mat_unsafe.go

// Copyright ©2021 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

//go:build !safe
// +build !safe

package r3

import (
	"unsafe"

	"gonum.org/v1/gonum/blas/blas64"
	"gonum.org/v1/gonum/mat"
)

type array [3][3]float64

// At returns the value of a matrix element at row i, column j.
// At expects indices in the range [0,2].
// It will panic if i or j are out of bounds for the matrix.
func (m *Mat) At(i, j int) float64 {
	if m.data == nil {
		m.data = new(array)
	}
	return m.data[i][j]
}

// Set sets the element at row i, column j to the value v.
func (m *Mat) Set(i, j int, v float64) {
	if m.data == nil {
		m.data = new(array)
	}
	m.data[i][j] = v
}

// Eye returns the 3×3 Identity matrix
func Eye() *Mat {
	return &Mat{&array{
		{1, 0, 0},
		{0, 1, 0},
		{0, 0, 1},
	}}
}

// Skew returns the 3×3 skew symmetric matrix (right hand system) of v.
//
//	                ⎡ 0 -z  y⎤
//	Skew({x,y,z}) = ⎢ z  0 -x⎥
//	                ⎣-y  x  0⎦
//
// Deprecated: use Mat.Skew()
func Skew(v Vec) (M *Mat) {
	return &Mat{&array{
		{0, -v.Z, v.Y},
		{v.Z, 0, -v.X},
		{-v.Y, v.X, 0},
	}}
}

// Mul takes the matrix product of a and b, placing the result in the receiver.
// If the number of columns in a does not equal 3, Mul will panic.
func (m *Mat) Mul(a, b mat.Matrix) {
	ra, ca := a.Dims()
	rb, cb := b.Dims()
	switch {
	case ra != 3:
		panic(mat.ErrShape)
	case cb != 3:
		panic(mat.ErrShape)
	case ca != rb:
		panic(mat.ErrShape)
	}
	if m.data == nil {
		m.data = new(array)
	}
	if ca != 3 {
		// General matrix multiplication for the case where the inner dimension is not 3.
		t := mat.NewDense(3, 3, m.slice())
		t.Mul(a, b)
		return
	}

	a00 := a.At(0, 0)
	b00 := b.At(0, 0)
	a01 := a.At(0, 1)
	b01 := b.At(0, 1)
	a02 := a.At(0, 2)
	b02 := b.At(0, 2)
	a10 := a.At(1, 0)
	b10 := b.At(1, 0)
	a11 := a.At(1, 1)
	b11 := b.At(1, 1)
	a12 := a.At(1, 2)
	b12 := b.At(1, 2)
	a20 := a.At(2, 0)
	b20 := b.At(2, 0)
	a21 := a.At(2, 1)
	b21 := b.At(2, 1)
	a22 := a.At(2, 2)
	b22 := b.At(2, 2)
	m.data[0][0] = a00*b00 + a01*b10 + a02*b20
	m.data[0][1] = a00*b01 + a01*b11 + a02*b21
	m.data[0][2] = a00*b02 + a01*b12 + a02*b22
	m.data[1][0] = a10*b00 + a11*b10 + a12*b20
	m.data[1][1] = a10*b01 + a11*b11 + a12*b21
	m.data[1][2] = a10*b02 + a11*b12 + a12*b22
	m.data[2][0] = a20*b00 + a21*b10 + a22*b20
	m.data[2][1] = a20*b01 + a21*b11 + a22*b21
	m.data[2][2] = a20*b02 + a21*b12 + a22*b22
}

// RawMatrix returns the blas representation of the matrix with the backing
// data of this matrix. Changes to the returned matrix will be reflected in
// the receiver.
func (m *Mat) RawMatrix() blas64.General {
	if m.data == nil {
		m.data = new(array)
	}
	return blas64.General{Rows: 3, Cols: 3, Data: m.slice(), Stride: 3}
}

// Mat returns a 3×3 rotation matrix corresponding to the receiver. It
// may be used to perform rotations on a 3-vector or to apply the rotation
// to a 3×n matrix of column vectors. If the receiver is not a unit
// quaternion, the returned matrix will not be a pure rotation.
func (r Rotation) Mat() *Mat {
	w, i, j, k := r.Real, r.Imag, r.Jmag, r.Kmag
	ii := 2 * i * i
	jj := 2 * j * j
	kk := 2 * k * k
	wi := 2 * w * i
	wj := 2 * w * j
	wk := 2 * w * k
	ij := 2 * i * j
	jk := 2 * j * k
	ki := 2 * k * i
	return &Mat{&array{
		{1 - (jj + kk), ij - wk, ki + wj},
		{ij + wk, 1 - (ii + kk), jk - wi},
		{ki - wj, jk + wi, 1 - (ii + jj)},
	}}
}

func arrayFrom(vals []float64) *array {
	return (*array)(unsafe.Pointer(&vals[0]))
}

func (m *Mat) slice() []float64 {
	return (*[9]float64)(unsafe.Pointer(m.data))[:]
}