- Rust로 간단한 iterative power method 구현해 고유값/고유벡터 찾기.
- 선형대수학에 대한 이해.
- Rust/C++에 대한 이해.
- Rust 버전 1.74.0
- 참고: Rust Installation[https://rinthel.github.io/rust-lang-book-ko/ch01-01-installation.html]
- 인덱스를 통해 행렬에[행][열]꼴로 접근할 수 있게 다음과 같이 정의합니다.
struct Matrix<const ROW_COUNT: usize, const COLUMN_COUNT: usize>{ elements: [[f64;COLUMN_COUNT];ROW_COUNT] }
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행렬-열벡터 곱 구현.
fn mul(self, other_vector: Vec3) -> Vec3{ Matrix{ elements :[ [ self.elements[0][0] * other_vector.elements[0][0] + self.elements[0][1] * other_vector.elements[1][0] + self.elements[0][2] * other_vector.elements[2][0] ], [ self.elements[1][0] * other_vector.elements[0][0] + self.elements[1][1] * other_vector.elements[1][0] + self.elements[1][2] * other_vector.elements[2][0] ], [ self.elements[2][0] * other_vector.elements[0][0] + self.elements[2][1] * other_vector.elements[1][0] + self.elements[2][2] * other_vector.elements[2][0] ] ] } }
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(A - I α) 식 해석을 위해 행렬-행렬 뺄셈 구현.
fn sub(self, other_matrix: Self) -> Matrix<ROW_COUNT,COLUMN_COUNT>{ let mut result = Matrix{elements:[[0.0;COLUMN_COUNT];ROW_COUNT]}; for i in 0..ROW_COUNT{ for j in 0..COLUMN_COUNT{ result.elements[i][j] = self.elements[i][j] - other_matrix.elements[i][j]; } } result }
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(A - I α) 식 해석을 위해 행렬-스칼라 곱 구현.
fn mul(self, other_scala: f64) -> Matrix<ROW_COUNT,COLUMN_COUNT>{ let mut result = Matrix{elements: [[0.0;COLUMN_COUNT];ROW_COUNT]}; for row in 0..ROW_COUNT{ for col in 0..COLUMN_COUNT{ result.elements[row][col] = self.elements[row][col] * other_scala; } } result }
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Power method 구현을 위해 행렬/벡터-스칼라 나눗셈 구현.
fn div(self, other_scala:f64) -> Matrix<ROW_COUNT,COLUMN_COUNT>{ let mut result = Matrix{elements:[[0.0;COLUMN_COUNT];ROW_COUNT]}; for i in 0..ROW_COUNT{ for j in 0..COLUMN_COUNT{ result.elements[i][j] = self.elements[i][j] / other_scala; } } result }
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Power method 구현을 위해 벡터 절대값 최대값 구현.
pub fn get_abs_max(&self) -> f64{ let mut max:f64 = 0.0; for i in self.elements{ if max.abs() < i[0].abs() { max = i[0]; } } max }
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Inverse power method 구현을 위해 역행렬을 구하는 가우스-조르단 소거법을 구현.
pub fn get_inverse_matrix(&self) -> Self { let mut self_copy = self.clone(); let mut result = Self::get_identity_matrix(); for i in 0..N{ let pivot = self_copy.elements[i][i]; for j in 0..N{ self_copy.elements[i][j] /= pivot; result.elements[i][j] /= pivot; } for j in 0..i{ let ratio = self_copy.elements[j][i]; for k in 0..N{ result.elements[j][k] -= ratio * result.elements[i][k]; self_copy.elements[j][k] -= ratio * self_copy.elements[i][k]; } } for j in i + 1..N{ let ratio = self_copy.elements[j][i]; for k in 0..N{ result.elements[j][k] -= ratio * result.elements[i][k]; self_copy.elements[j][k] -= ratio * self_copy.elements[i][k]; } } } result }
- power method로 dominant eigen을 탐색.
pub fn get_dominant_eigen(&self, x: Matrix<N,1>, try_count: usize) -> (Matrix<N,1>, Matrix<N,1>, f64) { let mut try_count = try_count; let mut x= x.clone(); let mat_a = self.clone(); loop{ let a_mul_x = mat_a * x; if try_count == 0 { return (x, a_mul_x, a_mul_x.get_abs_max()); } x = a_mul_x / a_mul_x.get_abs_max(); try_count -= 1; } }
- inverse power method로 근삿값과 가장 가까운 eigen을 탐색.
pub fn get_alpha_nearest_eigen(&self, x: Matrix<N,1>, try_count: usize, alpha:f64)-> (Matrix<N,1>, Matrix<N,1>, f64, f64){ let mut try_count = try_count; let mut x= x.clone(); let solution_with_matrix: Matrix<N, N> = (*self - Self::get_identity_matrix() * alpha).get_inverse_matrix(); loop{ let y = solution_with_matrix * x; let mu = y.get_abs_max(); let v = alpha + (1.0 / mu); if try_count == 0 { return (x, y, mu, v); } x = y / mu; try_count -= 1; } }
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