gonum.org/v1/gonum@v0.14.0/spatial/r3/mat_unsafe.go (about)

     1  // Copyright ©2021 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  //go:build !safe
     6  // +build !safe
     7  
     8  package r3
     9  
    10  import (
    11  	"unsafe"
    12  
    13  	"gonum.org/v1/gonum/blas/blas64"
    14  	"gonum.org/v1/gonum/mat"
    15  )
    16  
    17  type array [3][3]float64
    18  
    19  // At returns the value of a matrix element at row i, column j.
    20  // At expects indices in the range [0,2].
    21  // It will panic if i or j are out of bounds for the matrix.
    22  func (m *Mat) At(i, j int) float64 {
    23  	if m.data == nil {
    24  		m.data = new(array)
    25  	}
    26  	return m.data[i][j]
    27  }
    28  
    29  // Set sets the element at row i, column j to the value v.
    30  func (m *Mat) Set(i, j int, v float64) {
    31  	if m.data == nil {
    32  		m.data = new(array)
    33  	}
    34  	m.data[i][j] = v
    35  }
    36  
    37  // Eye returns the 3×3 Identity matrix
    38  func Eye() *Mat {
    39  	return &Mat{&array{
    40  		{1, 0, 0},
    41  		{0, 1, 0},
    42  		{0, 0, 1},
    43  	}}
    44  }
    45  
    46  // Skew returns the 3×3 skew symmetric matrix (right hand system) of v.
    47  //
    48  //	                ⎡ 0 -z  y⎤
    49  //	Skew({x,y,z}) = ⎢ z  0 -x⎥
    50  //	                ⎣-y  x  0⎦
    51  //
    52  // Deprecated: use Mat.Skew()
    53  func Skew(v Vec) (M *Mat) {
    54  	return &Mat{&array{
    55  		{0, -v.Z, v.Y},
    56  		{v.Z, 0, -v.X},
    57  		{-v.Y, v.X, 0},
    58  	}}
    59  }
    60  
    61  // Mul takes the matrix product of a and b, placing the result in the receiver.
    62  // If the number of columns in a does not equal 3, Mul will panic.
    63  func (m *Mat) Mul(a, b mat.Matrix) {
    64  	ra, ca := a.Dims()
    65  	rb, cb := b.Dims()
    66  	switch {
    67  	case ra != 3:
    68  		panic(mat.ErrShape)
    69  	case cb != 3:
    70  		panic(mat.ErrShape)
    71  	case ca != rb:
    72  		panic(mat.ErrShape)
    73  	}
    74  	if m.data == nil {
    75  		m.data = new(array)
    76  	}
    77  	if ca != 3 {
    78  		// General matrix multiplication for the case where the inner dimension is not 3.
    79  		t := mat.NewDense(3, 3, m.slice())
    80  		t.Mul(a, b)
    81  		return
    82  	}
    83  
    84  	a00 := a.At(0, 0)
    85  	b00 := b.At(0, 0)
    86  	a01 := a.At(0, 1)
    87  	b01 := b.At(0, 1)
    88  	a02 := a.At(0, 2)
    89  	b02 := b.At(0, 2)
    90  	a10 := a.At(1, 0)
    91  	b10 := b.At(1, 0)
    92  	a11 := a.At(1, 1)
    93  	b11 := b.At(1, 1)
    94  	a12 := a.At(1, 2)
    95  	b12 := b.At(1, 2)
    96  	a20 := a.At(2, 0)
    97  	b20 := b.At(2, 0)
    98  	a21 := a.At(2, 1)
    99  	b21 := b.At(2, 1)
   100  	a22 := a.At(2, 2)
   101  	b22 := b.At(2, 2)
   102  	m.data[0][0] = a00*b00 + a01*b10 + a02*b20
   103  	m.data[0][1] = a00*b01 + a01*b11 + a02*b21
   104  	m.data[0][2] = a00*b02 + a01*b12 + a02*b22
   105  	m.data[1][0] = a10*b00 + a11*b10 + a12*b20
   106  	m.data[1][1] = a10*b01 + a11*b11 + a12*b21
   107  	m.data[1][2] = a10*b02 + a11*b12 + a12*b22
   108  	m.data[2][0] = a20*b00 + a21*b10 + a22*b20
   109  	m.data[2][1] = a20*b01 + a21*b11 + a22*b21
   110  	m.data[2][2] = a20*b02 + a21*b12 + a22*b22
   111  }
   112  
   113  // RawMatrix returns the blas representation of the matrix with the backing
   114  // data of this matrix. Changes to the returned matrix will be reflected in
   115  // the receiver.
   116  func (m *Mat) RawMatrix() blas64.General {
   117  	if m.data == nil {
   118  		m.data = new(array)
   119  	}
   120  	return blas64.General{Rows: 3, Cols: 3, Data: m.slice(), Stride: 3}
   121  }
   122  
   123  // Mat returns a 3×3 rotation matrix corresponding to the receiver. It
   124  // may be used to perform rotations on a 3-vector or to apply the rotation
   125  // to a 3×n matrix of column vectors. If the receiver is not a unit
   126  // quaternion, the returned matrix will not be a pure rotation.
   127  func (r Rotation) Mat() *Mat {
   128  	w, i, j, k := r.Real, r.Imag, r.Jmag, r.Kmag
   129  	ii := 2 * i * i
   130  	jj := 2 * j * j
   131  	kk := 2 * k * k
   132  	wi := 2 * w * i
   133  	wj := 2 * w * j
   134  	wk := 2 * w * k
   135  	ij := 2 * i * j
   136  	jk := 2 * j * k
   137  	ki := 2 * k * i
   138  	return &Mat{&array{
   139  		{1 - (jj + kk), ij - wk, ki + wj},
   140  		{ij + wk, 1 - (ii + kk), jk - wi},
   141  		{ki - wj, jk + wi, 1 - (ii + jj)},
   142  	}}
   143  }
   144  
   145  func arrayFrom(vals []float64) *array {
   146  	return (*array)(unsafe.Pointer(&vals[0]))
   147  }
   148  
   149  func (m *Mat) slice() []float64 {
   150  	return (*[9]float64)(unsafe.Pointer(m.data))[:]
   151  }