Adding upstream version 2.1.2.

Signed-off-by: Daniel Baumann <daniel@debian.org>

matrix/matrix.go

@@ -0,0 +1,592 @@
+package matrix
+
+import (
+	"bytes"
+	"errors"
+	"fmt"
+	"math"
+)
+
+const (
+	// DefaultEpsilon represents the minimum precision for matrix math operations.
+	DefaultEpsilon = 0.000001
+)
+
+var (
+	// ErrDimensionMismatch is a typical error.
+	ErrDimensionMismatch = errors.New("dimension mismatch")
+
+	// ErrSingularValue is a typical error.
+	ErrSingularValue = errors.New("singular value")
+)
+
+// New returns a new matrix.
+func New(rows, cols int, values ...float64) *Matrix {
+	if len(values) == 0 {
+		return &Matrix{
+			stride:   cols,
+			epsilon:  DefaultEpsilon,
+			elements: make([]float64, rows*cols),
+		}
+	}
+	elems := make([]float64, rows*cols)
+	copy(elems, values)
+	return &Matrix{
+		stride:   cols,
+		epsilon:  DefaultEpsilon,
+		elements: elems,
+	}
+}
+
+// Identity returns the identity matrix of a given order.
+func Identity(order int) *Matrix {
+	m := New(order, order)
+	for i := 0; i < order; i++ {
+		m.Set(i, i, 1)
+	}
+	return m
+}
+
+// Zero returns a matrix of a given size zeroed.
+func Zero(rows, cols int) *Matrix {
+	return New(rows, cols)
+}
+
+// Ones returns an matrix of ones.
+func Ones(rows, cols int) *Matrix {
+	ones := make([]float64, rows*cols)
+	for i := 0; i < (rows * cols); i++ {
+		ones[i] = 1
+	}
+
+	return &Matrix{
+		stride:   cols,
+		epsilon:  DefaultEpsilon,
+		elements: ones,
+	}
+}
+
+// Eye returns the eye matrix.
+func Eye(n int) *Matrix {
+	m := Zero(n, n)
+	for i := 0; i < len(m.elements); i += n + 1 {
+		m.elements[i] = 1
+	}
+	return m
+}
+
+// NewFromArrays creates a matrix from a jagged array set.
+func NewFromArrays(a [][]float64) *Matrix {
+	rows := len(a)
+	if rows == 0 {
+		return nil
+	}
+	cols := len(a[0])
+	m := New(rows, cols)
+	for row := 0; row < rows; row++ {
+		for col := 0; col < cols; col++ {
+			m.Set(row, col, a[row][col])
+		}
+	}
+	return m
+}
+
+// Matrix represents a 2d dense array of floats.
+type Matrix struct {
+	epsilon  float64
+	elements []float64
+	stride   int
+}
+
+// String returns a string representation of the matrix.
+func (m *Matrix) String() string {
+	buffer := bytes.NewBuffer(nil)
+	rows, cols := m.Size()
+
+	for row := 0; row < rows; row++ {
+		for col := 0; col < cols; col++ {
+			buffer.WriteString(f64s(m.Get(row, col)))
+			buffer.WriteRune(' ')
+		}
+		buffer.WriteRune('\n')
+	}
+	return buffer.String()
+}
+
+// Epsilon returns the maximum precision for math operations.
+func (m *Matrix) Epsilon() float64 {
+	return m.epsilon
+}
+
+// WithEpsilon sets the epsilon on the matrix and returns a reference to the matrix.
+func (m *Matrix) WithEpsilon(epsilon float64) *Matrix {
+	m.epsilon = epsilon
+	return m
+}
+
+// Each applies the action to each element of the matrix in
+// rows => cols order.
+func (m *Matrix) Each(action func(row, col int, value float64)) {
+	rows, cols := m.Size()
+	for row := 0; row < rows; row++ {
+		for col := 0; col < cols; col++ {
+			action(row, col, m.Get(row, col))
+		}
+	}
+}
+
+// Round rounds all the values in a matrix to it epsilon,
+// returning a reference to the original
+func (m *Matrix) Round() *Matrix {
+	rows, cols := m.Size()
+	for row := 0; row < rows; row++ {
+		for col := 0; col < cols; col++ {
+			m.Set(row, col, roundToEpsilon(m.Get(row, col), m.epsilon))
+		}
+	}
+	return m
+}
+
+// Arrays returns the matrix as a two dimensional jagged array.
+func (m *Matrix) Arrays() [][]float64 {
+	rows, cols := m.Size()
+	a := make([][]float64, rows)
+
+	for row := 0; row < rows; row++ {
+		a[row] = make([]float64, cols)
+
+		for col := 0; col < cols; col++ {
+			a[row][col] = m.Get(row, col)
+		}
+	}
+	return a
+}
+
+// Size returns the dimensions of the matrix.
+func (m *Matrix) Size() (rows, cols int) {
+	rows = len(m.elements) / m.stride
+	cols = m.stride
+	return
+}
+
+// IsSquare returns if the row count is equal to the column count.
+func (m *Matrix) IsSquare() bool {
+	return m.stride == (len(m.elements) / m.stride)
+}
+
+// IsSymmetric returns if the matrix is symmetric about its diagonal.
+func (m *Matrix) IsSymmetric() bool {
+	rows, cols := m.Size()
+
+	if rows != cols {
+		return false
+	}
+
+	for i := 0; i < rows; i++ {
+		for j := 0; j < i; j++ {
+			if m.Get(i, j) != m.Get(j, i) {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// Get returns the element at the given row, col.
+func (m *Matrix) Get(row, col int) float64 {
+	index := (m.stride * row) + col
+	return m.elements[index]
+}
+
+// Set sets a value.
+func (m *Matrix) Set(row, col int, val float64) {
+	index := (m.stride * row) + col
+	m.elements[index] = val
+}
+
+// Col returns a column of the matrix as a vector.
+func (m *Matrix) Col(col int) Vector {
+	rows, _ := m.Size()
+	values := make([]float64, rows)
+	for row := 0; row < rows; row++ {
+		values[row] = m.Get(row, col)
+	}
+	return Vector(values)
+}
+
+// Row returns a row of the matrix as a vector.
+func (m *Matrix) Row(row int) Vector {
+	_, cols := m.Size()
+	values := make([]float64, cols)
+	for col := 0; col < cols; col++ {
+		values[col] = m.Get(row, col)
+	}
+	return Vector(values)
+}
+
+// SubMatrix returns a sub matrix from a given outer matrix.
+func (m *Matrix) SubMatrix(i, j, rows, cols int) *Matrix {
+	return &Matrix{
+		elements: m.elements[i*m.stride+j : i*m.stride+j+(rows-1)*m.stride+cols],
+		stride:   m.stride,
+		epsilon:  m.epsilon,
+	}
+}
+
+// ScaleRow applies a scale to an entire row.
+func (m *Matrix) ScaleRow(row int, scale float64) {
+	startIndex := row * m.stride
+	for i := startIndex; i < m.stride; i++ {
+		m.elements[i] = m.elements[i] * scale
+	}
+}
+
+func (m *Matrix) scaleAddRow(rd int, rs int, f float64) {
+	indexd := rd * m.stride
+	indexs := rs * m.stride
+	for col := 0; col < m.stride; col++ {
+		m.elements[indexd] += f * m.elements[indexs]
+		indexd++
+		indexs++
+	}
+}
+
+// SwapRows swaps a row in the matrix in place.
+func (m *Matrix) SwapRows(i, j int) {
+	var vi, vj float64
+	for col := 0; col < m.stride; col++ {
+		vi = m.Get(i, col)
+		vj = m.Get(j, col)
+		m.Set(i, col, vj)
+		m.Set(j, col, vi)
+	}
+}
+
+// Augment concatenates two matrices about the horizontal.
+func (m *Matrix) Augment(m2 *Matrix) (*Matrix, error) {
+	mr, mc := m.Size()
+	m2r, m2c := m2.Size()
+	if mr != m2r {
+		return nil, ErrDimensionMismatch
+	}
+
+	m3 := Zero(mr, mc+m2c)
+	for row := 0; row < mr; row++ {
+		for col := 0; col < mc; col++ {
+			m3.Set(row, col, m.Get(row, col))
+		}
+		for col := 0; col < m2c; col++ {
+			m3.Set(row, mc+col, m2.Get(row, col))
+		}
+	}
+	return m3, nil
+}
+
+// Copy returns a duplicate of a given matrix.
+func (m *Matrix) Copy() *Matrix {
+	m2 := &Matrix{stride: m.stride, epsilon: m.epsilon, elements: make([]float64, len(m.elements))}
+	copy(m2.elements, m.elements)
+	return m2
+}
+
+// DiagonalVector returns a vector from the diagonal of a matrix.
+func (m *Matrix) DiagonalVector() Vector {
+	rows, cols := m.Size()
+	rank := minInt(rows, cols)
+	values := make([]float64, rank)
+
+	for index := 0; index < rank; index++ {
+		values[index] = m.Get(index, index)
+	}
+	return Vector(values)
+}
+
+// Diagonal returns a matrix from the diagonal of a matrix.
+func (m *Matrix) Diagonal() *Matrix {
+	rows, cols := m.Size()
+	rank := minInt(rows, cols)
+	m2 := New(rank, rank)
+
+	for index := 0; index < rank; index++ {
+		m2.Set(index, index, m.Get(index, index))
+	}
+	return m2
+}
+
+// Equals returns if a matrix equals another matrix.
+func (m *Matrix) Equals(other *Matrix) bool {
+	if other == nil && m != nil {
+		return false
+	} else if other == nil {
+		return true
+	}
+
+	if m.stride != other.stride {
+		return false
+	}
+
+	msize := len(m.elements)
+	m2size := len(other.elements)
+
+	if msize != m2size {
+		return false
+	}
+
+	for i := 0; i < msize; i++ {
+		if m.elements[i] != other.elements[i] {
+			return false
+		}
+	}
+	return true
+}
+
+// L returns the matrix with zeros below the diagonal.
+func (m *Matrix) L() *Matrix {
+	rows, cols := m.Size()
+	m2 := New(rows, cols)
+	for row := 0; row < rows; row++ {
+		for col := row; col < cols; col++ {
+			m2.Set(row, col, m.Get(row, col))
+		}
+	}
+	return m2
+}
+
+// U returns the matrix with zeros above the diagonal.
+// Does not include the diagonal.
+func (m *Matrix) U() *Matrix {
+	rows, cols := m.Size()
+	m2 := New(rows, cols)
+	for row := 0; row < rows; row++ {
+		for col := 0; col < row && col < cols; col++ {
+			m2.Set(row, col, m.Get(row, col))
+		}
+	}
+	return m2
+}
+
+// math operations
+
+// Multiply multiplies two matrices.
+func (m *Matrix) Multiply(m2 *Matrix) (m3 *Matrix, err error) {
+	if m.stride*m2.stride != len(m2.elements) {
+		return nil, ErrDimensionMismatch
+	}
+
+	m3 = &Matrix{epsilon: m.epsilon, stride: m2.stride, elements: make([]float64, (len(m.elements)/m.stride)*m2.stride)}
+	for m1c0, m3x := 0, 0; m1c0 < len(m.elements); m1c0 += m.stride {
+		for m2r0 := 0; m2r0 < m2.stride; m2r0++ {
+			for m1x, m2x := m1c0, m2r0; m2x < len(m2.elements); m2x += m2.stride {
+				m3.elements[m3x] += m.elements[m1x] * m2.elements[m2x]
+				m1x++
+			}
+			m3x++
+		}
+	}
+	return
+}
+
+// Pivotize does something i'm not sure what.
+func (m *Matrix) Pivotize() *Matrix {
+	pv := make([]int, m.stride)
+
+	for i := range pv {
+		pv[i] = i
+	}
+
+	for j, dx := 0, 0; j < m.stride; j++ {
+		row := j
+		max := m.elements[dx]
+		for i, ixcj := j, dx; i < m.stride; i++ {
+			if m.elements[ixcj] > max {
+				max = m.elements[ixcj]
+				row = i
+			}
+			ixcj += m.stride
+		}
+		if j != row {
+			pv[row], pv[j] = pv[j], pv[row]
+		}
+		dx += m.stride + 1
+	}
+	p := Zero(m.stride, m.stride)
+	for r, c := range pv {
+		p.elements[r*m.stride+c] = 1
+	}
+	return p
+}
+
+// Times returns the product of a matrix and another.
+func (m *Matrix) Times(m2 *Matrix) (*Matrix, error) {
+	mr, mc := m.Size()
+	m2r, m2c := m2.Size()
+
+	if mc != m2r {
+		return nil, fmt.Errorf("cannot multiply (%dx%d) and (%dx%d)", mr, mc, m2r, m2c)
+		//return nil, ErrDimensionMismatch
+	}
+
+	c := Zero(mr, m2c)
+
+	for i := 0; i < mr; i++ {
+		sums := c.elements[i*c.stride : (i+1)*c.stride]
+		for k, a := range m.elements[i*m.stride : i*m.stride+m.stride] {
+			for j, b := range m2.elements[k*m2.stride : k*m2.stride+m2.stride] {
+				sums[j] += a * b
+			}
+		}
+	}
+
+	return c, nil
+}
+
+// Decompositions
+
+// LU performs the LU decomposition.
+func (m *Matrix) LU() (l, u, p *Matrix) {
+	l = Zero(m.stride, m.stride)
+	u = Zero(m.stride, m.stride)
+	p = m.Pivotize()
+	m, _ = p.Multiply(m)
+	for j, jxc0 := 0, 0; j < m.stride; j++ {
+		l.elements[jxc0+j] = 1
+		for i, ixc0 := 0, 0; ixc0 <= jxc0; i++ {
+			sum := 0.
+			for k, kxcj := 0, j; k < i; k++ {
+				sum += u.elements[kxcj] * l.elements[ixc0+k]
+				kxcj += m.stride
+			}
+			u.elements[ixc0+j] = m.elements[ixc0+j] - sum
+			ixc0 += m.stride
+		}
+		for ixc0 := jxc0; ixc0 < len(m.elements); ixc0 += m.stride {
+			sum := 0.
+			for k, kxcj := 0, j; k < j; k++ {
+				sum += u.elements[kxcj] * l.elements[ixc0+k]
+				kxcj += m.stride
+			}
+			l.elements[ixc0+j] = (m.elements[ixc0+j] - sum) / u.elements[jxc0+j]
+		}
+		jxc0 += m.stride
+	}
+	return
+}
+
+// QR performs the qr decomposition.
+func (m *Matrix) QR() (q, r *Matrix) {
+	defer func() {
+		q = q.Round()
+		r = r.Round()
+	}()
+
+	rows, cols := m.Size()
+	qr := m.Copy()
+	q = New(rows, cols)
+	r = New(rows, cols)
+
+	var i, j, k int
+	var norm, s float64
+
+	for k = 0; k < cols; k++ {
+		norm = 0
+		for i = k; i < rows; i++ {
+			norm = math.Hypot(norm, qr.Get(i, k))
+		}
+
+		if norm != 0 {
+			if qr.Get(k, k) < 0 {
+				norm = -norm
+			}
+
+			for i = k; i < rows; i++ {
+				qr.Set(i, k, qr.Get(i, k)/norm)
+			}
+			qr.Set(k, k, qr.Get(k, k)+1.0)
+
+			for j = k + 1; j < cols; j++ {
+				s = 0
+				for i = k; i < rows; i++ {
+					s += qr.Get(i, k) * qr.Get(i, j)
+				}
+				s = -s / qr.Get(k, k)
+				for i = k; i < rows; i++ {
+					qr.Set(i, j, qr.Get(i, j)+s*qr.Get(i, k))
+
+					if i < j {
+						r.Set(i, j, qr.Get(i, j))
+					}
+				}
+
+			}
+		}
+
+		r.Set(k, k, -norm)
+
+	}
+
+	//Q Matrix:
+	i, j, k = 0, 0, 0
+
+	for k = cols - 1; k >= 0; k-- {
+		q.Set(k, k, 1.0)
+		for j = k; j < cols; j++ {
+			if qr.Get(k, k) != 0 {
+				s = 0
+				for i = k; i < rows; i++ {
+					s += qr.Get(i, k) * q.Get(i, j)
+				}
+				s = -s / qr.Get(k, k)
+				for i = k; i < rows; i++ {
+					q.Set(i, j, q.Get(i, j)+s*qr.Get(i, k))
+				}
+			}
+		}
+	}
+
+	return
+}
+
+// Transpose flips a matrix about its diagonal, returning a new copy.
+func (m *Matrix) Transpose() *Matrix {
+	rows, cols := m.Size()
+	m2 := Zero(cols, rows)
+	for i := 0; i < rows; i++ {
+		for j := 0; j < cols; j++ {
+			m2.Set(j, i, m.Get(i, j))
+		}
+	}
+	return m2
+}
+
+// Inverse returns a matrix such that M*I==1.
+func (m *Matrix) Inverse() (*Matrix, error) {
+	if !m.IsSymmetric() {
+		return nil, ErrDimensionMismatch
+	}
+
+	rows, cols := m.Size()
+
+	aug, _ := m.Augment(Eye(rows))
+	for i := 0; i < rows; i++ {
+		j := i
+		for k := i; k < rows; k++ {
+			if math.Abs(aug.Get(k, i)) > math.Abs(aug.Get(j, i)) {
+				j = k
+			}
+		}
+		if j != i {
+			aug.SwapRows(i, j)
+		}
+		if aug.Get(i, i) == 0 {
+			return nil, ErrSingularValue
+		}
+		aug.ScaleRow(i, 1.0/aug.Get(i, i))
+		for k := 0; k < rows; k++ {
+			if k == i {
+				continue
+			}
+			aug.scaleAddRow(k, i, -aug.Get(k, i))
+		}
+	}
+	return aug.SubMatrix(0, cols, rows, cols), nil
+}

matrix/matrix_test.go

@@ -0,0 +1,396 @@
+package matrix
+
+import (
+	"testing"
+
+	"github.com/wcharczuk/go-chart/v2/testutil"
+)
+
+func TestNew(t *testing.T) {
+	// replaced new assertions helper
+
+	m := New(10, 5)
+	rows, cols := m.Size()
+	testutil.AssertEqual(t, 10, rows)
+	testutil.AssertEqual(t, 5, cols)
+	testutil.AssertZero(t, m.Get(0, 0))
+	testutil.AssertZero(t, m.Get(9, 4))
+}
+
+func TestNewWithValues(t *testing.T) {
+	// replaced new assertions helper
+
+	m := New(5, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
+	rows, cols := m.Size()
+	testutil.AssertEqual(t, 5, rows)
+	testutil.AssertEqual(t, 2, cols)
+	testutil.AssertEqual(t, 1, m.Get(0, 0))
+	testutil.AssertEqual(t, 10, m.Get(4, 1))
+}
+
+func TestIdentitiy(t *testing.T) {
+	// replaced new assertions helper
+
+	id := Identity(5)
+	rows, cols := id.Size()
+	testutil.AssertEqual(t, 5, rows)
+	testutil.AssertEqual(t, 5, cols)
+	testutil.AssertEqual(t, 1, id.Get(0, 0))
+	testutil.AssertEqual(t, 1, id.Get(1, 1))
+	testutil.AssertEqual(t, 1, id.Get(2, 2))
+	testutil.AssertEqual(t, 1, id.Get(3, 3))
+	testutil.AssertEqual(t, 1, id.Get(4, 4))
+	testutil.AssertEqual(t, 0, id.Get(0, 1))
+	testutil.AssertEqual(t, 0, id.Get(1, 0))
+	testutil.AssertEqual(t, 0, id.Get(4, 0))
+	testutil.AssertEqual(t, 0, id.Get(0, 4))
+}
+
+func TestNewFromArrays(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3, 4},
+		{5, 6, 7, 8},
+	})
+	testutil.AssertNotNil(t, m)
+
+	rows, cols := m.Size()
+	testutil.AssertEqual(t, 2, rows)
+	testutil.AssertEqual(t, 4, cols)
+}
+
+func TestOnes(t *testing.T) {
+	// replaced new assertions helper
+
+	ones := Ones(5, 10)
+	rows, cols := ones.Size()
+	testutil.AssertEqual(t, 5, rows)
+	testutil.AssertEqual(t, 10, cols)
+
+	for row := 0; row < rows; row++ {
+		for col := 0; col < cols; col++ {
+			testutil.AssertEqual(t, 1, ones.Get(row, col))
+		}
+	}
+}
+
+func TestMatrixEpsilon(t *testing.T) {
+	// replaced new assertions helper
+
+	ones := Ones(2, 2)
+	ones = ones.WithEpsilon(0.001)
+	testutil.AssertEqual(t, 0.001, ones.Epsilon())
+}
+
+func TestMatrixArrays(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+	})
+
+	testutil.AssertNotNil(t, m)
+
+	arrays := m.Arrays()
+
+	testutil.AssertEqual(t, arrays, [][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+	})
+}
+
+func TestMatrixIsSquare(t *testing.T) {
+	// replaced new assertions helper
+
+	testutil.AssertFalse(t, NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+	}).IsSquare())
+
+	testutil.AssertFalse(t, NewFromArrays([][]float64{
+		{1, 2},
+		{3, 4},
+		{5, 6},
+	}).IsSquare())
+
+	testutil.AssertTrue(t, NewFromArrays([][]float64{
+		{1, 2},
+		{3, 4},
+	}).IsSquare())
+}
+
+func TestMatrixIsSymmetric(t *testing.T) {
+	// replaced new assertions helper
+
+	testutil.AssertFalse(t, NewFromArrays([][]float64{
+		{1, 2, 3},
+		{2, 1, 2},
+	}).IsSymmetric())
+
+	testutil.AssertFalse(t, NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	}).IsSymmetric())
+
+	testutil.AssertTrue(t, NewFromArrays([][]float64{
+		{1, 2, 3},
+		{2, 1, 2},
+		{3, 2, 1},
+	}).IsSymmetric())
+
+}
+
+func TestMatrixGet(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	testutil.AssertEqual(t, 1, m.Get(0, 0))
+	testutil.AssertEqual(t, 2, m.Get(0, 1))
+	testutil.AssertEqual(t, 3, m.Get(0, 2))
+	testutil.AssertEqual(t, 4, m.Get(1, 0))
+	testutil.AssertEqual(t, 5, m.Get(1, 1))
+	testutil.AssertEqual(t, 6, m.Get(1, 2))
+	testutil.AssertEqual(t, 7, m.Get(2, 0))
+	testutil.AssertEqual(t, 8, m.Get(2, 1))
+	testutil.AssertEqual(t, 9, m.Get(2, 2))
+}
+
+func TestMatrixSet(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	m.Set(1, 1, 99)
+	testutil.AssertEqual(t, 99, m.Get(1, 1))
+}
+
+func TestMatrixCol(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	testutil.AssertEqual(t, []float64{1, 4, 7}, m.Col(0))
+	testutil.AssertEqual(t, []float64{2, 5, 8}, m.Col(1))
+	testutil.AssertEqual(t, []float64{3, 6, 9}, m.Col(2))
+}
+
+func TestMatrixRow(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	testutil.AssertEqual(t, []float64{1, 2, 3}, m.Row(0))
+	testutil.AssertEqual(t, []float64{4, 5, 6}, m.Row(1))
+	testutil.AssertEqual(t, []float64{7, 8, 9}, m.Row(2))
+}
+
+func TestMatrixSwapRows(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	m.SwapRows(0, 1)
+
+	testutil.AssertEqual(t, []float64{4, 5, 6}, m.Row(0))
+	testutil.AssertEqual(t, []float64{1, 2, 3}, m.Row(1))
+	testutil.AssertEqual(t, []float64{7, 8, 9}, m.Row(2))
+}
+
+func TestMatrixCopy(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	m2 := m.Copy()
+	testutil.AssertFalse(t, m == m2)
+	testutil.AssertTrue(t, m.Equals(m2))
+}
+
+func TestMatrixDiagonalVector(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 4, 7},
+		{4, 2, 8},
+		{7, 8, 3},
+	})
+
+	diag := m.DiagonalVector()
+	testutil.AssertEqual(t, []float64{1, 2, 3}, diag)
+}
+
+func TestMatrixDiagonalVectorLandscape(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 4, 7, 99},
+		{4, 2, 8, 99},
+	})
+
+	diag := m.DiagonalVector()
+	testutil.AssertEqual(t, []float64{1, 2}, diag)
+}
+
+func TestMatrixDiagonalVectorPortrait(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 4},
+		{4, 2},
+		{99, 99},
+	})
+
+	diag := m.DiagonalVector()
+	testutil.AssertEqual(t, []float64{1, 2}, diag)
+}
+
+func TestMatrixDiagonal(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 4, 7},
+		{4, 2, 8},
+		{7, 8, 3},
+	})
+
+	m2 := NewFromArrays([][]float64{
+		{1, 0, 0},
+		{0, 2, 0},
+		{0, 0, 3},
+	})
+
+	testutil.AssertTrue(t, m.Diagonal().Equals(m2))
+}
+
+func TestMatrixEquals(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 4, 7},
+		{4, 2, 8},
+		{7, 8, 3},
+	})
+
+	testutil.AssertFalse(t, m.Equals(nil))
+	var nilMatrix *Matrix
+	testutil.AssertTrue(t, nilMatrix.Equals(nil))
+	testutil.AssertFalse(t, m.Equals(New(1, 1)))
+	testutil.AssertFalse(t, m.Equals(New(3, 3)))
+	testutil.AssertTrue(t, m.Equals(New(3, 3, 1, 4, 7, 4, 2, 8, 7, 8, 3)))
+}
+
+func TestMatrixL(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	l := m.L()
+	testutil.AssertTrue(t, l.Equals(New(3, 3, 1, 2, 3, 0, 5, 6, 0, 0, 9)))
+}
+
+func TestMatrixU(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	u := m.U()
+	testutil.AssertTrue(t, u.Equals(New(3, 3, 0, 0, 0, 4, 0, 0, 7, 8, 0)))
+}
+
+func TestMatrixString(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+	})
+
+	testutil.AssertEqual(t, "1 2 3 \n4 5 6 \n7 8 9 \n", m.String())
+}
+
+func TestMatrixLU(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 3, 5},
+		{2, 4, 7},
+		{1, 1, 0},
+	})
+
+	l, u, p := m.LU()
+	testutil.AssertNotNil(t, l)
+	testutil.AssertNotNil(t, u)
+	testutil.AssertNotNil(t, p)
+}
+
+func TestMatrixQR(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{12, -51, 4},
+		{6, 167, -68},
+		{-4, 24, -41},
+	})
+
+	q, r := m.QR()
+	testutil.AssertNotNil(t, q)
+	testutil.AssertNotNil(t, r)
+}
+
+func TestMatrixTranspose(t *testing.T) {
+	// replaced new assertions helper
+
+	m := NewFromArrays([][]float64{
+		{1, 2, 3},
+		{4, 5, 6},
+		{7, 8, 9},
+		{10, 11, 12},
+	})
+
+	m2 := m.Transpose()
+
+	rows, cols := m2.Size()
+	testutil.AssertEqual(t, 3, rows)
+	testutil.AssertEqual(t, 4, cols)
+
+	testutil.AssertEqual(t, 1, m2.Get(0, 0))
+	testutil.AssertEqual(t, 10, m2.Get(0, 3))
+	testutil.AssertEqual(t, 3, m2.Get(2, 0))
+}

matrix/regression.go

@@ -0,0 +1,45 @@
+package matrix
+
+import "errors"
+
+var (
+	// ErrPolyRegArraysSameLength is a common error.
+	ErrPolyRegArraysSameLength = errors.New("polynomial array inputs must be the same length")
+)
+
+// Poly returns the polynomial regress of a given degree over the given values.
+func Poly(xvalues, yvalues []float64, degree int) ([]float64, error) {
+	if len(xvalues) != len(yvalues) {
+		return nil, ErrPolyRegArraysSameLength
+	}
+
+	m := len(yvalues)
+	n := degree + 1
+	y := New(m, 1, yvalues...)
+	x := Zero(m, n)
+
+	for i := 0; i < m; i++ {
+		ip := float64(1)
+		for j := 0; j < n; j++ {
+			x.Set(i, j, ip)
+			ip *= xvalues[i]
+		}
+	}
+
+	q, r := x.QR()
+	qty, err := q.Transpose().Times(y)
+	if err != nil {
+		return nil, err
+	}
+
+	c := make([]float64, n)
+	for i := n - 1; i >= 0; i-- {
+		c[i] = qty.Get(i, 0)
+		for j := i + 1; j < n; j++ {
+			c[i] -= c[j] * r.Get(i, j)
+		}
+		c[i] /= r.Get(i, i)
+	}
+
+	return c, nil
+}

matrix/regression_test.go

@@ -0,0 +1,22 @@
+package matrix
+
+import (
+	"testing"
+
+	"github.com/wcharczuk/go-chart/v2/testutil"
+)
+
+func TestPoly(t *testing.T) {
+	// replaced new assertions helper
+	var xGiven = []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
+	var yGiven = []float64{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
+	var degree = 2
+
+	c, err := Poly(xGiven, yGiven, degree)
+	testutil.AssertNil(t, err)
+	testutil.AssertLen(t, c, 3)
+
+	testutil.AssertInDelta(t, c[0], 0.999999999, DefaultEpsilon)
+	testutil.AssertInDelta(t, c[1], 2, DefaultEpsilon)
+	testutil.AssertInDelta(t, c[2], 3, DefaultEpsilon)
+}

matrix/util.go

@@ -0,0 +1,36 @@
+package matrix
+
+import (
+	"math"
+	"strconv"
+)
+
+func minInt(values ...int) int {
+	min := math.MaxInt32
+
+	for x := 0; x < len(values); x++ {
+		if values[x] < min {
+			min = values[x]
+		}
+	}
+	return min
+}
+
+func maxInt(values ...int) int {
+	max := math.MinInt32
+
+	for x := 0; x < len(values); x++ {
+		if values[x] > max {
+			max = values[x]
+		}
+	}
+	return max
+}
+
+func f64s(v float64) string {
+	return strconv.FormatFloat(v, 'f', -1, 64)
+}
+
+func roundToEpsilon(value, epsilon float64) float64 {
+	return math.Nextafter(value, value)
+}

matrix/vector.go

@@ -0,0 +1,17 @@
+package matrix
+
+// Vector is just an array of values.
+type Vector []float64
+
+// DotProduct returns the dot product of two vectors.
+func (v Vector) DotProduct(v2 Vector) (result float64, err error) {
+	if len(v) != len(v2) {
+		err = ErrDimensionMismatch
+		return
+	}
+
+	for i := 0; i < len(v); i++ {
+		result = result + (v[i] * v2[i])
+	}
+	return
+}