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mat.go
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mat.go
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// Generated code. DO NOT EDIT
package mat
import (
"github.com/chewxy/math32"
"github.com/itohio/EasyRobot/pkg/core/math/vec"
)
type Matrix [][]float32
func New(rows, cols int, arr ...float32) Matrix {
m := make([][]float32, rows)
backing := make([]float32, rows*cols)
s := 0
for i := range m {
m[i] = backing[s : s+cols]
s += cols
}
if arr != nil {
s = 0
for i := range m {
copy(m[i], arr[s:s+cols])
s += cols
}
}
return m
}
// Returns a flat representation of this matrix.
func (m Matrix) Flat(v vec.Vector) vec.Vector {
N := len(m[0])
for i, row := range m {
copy(v[i*N:i*N+N], row[:])
}
return v
}
// Returns a Matrix view of this matrix.
// The view actually contains slices of original matrix rows.
// This way original matrix can be modified.
func (m Matrix) Matrix() Matrix {
m1 := make(Matrix, len(m))
for i := range m {
m1[i] = m[i][:]
}
return m1
}
// Fills destination matrix with a 2D rotation
// Matrix size must be at least 2x2
func (m Matrix) Rotation2D(a float32) Matrix {
c := math32.Cos(a)
s := math32.Sin(a)
return m.SetSubmatrixRaw(0, 0, 2, 2,
c, -s,
s, c,
)
}
// Fills destination matrix with a rotation around X axis
// Matrix size must be at least 3x3
func (m Matrix) RotationX(a float32) Matrix {
c := math32.Cos(a)
s := math32.Sin(a)
return m.SetSubmatrixRaw(0, 0, 3, 3,
1, 0, 0,
0, c, -s,
0, s, c,
)
}
// Fills destination matrix with a rotation around Y axis
// Matrix size must be at least 3x3
func (m Matrix) RotationY(a float32) Matrix {
c := math32.Cos(a)
s := math32.Sin(a)
return m.SetSubmatrixRaw(0, 0, 3, 3,
c, 0, s,
0, 1, 0,
-s, 0, c,
)
}
// Fills destination matrix with a rotation around Z axis
// Matrix size must be at least 3x3
func (m Matrix) RotationZ(a float32) Matrix {
c := math32.Cos(a)
s := math32.Sin(a)
return m.SetSubmatrixRaw(0, 0, 3, 3,
c, -s, 0,
s, c, 0,
0, 0, 1,
)
}
// Build orientation matrix from quaternion
// Matrix size must be at least 3x3
// Quaternion axis must be unit vector
func (m Matrix) Orientation(q vec.Quaternion) Matrix {
theta := q.Theta() / 2
qr := math32.Cos(theta)
s := math32.Sin(theta)
qi := q[0] * s
qj := q[1] * s
qk := q[2] * s
// calculate quaternion rotation matrix
qjqj := qj * qj
qiqi := qi * qi
qkqk := qk * qk
qiqj := qi * qj
qjqr := qj * qr
qiqk := qi * qk
qiqr := qi * qr
qkqr := qk * qr
qjqk := qj * qk
return m.SetSubmatrixRaw(0, 0, 3, 3,
1.0-2.0*(qjqj+qkqk),
2.0*(qiqj+qkqr),
2.0*(qiqk+qjqr),
2.0*(qiqj+qkqr),
1.0-2.0*(qiqi+qkqk),
2.0*(qjqk+qiqr),
2.0*(qiqk+qjqr),
2.0*(qjqk+qiqr),
1.0-2.0*(qiqi+qjqj),
)
}
// Fills destination matrix with identity matrix.
func (m Matrix) Eye() Matrix {
for i := range m {
row := m[i][:]
for j := range row {
row[j] = 0
}
}
for i := range m {
m[i][i] = 1
}
return m
}
// Returns a slice to the row.
func (m Matrix) Row(row int) vec.Vector {
return m[row][:]
}
// Returns a copy of the matrix column.
func (m Matrix) Col(col int, v vec.Vector) vec.Vector {
for i, row := range m {
v[i] = row[col]
}
return v
}
func (m Matrix) SetRow(row int, v vec.Vector) Matrix {
copy(m[row][:], v[:])
return m
}
func (m Matrix) SetCol(col int, v vec.Vector) Matrix {
for i, v := range v {
m[i][col] = v
}
return m
}
// Size of the destination vector must equal to number of rows
func (m Matrix) Diagonal(dst vec.Vector) vec.Vector {
for i, row := range m {
dst[i] = row[i]
}
return dst
}
// Size of the vector must equal to number of rows
func (m Matrix) SetDiagonal(v vec.Vector) Matrix {
for i, v := range v {
m[i][i] = v
}
return m
}
func (m Matrix) Submatrix(row, col int, m1 Matrix) Matrix {
cols := len(m1[0])
for i, m1row := range m1 {
copy(m1row, m[row+i][col : cols+col][:])
}
return m1
}
func (m Matrix) SetSubmatrix(row, col int, m1 Matrix) Matrix {
for i := range m[row : row+len(m1)] {
copy(m[row+i][col : col+len(m1[i])][:], m1[i][:])
}
return m
}
func (m Matrix) SetSubmatrixRaw(row, col, rows1, cols1 int, m1 ...float32) Matrix {
for i := 0; i < rows1; i++ {
copy(m[row+i][col : col+cols1][:], m1[i*cols1:i*cols1+cols1])
}
return m
}
func (m Matrix) Clone() Matrix {
m1 := New(len(m), len(m[0]))
for i, row := range m {
copy(m1[i][:], row[:])
}
return m1
}
// Transposes matrix m1 and stores the result in the destination matrix
// destination matrix must be of appropriate size.
// NOTE: Does not support in place transpose
func (m Matrix) Transpose(m1 Matrix) Matrix {
for i, row := range m1 {
for j, val := range row {
m[j][i] = val
}
}
return m
}
func (m Matrix) Add(m1 Matrix) Matrix {
for i := range m {
vec.Vector(m[i][:]).Add(m1[i][:])
}
return m
}
func (m Matrix) Sub(m1 Matrix) Matrix {
for i := range m {
vec.Vector(m[i][:]).Sub(m1[i][:])
}
return m
}
func (m Matrix) MulC(c float32) Matrix {
for i := range m {
vec.Vector(m[i][:]).MulC(c)
}
return m
}
func (m Matrix) DivC(c float32) Matrix {
for i := range m {
vec.Vector(m[i][:]).DivC(c)
}
return m
}
// Destination matrix must be properly sized.
// given that a is MxN and b is NxK
// then destinatiom matrix must be MxK
func (m Matrix) Mul(a Matrix, b Matrix) Matrix {
for i, row := range a {
mrow := m[i][:]
for j := range mrow {
var sum float32
for k, brow := range b {
sum += row[k] * brow[j]
}
mrow[j] = sum
}
}
return m
}
// Only makes sense for square matrices.
// Vector size must be equal to number of rows/cols
func (m Matrix) MulDiag(a Matrix, b vec.Vector) Matrix {
for i, row := range a {
mrow := m[i][:]
for j := range row {
mrow[j] = row[j] * b[j]
}
}
return m
}
// Vector must have a size equal to number of cols.
// Destination vector must have a size equal to number of rows.
func (m Matrix) MulVec(v vec.Vector, dst vec.Vector) vec.Vector {
for i, row := range m {
var sum float32
for j, val := range row {
sum += v[j] * val
}
dst[i] = sum
}
return dst
}
// Vector must have a size equal to number of rows.
// Destination vector must have a size equal to number of cols.
func (m Matrix) MulVecT(v vec.Vector, dst vec.Vector) vec.Vector {
for i := range m[0] {
var sum float32
for j, val := range m {
sum += v[j] * val[i]
}
dst[i] = sum
}
return dst
}
// Determinant only valid for square matrix
// Undefined behavior for non square matrices
func (m Matrix) Det() float32 {
tmp := m.Clone()
var ratio float32
var det float32 = 1
// upper triangular
for i, row := range tmp {
for j := range row {
if j > i {
tmpj := tmp[j][:]
ratio = tmpj[i] / row[i]
for k := range tmp {
tmpj[k] -= ratio * row[k]
}
}
}
}
for i, row := range tmp {
det *= row[i]
}
return det
}
//
// LU decomposition into two triangular matrices
// NOTE: Assume, that l&u matrices are set to zero
// Matrix must be square and M, L and U matrix sizes must be equal
func (m Matrix) LU(L, U Matrix) {
for i := range m {
// Upper Triangular
for k := i; k < len(m); k++ {
// Summation of L(i, j) * U(j, k)
var sum float32
for j := 0; j < i; j++ {
sum += L[i][j] * U[j][k]
}
// Evaluating U(i, k)
U[i][k] = m[i][k] - sum
}
// Lower Triangular
for k := i; k < len(m); k++ {
if i == k {
L[i][i] = 1 // Diagonal as 1
} else {
// Summation of L(k, j) * U(j, i)
var sum float32
for j := 0; j < i; j++ {
sum += L[k][j] * U[j][i]
}
// Evaluating L(k, i)
L[k][i] = (m[k][i] - sum) / U[i][i]
}
}
}
}
/// https://math.stackexchange.com/questions/893984/conversion-of-rotation-matrix-to-quaternion
/// Must be at least 3x3 matrix
func (m Matrix) Quaternion() (q *vec.Quaternion) {
var t float32
if m[2][2] < 0 {
if m[0][0] > m[1][1] {
t = 1 + m[0][0] - m[1][1] - m[2][2]
q = &vec.Quaternion{t, m[0][1] + m[1][0], m[2][0] + m[0][2], m[1][2] - m[2][1]}
} else {
t = 1 - m[0][0] + m[1][1] - m[2][2]
q = &vec.Quaternion{m[0][1] + m[1][0], t, m[1][2] + m[2][1], m[2][0] - m[0][2]}
}
} else {
if m[0][0] < -m[1][1] {
t = 1 - m[0][0] - m[1][1] + m[2][2]
q = &vec.Quaternion{m[2][0] + m[0][2], m[1][2] + m[2][1], t, m[0][1] - m[1][0]}
} else {
t = 1 + m[0][0] + m[1][1] + m[2][2]
q = &vec.Quaternion{m[1][2] - m[2][1], m[2][0] - m[0][2], m[0][1] - m[1][0], t}
}
}
q.Vector().MulC(0.5 / math32.Sqrt(t))
return
}