Ones returns an matrix of ones.
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func Ones(rows, cols int) *Matrix {
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ones := make([]float64, rows*cols)
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for i := 0; i < (rows * cols); i++ {
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ones[i] = 1
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}
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return &Matrix{
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stride: cols,
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epsilon: DefaultEpsilon,
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elements: ones,
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}
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}
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// Eye returns the eye matrix.
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func Eye(n int) *Matrix {
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m := Zero(n, n)
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for i := 0; i < len(m.elements); i += n + 1 {
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m.elements[i] = 1
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}
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return m
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}
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// NewFromArrays creates a matrix from a jagged array set.
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func NewFromArrays(a [][]float64) *Matrix {
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rows := len(a)
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if rows == 0 {
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return nil
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}
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cols := len(a[0])
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m := New(rows, cols)
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for row := 0; row < rows; row++ {
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for col := 0; col < cols; col++ {
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m.Set(row, col, a[row][col])
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}
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}
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return m
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}
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// Matrix represents a 2d dense array of floats.
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type Matrix struct {
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epsilon float64
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elements []float64
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stride int
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}
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// String returns a string representation of the matrix.
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func (m *Matrix) String() string {
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buffer := bytes.NewBuffer(nil)
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rows, cols := m.Size()
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for row := 0; row < rows; row++ {
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for col := 0; col < cols; col++ {
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buffer.WriteString(f64s(m.Get(row, col)))
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buffer.WriteRune(' ')
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}
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buffer.WriteRune('\n')
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}
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return buffer.String()
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}
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// Epsilon returns the maximum precision for math operations.
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func (m *Matrix) Epsilon() float64 {
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return m.epsilon
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}
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// WithEpsilon sets the epsilon on the matrix and returns a reference to the matrix.
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func (m *Matrix) WithEpsilon(epsilon float64) *Matrix {
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m.epsilon = epsilon
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return m
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}
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// Each applies the action to each element of the matrix in
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// rows => cols order.
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func (m *Matrix) Each(action func(row, cow int, value float64)) {
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rows, cols := m.Size()
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for row := 0; row < rows; row++ {
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for col := 0; col < cols; col++ {
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action(row, col, m.Get(row, col))
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}
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}
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}
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// Round rounds all the values in a matrix to it epsilon,
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// returning a reference to the original
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func (m *Matrix) Round() *Matrix {
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rows, cols := m.Size()
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for row := 0; row < rows; row++ {
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for col := 0; col < cols; col++ {
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m.Set(row, col, roundToEpsilon(m.Get(row, col), m.epsilon))
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}
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}
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return m
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}
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// Arrays returns the matrix as a two dimensional jagged array.
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func (m *Matrix) Arrays() [][]float64 {
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rows, cols := m.Size()
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a := make([][]float64, rows)
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for row := 0; row < rows; row++ {
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a[row] = make([]float64, cols)
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for col := 0; col < cols; col++ {
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a[row][col] = m.Get(row, col)
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}
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}
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return a
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}
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// Size returns the dimensions of the matrix.
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func (m *Matrix) Size() (rows, cols int) {
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rows = len(m.elements) / m.stride
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cols = m.stride
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return
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}
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// IsSquare returns if the row count is equal to the column count.
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func (m *Matrix) IsSquare() bool {
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return m.stride == (len(m.elements) / m.stride)
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}
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// IsSymmetric returns if the matrix is symmetric about its diagonal.
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func (m *Matrix) IsSymmetric() bool {
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rows, cols := m.Size()
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if rows != cols {
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return false
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}
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for i := 0; i < rows; i++ {
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for j := 0; j < i; j++ {
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if m.Get(i, j) != m.Get(j, i) {
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return false
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}
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}
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}
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return true
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}
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// Get returns the element at the given row, col.
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func (m *Matrix) Get(row, col int) float64 {
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index := (m.stride * row) + col
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return m.elements[index]
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}
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// Set sets a value.
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func (m *Matrix) Set(row, col int, val float64) {
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index := (m.stride * row) + col
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m.elements[index] = val
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}
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// Col returns a column of the matrix as a vector.
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func (m *Matrix) Col(col int) Vector {
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rows, _ := m.Size()
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values := make([]float64, rows)
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for row := 0; row < rows; row++ {
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values[row] = m.Get(row, col)
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}
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return Vector(values)
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}
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// Row returns a row of the matrix as a vector.
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func (m *Matrix) Row(row int) Vector {
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_, cols := m.Size()
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values := make([]float64, cols)
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for col := 0; col < cols; col++ {
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values[col] = m.Get(row, col)
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}
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return Vector(values)
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}
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// Copy returns a duplicate of a given matrix.
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func (m *Matrix) Copy() *Matrix {
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m2 := &Matrix{stride: m.stride, epsilon: m.epsilon, elements: make([]float64, len(m.elements))}
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copy(m2.elements, m.elements)
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return m2
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}
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// DiagonalVector returns a vector from the diagonal of a matrix.
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func (m *Matrix) DiagonalVector() Vector {
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rows, cols := m.Size()
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rank := minInt(rows, cols)
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values := make([]float64, rank)
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for index := 0; index < rank; index++ {
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values[index] = m.Get(index, index)
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}
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return Vector(values)
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}
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// Diagonal returns a matrix from the diagonal of a matrix.
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func (m *Matrix) Diagonal() *Matrix {
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rows, cols := m.Size()
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rank := minInt(rows, cols)
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m2 := New(rank, rank)
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for index := 0; index < rank; index++ {
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m2.Set(index, index, m.Get(index, index))
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}
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return m2
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}
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// Equals returns if a matrix equals another matrix.
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func (m *Matrix) Equals(other *Matrix) bool {
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if other == nil && m != nil {
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return false
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} else if other == nil {
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return true
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}
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if m.stride != other.stride {
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return false
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}
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msize := len(m.elements)
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m2size := len(other.elements)
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if msize != m2size {
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return false
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}
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for i := 0; i < msize; i++ {
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if m.elements[i] != other.elements[i] {
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return false
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}
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}
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return true
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}
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// L returns the matrix with zeros below the diagonal.
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func (m *Matrix) L() *Matrix {
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rows, cols := m.Size()
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m2 := New(rows, cols)
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for row := 0; row < rows; row++ {
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for col := row; col < cols; col++ {
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m2.Set(row, col, m.Get(row, col))
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}
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}
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return m2
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}
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// U returns the matrix with zeros above the diagonal.
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// Does not include the diagonal.
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func (m *Matrix) U() *Matrix {
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rows, cols := m.Size()
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m2 := New(rows, cols)
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for row := 0; row < rows; row++ {
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for col := 0; col < row && col < cols; col++ {
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m2.Set(row, col, m.Get(row, col))
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}
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}
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return m2
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}
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// math operations
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// Multiply multiplies two matrices.
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func (m *Matrix) Multiply(m2 *Matrix) (m3 *Matrix, err error) {
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if m.stride*m2.stride != len(m2.elements) {
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return nil, ErrDimensionMismatch
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}
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m3 = &Matrix{epsilon: m.epsilon, stride: m2.stride, elements: make([]float64, (len(m.elements)/m.stride)*m2.stride)}
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for m1c0, m3x := 0, 0; m1c0 < len(m.elements); m1c0 += m.stride {
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for m2r0 := 0; m2r0 < m2.stride; m2r0++ {
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for m1x, m2x := m1c0, m2r0; m2x < len(m2.elements); m2x += m2.stride {
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m3.elements[m3x] += m.elements[m1x] * m2.elements[m2x]
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m1x++
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}
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m3x++
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}
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}
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return
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}
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// Decompositions
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// QR performs the qr decomposition.
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func (m *Matrix) QR() (q, r *Matrix) {
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defer func() {
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q = q.Round()
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r = r.Round()
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}()
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rows, cols := m.Size()
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qr := m.Copy()
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q = New(rows, cols)
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r = New(rows, cols)
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var i, j, k int
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var norm, s float64
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for k = 0; k < cols; k++ {
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norm = 0
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for i = k; i < rows; i++ {
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norm = math.Hypot(norm, qr.Get(i, k))
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}
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if norm != 0 {
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if qr.Get(k, k) < 0 {
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norm = -norm
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}
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for i = k; i < rows; i++ {
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qr.Set(i, k, qr.Get(i, k)/norm)
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}
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qr.Set(k, k, qr.Get(k, k)+1.0)
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for j = k + 1; j < cols; j++ {
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s = 0
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for i = k; i < rows; i++ {
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s += qr.Get(i, k) * qr.Get(i, j)
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}
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s = -s / qr.Get(k, k)
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for i = k; i < rows; i++ {
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qr.Set(i, j, qr.Get(i, j)+s*qr.Get(i, k))
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if i < j {
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r.Set(i, j, qr.Get(i, j))
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}
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}
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}
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}
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r.Set(k, k, -norm)
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}
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//Q Matrix:
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i, j, k = 0, 0, 0
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for k = cols - 1; k >= 0; k-- {
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q.Set(k, k, 1.0)
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for j = k; j < cols; j++ {
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if qr.Get(k, k) != 0 {
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s = 0
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for i = k; i < rows; i++ {
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s += qr.Get(i, k) * q.Get(i, j)
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}
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s = -s / qr.Get(k, k)
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for i = k; i < rows; i++ {
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q.Set(i, j, q.Get(i, j)+s*qr.Get(i, k))
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}
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}
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}
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}
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return
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}
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