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| 1 | +// RUN: %target-typecheck-verify-swift -solver-scope-threshold=500 |
| 2 | + |
| 3 | +// https://github.com/swiftlang/swift/issues/48155 |
| 4 | + |
| 5 | +public struct MatrixNxM<T> { |
| 6 | + var m: [T] |
| 7 | + private let xdim : Int |
| 8 | + private let ydim : Int |
| 9 | + |
| 10 | + subscript(i: Int, j: Int) -> T { |
| 11 | + get { |
| 12 | + precondition(i*xdim + j < self.m.count, "Index out of matrix bounds \(i) \(j)") |
| 13 | + |
| 14 | + return self.m[i*xdim + j] |
| 15 | + } |
| 16 | + set { |
| 17 | + self.m[i*xdim + j] = newValue |
| 18 | + } |
| 19 | + } |
| 20 | + |
| 21 | + public init(xdim: Int, ydim: Int) { |
| 22 | + self.xdim = xdim |
| 23 | + self.ydim = ydim |
| 24 | + self.m = [Any](repeating: 0.0, count: xdim*ydim) as! [T] |
| 25 | + } |
| 26 | +} |
| 27 | + |
| 28 | +public struct Matrix4x4 { |
| 29 | + var m: [Double] |
| 30 | + |
| 31 | + subscript(i: Int, j: Int) -> Double { |
| 32 | + get { |
| 33 | + precondition(i*4 + j < self.m.count, "Index out of matrix bounds \(i) \(j)") |
| 34 | + |
| 35 | + return self.m[i*4 + j] |
| 36 | + } |
| 37 | + set { |
| 38 | + self.m[i*4 + j] = newValue |
| 39 | + } |
| 40 | + } |
| 41 | + |
| 42 | + public init() { |
| 43 | + m = [Double](repeating: 0.0, count: 16) |
| 44 | + } |
| 45 | + |
| 46 | + public static func identity() -> Matrix4x4 { |
| 47 | + var identity = Matrix4x4() |
| 48 | + |
| 49 | + identity[0,0] = 1.0; |
| 50 | + identity[1,1] = 1.0; |
| 51 | + identity[2,2] = 1.0; |
| 52 | + identity[3,3] = 1.0; |
| 53 | + |
| 54 | + return identity |
| 55 | + } |
| 56 | + |
| 57 | + public func determinant() -> Double { |
| 58 | + let det = self[0,0] * self[1,1] * self[2,2] * self[3,3] + |
| 59 | + self[0,0] * self[1,2] * self[2,3] * self[3,1] + |
| 60 | + self[0,0] * self[1,3] * self[2,1] * self[3,2] + |
| 61 | + |
| 62 | + self[0,1] * self[1,0] * self[2,3] * self[3,2] + |
| 63 | + self[0,1] * self[1,2] * self[2,1] * self[3,3] + |
| 64 | + self[0,1] * self[1,3] * self[2,2] * self[3,0] + |
| 65 | + |
| 66 | + self[0,2] * self[1,0] * self[2,1] * self[3,3] + |
| 67 | + self[0,2] * self[1,1] * self[2,3] * self[3,0] + |
| 68 | + self[0,2] * self[1,3] * self[2,0] * self[3,0] + |
| 69 | + |
| 70 | + self[0,3] * self[1,0] * self[2,2] * self[3,1] + |
| 71 | + self[0,3] * self[1,1] * self[2,0] * self[3,2] + |
| 72 | + self[0,3] * self[1,2] * self[2,1] * self[3,0] - |
| 73 | + |
| 74 | + self[0,0] * self[1,1] * self[2,3] * self[3,2] - |
| 75 | + self[0,0] * self[1,2] * self[2,1] * self[3,3] - |
| 76 | + self[0,0] * self[1,3] * self[2,2] * self[3,1] - |
| 77 | + |
| 78 | + self[0,1] * self[1,0] * self[2,2] * self[3,3] - |
| 79 | + self[0,1] * self[1,2] * self[2,3] * self[3,0] - |
| 80 | + self[0,1] * self[1,3] * self[2,0] * self[3,2] - |
| 81 | + |
| 82 | + self[0,2] * self[1,0] * self[2,3] * self[3,1] - |
| 83 | + self[0,2] * self[1,1] * self[2,0] * self[3,3] - |
| 84 | + self[0,2] * self[1,3] * self[2,1] * self[3,0] - |
| 85 | + |
| 86 | + self[0,3] * self[1,0] * self[2,1] * self[3,2] - |
| 87 | + self[0,3] * self[1,1] * self[2,2] * self[3,0] - |
| 88 | + self[0,3] * self[1,2] * self[2,0] * self[3,1] |
| 89 | + |
| 90 | + return det |
| 91 | + } |
| 92 | + |
| 93 | + public func inverse() -> Matrix4x4 { |
| 94 | + let det = self.determinant() |
| 95 | + precondition(det != 0, "Determinant is zero, unable to calculate inverse Matrix") |
| 96 | + |
| 97 | + let inv_det = 1.0 / det |
| 98 | + var inverse = Matrix4x4() |
| 99 | + |
| 100 | + inverse[0, 0] = (self[1,1] * self[2,2] * self[3,3] + |
| 101 | + self[1,2] * self[2,3] * self[3,1] + |
| 102 | + self[1,3] * self[2,1] * self[3,2] - |
| 103 | + self[1,1] * self[2,3] * self[3,2] - |
| 104 | + self[1,2] * self[2,1] * self[3,3] - |
| 105 | + self[1,3] * self[2,2] * self[3,1]) * inv_det; |
| 106 | + |
| 107 | + inverse[0, 1] = (self[0,1] * self[2,3] * self[3,2] + |
| 108 | + self[0,2] * self[2,1] * self[3,3] + |
| 109 | + self[1,3] * self[2,2] * self[3,1] - |
| 110 | + self[0,1] * self[2,2] * self[3,3] - |
| 111 | + self[0,2] * self[2,3] * self[3,1] - |
| 112 | + self[0,3] * self[2,1] * self[3,2]) * inv_det; |
| 113 | + |
| 114 | + inverse[0, 2] = (self[0,1] * self[1,2] * self[3,3] + |
| 115 | + self[0,2] * self[1,3] * self[3,1] + |
| 116 | + self[0,3] * self[1,1] * self[3,2] - |
| 117 | + self[0,1] * self[1,3] * self[3,2] - |
| 118 | + self[0,2] * self[1,1] * self[3,3] - |
| 119 | + self[0,3] * self[1,2] * self[3,1]) * inv_det; |
| 120 | + |
| 121 | + inverse[0, 3] = (self[0,1] * self[1,3] * self[2,2] + |
| 122 | + self[0,2] * self[1,1] * self[2,3] + |
| 123 | + self[0,3] * self[1,2] * self[2,1] - |
| 124 | + self[0,1] * self[1,2] * self[2,3] - |
| 125 | + self[0,2] * self[1,3] * self[2,1] - |
| 126 | + self[0,3] * self[1,1] * self[2,2]) * inv_det; |
| 127 | + |
| 128 | + inverse[1, 0] = (self[1,0] * self[2,3] * self[3,2] + |
| 129 | + self[1,2] * self[2,0] * self[3,3] + |
| 130 | + self[1,3] * self[2,2] * self[3,1] - |
| 131 | + self[1,0] * self[2,2] * self[3,3] - |
| 132 | + self[1,2] * self[2,3] * self[3,1] - |
| 133 | + self[1,3] * self[2,0] * self[3,2]) * inv_det; |
| 134 | + |
| 135 | + inverse[1, 1] = (self[0,0] * self[2,2] * self[3,3] + |
| 136 | + self[0,2] * self[2,3] * self[3,1] + |
| 137 | + self[0,3] * self[2,0] * self[3,2] - |
| 138 | + self[0,0] * self[2,3] * self[3,2] - |
| 139 | + self[0,2] * self[2,0] * self[3,3] - |
| 140 | + self[0,3] * self[2,2] * self[3,0]) * inv_det; |
| 141 | + |
| 142 | + |
| 143 | + inverse[1, 2] = (self[0,0] * self[1,3] * self[3,2] + |
| 144 | + self[0,2] * self[1,0] * self[3,3] + |
| 145 | + self[0,3] * self[1,2] * self[3,1] - |
| 146 | + self[0,0] * self[1,2] * self[3,3] - |
| 147 | + self[0,2] * self[1,3] * self[3,0] - |
| 148 | + self[0,3] * self[1,0] * self[3,2]) * inv_det; |
| 149 | + |
| 150 | + inverse[1, 3] = (self[0,0] * self[1,2] * self[2,3] + |
| 151 | + self[0,2] * self[1,3] * self[2,2] + |
| 152 | + self[0,3] * self[1,0] * self[2,2] - |
| 153 | + self[0,0] * self[1,3] * self[2,2] - |
| 154 | + self[0,2] * self[1,0] * self[2,3] - |
| 155 | + self[0,3] * self[1,2] * self[2,0]) * inv_det; |
| 156 | + |
| 157 | + inverse[2, 0] = (self[1,0] * self[2,1] * self[3,3] + |
| 158 | + self[1,1] * self[2,3] * self[3,1] + |
| 159 | + self[1,3] * self[2,1] * self[3,2] - |
| 160 | + self[1,0] * self[2,3] * self[3,1] - |
| 161 | + self[1,1] * self[2,0] * self[3,3] - |
| 162 | + self[1,3] * self[2,1] * self[3,0]) * inv_det; |
| 163 | + |
| 164 | + inverse[2, 1] = (self[0,0] * self[2,3] * self[3,1] + |
| 165 | + self[0,1] * self[2,0] * self[3,3] + |
| 166 | + self[0,3] * self[2,1] * self[3,1] - |
| 167 | + self[0,0] * self[2,1] * self[3,3] - |
| 168 | + self[0,1] * self[2,3] * self[3,0] - |
| 169 | + self[0,3] * self[2,0] * self[3,1]) * inv_det; |
| 170 | + |
| 171 | + inverse[2, 2] = (self[0,0] * self[1,1] * self[3,3] + |
| 172 | + self[0,1] * self[1,3] * self[3,0] + |
| 173 | + self[0,3] * self[1,0] * self[3,1] - |
| 174 | + self[0,0] * self[1,3] * self[3,1] - |
| 175 | + self[0,1] * self[1,0] * self[3,3] - |
| 176 | + self[0,3] * self[1,1] * self[3,0]) * inv_det; |
| 177 | + |
| 178 | + inverse[2, 3] = (self[0,0] * self[1,3] * self[2,1] + |
| 179 | + self[0,1] * self[1,0] * self[2,3] + |
| 180 | + self[0,3] * self[1,1] * self[2,0] - |
| 181 | + self[0,0] * self[1,1] * self[2,3] - |
| 182 | + self[0,1] * self[1,3] * self[2,0] - |
| 183 | + self[0,3] * self[1,0] * self[2,1]) * inv_det; |
| 184 | + |
| 185 | + inverse[3, 0] = (self[1,0] * self[2,2] * self[3,1] + |
| 186 | + self[1,1] * self[2,0] * self[3,2] + |
| 187 | + self[1,2] * self[2,1] * self[3,0] - |
| 188 | + self[1,0] * self[2,1] * self[3,2] - |
| 189 | + self[1,1] * self[2,2] * self[3,0] - |
| 190 | + self[1,2] * self[2,0] * self[3,1]) * inv_det; |
| 191 | + |
| 192 | + inverse[3, 1] = (self[0,0] * self[2,1] * self[3,2] + |
| 193 | + self[0,1] * self[2,2] * self[3,0] + |
| 194 | + self[0,2] * self[2,0] * self[3,2] - |
| 195 | + self[0,0] * self[2,2] * self[3,1] - |
| 196 | + self[0,1] * self[2,0] * self[3,2] - |
| 197 | + self[0,2] * self[2,1] * self[3,0]) * inv_det; |
| 198 | + |
| 199 | + inverse[3, 2] = (self[0,0] * self[1,2] * self[3,1] + |
| 200 | + self[0,1] * self[1,0] * self[3,2] + |
| 201 | + self[0,2] * self[1,1] * self[3,0] - |
| 202 | + self[0,0] * self[1,1] * self[3,2] - |
| 203 | + self[0,1] * self[1,2] * self[3,0] - |
| 204 | + self[0,2] * self[1,0] * self[3,1]) * inv_det; |
| 205 | + |
| 206 | + inverse[3, 3] = (self[0,0] * self[1,1] * self[2,2] + |
| 207 | + self[0,1] * self[1,2] * self[2,0] + |
| 208 | + self[0,2] * self[2,1] * self[2,1] - |
| 209 | + self[0,0] * self[1,2] * self[2,1] - |
| 210 | + self[0,1] * self[1,0] * self[2,2] - |
| 211 | + self[0,2] * self[1,1] * self[2,0]) * inv_det; |
| 212 | + |
| 213 | + return inverse |
| 214 | + } |
| 215 | +} |
| 216 | + |
| 217 | +public func * (a: Matrix4x4, b: Matrix4x4) -> Matrix4x4 { |
| 218 | + var c = Matrix4x4(); |
| 219 | + |
| 220 | + for i in 0..<4 { |
| 221 | + for j in 0..<4 { |
| 222 | + var ab: Double = 0.0; |
| 223 | + for k in 0..<4 { |
| 224 | + ab += a[i,k] * b[k,j]; |
| 225 | + } |
| 226 | + |
| 227 | + c[i, j] = ab; |
| 228 | + } |
| 229 | + } |
| 230 | + |
| 231 | + return c |
| 232 | +} |
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