1358 lines
39 KiB
Rust
1358 lines
39 KiB
Rust
#![allow(clippy::ptr_arg)]
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use std::fmt;
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use std::fmt::Debug;
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#[cfg(feature = "serde")]
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use std::marker::PhantomData;
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use std::ops::Range;
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#[cfg(feature = "serde")]
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use serde::de::{Deserializer, MapAccess, SeqAccess, Visitor};
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#[cfg(feature = "serde")]
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use serde::ser::{SerializeStruct, Serializer};
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#[cfg(feature = "serde")]
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use serde::{Deserialize, Serialize};
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use crate::linalg::cholesky::CholeskyDecomposableMatrix;
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use crate::linalg::evd::EVDDecomposableMatrix;
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use crate::linalg::high_order::HighOrderOperations;
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use crate::linalg::lu::LUDecomposableMatrix;
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use crate::linalg::qr::QRDecomposableMatrix;
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use crate::linalg::stats::{MatrixPreprocessing, MatrixStats};
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use crate::linalg::svd::SVDDecomposableMatrix;
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use crate::linalg::Matrix;
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pub use crate::linalg::{BaseMatrix, BaseVector};
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use crate::math::num::RealNumber;
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impl<T: RealNumber> BaseVector<T> for Vec<T> {
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fn get(&self, i: usize) -> T {
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self[i]
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}
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fn set(&mut self, i: usize, x: T) {
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self[i] = x
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}
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fn len(&self) -> usize {
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self.len()
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}
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fn to_vec(&self) -> Vec<T> {
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self.clone()
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}
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fn zeros(len: usize) -> Self {
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vec![T::zero(); len]
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}
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fn ones(len: usize) -> Self {
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vec![T::one(); len]
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}
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fn fill(len: usize, value: T) -> Self {
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vec![value; len]
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}
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fn dot(&self, other: &Self) -> T {
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if self.len() != other.len() {
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panic!("A and B should have the same size");
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}
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let mut result = T::zero();
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for i in 0..self.len() {
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result += self[i] * other[i];
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}
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result
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}
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fn norm2(&self) -> T {
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let mut norm = T::zero();
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for xi in self.iter() {
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norm += *xi * *xi;
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}
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norm.sqrt()
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}
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fn norm(&self, p: T) -> T {
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if p.is_infinite() && p.is_sign_positive() {
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self.iter()
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.map(|x| x.abs())
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.fold(T::neg_infinity(), |a, b| a.max(b))
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} else if p.is_infinite() && p.is_sign_negative() {
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self.iter()
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.map(|x| x.abs())
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.fold(T::infinity(), |a, b| a.min(b))
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} else {
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let mut norm = T::zero();
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for xi in self.iter() {
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norm += xi.abs().powf(p);
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}
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norm.powf(T::one() / p)
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}
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}
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fn div_element_mut(&mut self, pos: usize, x: T) {
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self[pos] /= x;
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}
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fn mul_element_mut(&mut self, pos: usize, x: T) {
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self[pos] *= x;
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}
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fn add_element_mut(&mut self, pos: usize, x: T) {
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self[pos] += x
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}
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fn sub_element_mut(&mut self, pos: usize, x: T) {
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self[pos] -= x;
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}
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fn add_mut(&mut self, other: &Self) -> &Self {
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if self.len() != other.len() {
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panic!("A and B should have the same shape");
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}
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for i in 0..self.len() {
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self.add_element_mut(i, other.get(i));
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}
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self
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}
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fn sub_mut(&mut self, other: &Self) -> &Self {
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if self.len() != other.len() {
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panic!("A and B should have the same shape");
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}
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for i in 0..self.len() {
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self.sub_element_mut(i, other.get(i));
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}
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self
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}
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fn mul_mut(&mut self, other: &Self) -> &Self {
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if self.len() != other.len() {
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panic!("A and B should have the same shape");
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}
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for i in 0..self.len() {
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self.mul_element_mut(i, other.get(i));
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}
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self
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}
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fn div_mut(&mut self, other: &Self) -> &Self {
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if self.len() != other.len() {
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panic!("A and B should have the same shape");
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}
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for i in 0..self.len() {
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self.div_element_mut(i, other.get(i));
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}
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self
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}
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fn approximate_eq(&self, other: &Self, error: T) -> bool {
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if self.len() != other.len() {
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false
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} else {
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for i in 0..other.len() {
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if (self[i] - other[i]).abs() > error {
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return false;
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}
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}
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true
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}
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}
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fn sum(&self) -> T {
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let mut sum = T::zero();
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for self_i in self.iter() {
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sum += *self_i;
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}
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sum
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}
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fn unique(&self) -> Vec<T> {
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let mut result = self.clone();
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result.sort_by(|a, b| a.partial_cmp(b).unwrap());
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result.dedup();
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result
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}
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fn copy_from(&mut self, other: &Self) {
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if self.len() != other.len() {
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panic!(
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"Can't copy vector of length {} into a vector of length {}.",
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self.len(),
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other.len()
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);
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}
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self[..].clone_from_slice(&other[..]);
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}
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}
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/// Column-major, dense matrix. See [Simple Dense Matrix](../index.html).
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#[derive(Debug, Clone)]
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pub struct DenseMatrix<T: RealNumber> {
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ncols: usize,
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nrows: usize,
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values: Vec<T>,
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}
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/// Column-major, dense matrix. See [Simple Dense Matrix](../index.html).
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#[derive(Debug)]
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pub struct DenseMatrixIterator<'a, T: RealNumber> {
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cur_c: usize,
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cur_r: usize,
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max_c: usize,
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max_r: usize,
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m: &'a DenseMatrix<T>,
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}
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impl<T: RealNumber> fmt::Display for DenseMatrix<T> {
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
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let mut rows: Vec<Vec<f64>> = Vec::new();
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for r in 0..self.nrows {
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rows.push(
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self.get_row_as_vec(r)
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.iter()
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.map(|x| (x.to_f64().unwrap() * 1e4).round() / 1e4)
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.collect(),
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);
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}
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write!(f, "{:?}", rows)
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}
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}
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impl<T: RealNumber> DenseMatrix<T> {
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/// Create new instance of `DenseMatrix` without copying data.
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/// `values` should be in column-major order.
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pub fn new(nrows: usize, ncols: usize, values: Vec<T>) -> Self {
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DenseMatrix {
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ncols,
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nrows,
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values,
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}
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}
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/// New instance of `DenseMatrix` from 2d array.
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pub fn from_2d_array(values: &[&[T]]) -> Self {
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DenseMatrix::from_2d_vec(&values.iter().map(|row| Vec::from(*row)).collect())
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}
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/// New instance of `DenseMatrix` from 2d vector.
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pub fn from_2d_vec(values: &Vec<Vec<T>>) -> Self {
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let nrows = values.len();
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let ncols = values
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.first()
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.unwrap_or_else(|| panic!("Cannot create 2d matrix from an empty vector"))
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.len();
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let mut m = DenseMatrix {
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ncols,
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nrows,
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values: vec![T::zero(); ncols * nrows],
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};
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for (row_index, row) in values.iter().enumerate().take(nrows) {
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for (col_index, value) in row.iter().enumerate().take(ncols) {
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m.set(row_index, col_index, *value);
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}
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}
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m
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}
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/// Creates new matrix from an array.
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/// * `nrows` - number of rows in new matrix.
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/// * `ncols` - number of columns in new matrix.
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/// * `values` - values to initialize the matrix.
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pub fn from_array(nrows: usize, ncols: usize, values: &[T]) -> Self {
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DenseMatrix::from_vec(nrows, ncols, &Vec::from(values))
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}
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/// Creates new matrix from a vector.
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/// * `nrows` - number of rows in new matrix.
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/// * `ncols` - number of columns in new matrix.
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/// * `values` - values to initialize the matrix.
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pub fn from_vec(nrows: usize, ncols: usize, values: &[T]) -> DenseMatrix<T> {
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let mut m = DenseMatrix {
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ncols,
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nrows,
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values: vec![T::zero(); ncols * nrows],
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};
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for row in 0..nrows {
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for col in 0..ncols {
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m.set(row, col, values[col + row * ncols]);
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}
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}
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m
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}
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/// Creates new row vector (_1xN_ matrix) from an array.
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/// * `values` - values to initialize the matrix.
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pub fn row_vector_from_array(values: &[T]) -> Self {
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DenseMatrix::row_vector_from_vec(Vec::from(values))
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}
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/// Creates new row vector (_1xN_ matrix) from a vector.
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/// * `values` - values to initialize the matrix.
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pub fn row_vector_from_vec(values: Vec<T>) -> Self {
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DenseMatrix {
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ncols: values.len(),
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nrows: 1,
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values,
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}
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}
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/// Creates new column vector (_1xN_ matrix) from an array.
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/// * `values` - values to initialize the matrix.
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pub fn column_vector_from_array(values: &[T]) -> Self {
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DenseMatrix::column_vector_from_vec(Vec::from(values))
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}
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/// Creates new column vector (_1xN_ matrix) from a vector.
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/// * `values` - values to initialize the matrix.
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pub fn column_vector_from_vec(values: Vec<T>) -> Self {
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DenseMatrix {
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ncols: 1,
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nrows: values.len(),
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values,
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}
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}
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/// Creates new column vector (_1xN_ matrix) from a vector.
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/// * `values` - values to initialize the matrix.
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pub fn iter(&self) -> DenseMatrixIterator<'_, T> {
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DenseMatrixIterator {
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cur_c: 0,
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cur_r: 0,
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max_c: self.ncols,
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max_r: self.nrows,
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m: &self,
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}
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}
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}
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impl<'a, T: RealNumber> Iterator for DenseMatrixIterator<'a, T> {
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type Item = T;
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fn next(&mut self) -> Option<T> {
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if self.cur_r * self.max_c + self.cur_c >= self.max_c * self.max_r {
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None
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} else {
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let v = self.m.get(self.cur_r, self.cur_c);
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self.cur_c += 1;
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if self.cur_c >= self.max_c {
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self.cur_c = 0;
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self.cur_r += 1;
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}
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Some(v)
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}
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}
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}
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#[cfg(feature = "serde")]
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impl<'de, T: RealNumber + fmt::Debug + Deserialize<'de>> Deserialize<'de> for DenseMatrix<T> {
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fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
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where
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D: Deserializer<'de>,
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{
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#[derive(Deserialize)]
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#[serde(field_identifier, rename_all = "lowercase")]
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enum Field {
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NRows,
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NCols,
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Values,
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}
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struct DenseMatrixVisitor<T: RealNumber + fmt::Debug> {
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t: PhantomData<T>,
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}
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impl<'a, T: RealNumber + fmt::Debug + Deserialize<'a>> Visitor<'a> for DenseMatrixVisitor<T> {
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type Value = DenseMatrix<T>;
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fn expecting(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
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formatter.write_str("struct DenseMatrix")
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}
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fn visit_seq<V>(self, mut seq: V) -> Result<DenseMatrix<T>, V::Error>
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where
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V: SeqAccess<'a>,
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{
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let nrows = seq
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.next_element()?
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.ok_or_else(|| serde::de::Error::invalid_length(0, &self))?;
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let ncols = seq
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.next_element()?
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.ok_or_else(|| serde::de::Error::invalid_length(1, &self))?;
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let values = seq
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.next_element()?
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.ok_or_else(|| serde::de::Error::invalid_length(2, &self))?;
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Ok(DenseMatrix::new(nrows, ncols, values))
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}
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fn visit_map<V>(self, mut map: V) -> Result<DenseMatrix<T>, V::Error>
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where
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V: MapAccess<'a>,
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{
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let mut nrows = None;
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let mut ncols = None;
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let mut values = None;
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while let Some(key) = map.next_key()? {
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match key {
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Field::NRows => {
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if nrows.is_some() {
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return Err(serde::de::Error::duplicate_field("nrows"));
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}
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nrows = Some(map.next_value()?);
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}
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Field::NCols => {
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if ncols.is_some() {
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return Err(serde::de::Error::duplicate_field("ncols"));
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}
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ncols = Some(map.next_value()?);
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}
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Field::Values => {
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if values.is_some() {
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return Err(serde::de::Error::duplicate_field("values"));
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}
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values = Some(map.next_value()?);
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}
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}
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}
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let nrows = nrows.ok_or_else(|| serde::de::Error::missing_field("nrows"))?;
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let ncols = ncols.ok_or_else(|| serde::de::Error::missing_field("ncols"))?;
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let values = values.ok_or_else(|| serde::de::Error::missing_field("values"))?;
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Ok(DenseMatrix::new(nrows, ncols, values))
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}
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}
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const FIELDS: &[&str] = &["nrows", "ncols", "values"];
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deserializer.deserialize_struct(
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"DenseMatrix",
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FIELDS,
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DenseMatrixVisitor { t: PhantomData },
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)
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}
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}
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#[cfg(feature = "serde")]
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impl<T: RealNumber + fmt::Debug + Serialize> Serialize for DenseMatrix<T> {
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fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where
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S: Serializer,
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{
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let (nrows, ncols) = self.shape();
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let mut state = serializer.serialize_struct("DenseMatrix", 3)?;
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state.serialize_field("nrows", &nrows)?;
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state.serialize_field("ncols", &ncols)?;
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state.serialize_field("values", &self.values)?;
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state.end()
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}
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}
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impl<T: RealNumber> SVDDecomposableMatrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> EVDDecomposableMatrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> QRDecomposableMatrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> LUDecomposableMatrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> CholeskyDecomposableMatrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> HighOrderOperations<T> for DenseMatrix<T> {
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fn ab(&self, a_transpose: bool, b: &Self, b_transpose: bool) -> Self {
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if !a_transpose && !b_transpose {
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self.matmul(b)
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} else {
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let (d1, d2, d3, d4) = match (a_transpose, b_transpose) {
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(true, false) => (self.nrows, self.ncols, b.ncols, b.nrows),
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(false, true) => (self.ncols, self.nrows, b.nrows, b.ncols),
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_ => (self.nrows, self.ncols, b.nrows, b.ncols),
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};
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if d1 != d4 {
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panic!("Can not multiply {}x{} by {}x{} matrices", d2, d1, d4, d3);
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}
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let mut result = Self::zeros(d2, d3);
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for r in 0..d2 {
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for c in 0..d3 {
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let mut s = T::zero();
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for i in 0..d1 {
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match (a_transpose, b_transpose) {
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(true, false) => s += self.get(i, r) * b.get(i, c),
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(false, true) => s += self.get(r, i) * b.get(c, i),
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_ => s += self.get(i, r) * b.get(c, i),
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}
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}
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result.set(r, c, s);
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}
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}
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result
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}
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}
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}
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impl<T: RealNumber> MatrixStats<T> for DenseMatrix<T> {}
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impl<T: RealNumber> MatrixPreprocessing<T> for DenseMatrix<T> {}
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impl<T: RealNumber> Matrix<T> for DenseMatrix<T> {}
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impl<T: RealNumber> PartialEq for DenseMatrix<T> {
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fn eq(&self, other: &Self) -> bool {
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if self.ncols != other.ncols || self.nrows != other.nrows {
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return false;
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}
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|
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let len = self.values.len();
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let other_len = other.values.len();
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|
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if len != other_len {
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return false;
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}
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|
|
for i in 0..len {
|
|
if (self.values[i] - other.values[i]).abs() > T::epsilon() {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
true
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber> Into<Vec<T>> for DenseMatrix<T> {
|
|
fn into(self) -> Vec<T> {
|
|
self.values
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber> BaseMatrix<T> for DenseMatrix<T> {
|
|
type RowVector = Vec<T>;
|
|
|
|
fn from_row_vector(vec: Self::RowVector) -> Self {
|
|
DenseMatrix::new(1, vec.len(), vec)
|
|
}
|
|
|
|
fn to_row_vector(self) -> Self::RowVector {
|
|
let mut v = vec![T::zero(); self.nrows * self.ncols];
|
|
|
|
for r in 0..self.nrows {
|
|
for c in 0..self.ncols {
|
|
v[r * self.ncols + c] = self.get(r, c);
|
|
}
|
|
}
|
|
|
|
v
|
|
}
|
|
|
|
fn get(&self, row: usize, col: usize) -> T {
|
|
if row >= self.nrows || col >= self.ncols {
|
|
panic!(
|
|
"Invalid index ({},{}) for {}x{} matrix",
|
|
row, col, self.nrows, self.ncols
|
|
);
|
|
}
|
|
self.values[col * self.nrows + row]
|
|
}
|
|
|
|
fn get_row(&self, row: usize) -> Self::RowVector {
|
|
let mut v = vec![T::zero(); self.ncols];
|
|
|
|
for (c, v_c) in v.iter_mut().enumerate().take(self.ncols) {
|
|
*v_c = self.get(row, c);
|
|
}
|
|
|
|
v
|
|
}
|
|
|
|
fn get_row_as_vec(&self, row: usize) -> Vec<T> {
|
|
let mut result = vec![T::zero(); self.ncols];
|
|
for (c, result_c) in result.iter_mut().enumerate().take(self.ncols) {
|
|
*result_c = self.get(row, c);
|
|
}
|
|
result
|
|
}
|
|
|
|
fn copy_row_as_vec(&self, row: usize, result: &mut Vec<T>) {
|
|
for (c, result_c) in result.iter_mut().enumerate().take(self.ncols) {
|
|
*result_c = self.get(row, c);
|
|
}
|
|
}
|
|
|
|
fn get_col_as_vec(&self, col: usize) -> Vec<T> {
|
|
let mut result = vec![T::zero(); self.nrows];
|
|
for (r, result_r) in result.iter_mut().enumerate().take(self.nrows) {
|
|
*result_r = self.get(r, col);
|
|
}
|
|
result
|
|
}
|
|
|
|
fn copy_col_as_vec(&self, col: usize, result: &mut Vec<T>) {
|
|
for (r, result_r) in result.iter_mut().enumerate().take(self.nrows) {
|
|
*result_r = self.get(r, col);
|
|
}
|
|
}
|
|
|
|
fn set(&mut self, row: usize, col: usize, x: T) {
|
|
self.values[col * self.nrows + row] = x;
|
|
}
|
|
|
|
fn zeros(nrows: usize, ncols: usize) -> Self {
|
|
DenseMatrix::fill(nrows, ncols, T::zero())
|
|
}
|
|
|
|
fn ones(nrows: usize, ncols: usize) -> Self {
|
|
DenseMatrix::fill(nrows, ncols, T::one())
|
|
}
|
|
|
|
fn eye(size: usize) -> Self {
|
|
let mut matrix = Self::zeros(size, size);
|
|
|
|
for i in 0..size {
|
|
matrix.set(i, i, T::one());
|
|
}
|
|
|
|
matrix
|
|
}
|
|
|
|
fn shape(&self) -> (usize, usize) {
|
|
(self.nrows, self.ncols)
|
|
}
|
|
|
|
fn v_stack(&self, other: &Self) -> Self {
|
|
if self.ncols != other.ncols {
|
|
panic!("Number of columns in both matrices should be equal");
|
|
}
|
|
let mut result = Self::zeros(self.nrows + other.nrows, self.ncols);
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows + other.nrows {
|
|
if r < self.nrows {
|
|
result.set(r, c, self.get(r, c));
|
|
} else {
|
|
result.set(r, c, other.get(r - self.nrows, c));
|
|
}
|
|
}
|
|
}
|
|
result
|
|
}
|
|
|
|
fn h_stack(&self, other: &Self) -> Self {
|
|
if self.nrows != other.nrows {
|
|
panic!("Number of rows in both matrices should be equal");
|
|
}
|
|
let mut result = Self::zeros(self.nrows, self.ncols + other.ncols);
|
|
for r in 0..self.nrows {
|
|
for c in 0..self.ncols + other.ncols {
|
|
if c < self.ncols {
|
|
result.set(r, c, self.get(r, c));
|
|
} else {
|
|
result.set(r, c, other.get(r, c - self.ncols));
|
|
}
|
|
}
|
|
}
|
|
result
|
|
}
|
|
|
|
fn matmul(&self, other: &Self) -> Self {
|
|
if self.ncols != other.nrows {
|
|
panic!("Number of rows of A should equal number of columns of B");
|
|
}
|
|
let inner_d = self.ncols;
|
|
let mut result = Self::zeros(self.nrows, other.ncols);
|
|
|
|
for r in 0..self.nrows {
|
|
for c in 0..other.ncols {
|
|
let mut s = T::zero();
|
|
for i in 0..inner_d {
|
|
s += self.get(r, i) * other.get(i, c);
|
|
}
|
|
result.set(r, c, s);
|
|
}
|
|
}
|
|
|
|
result
|
|
}
|
|
|
|
fn dot(&self, other: &Self) -> T {
|
|
if (self.nrows != 1 && other.nrows != 1) && (self.ncols != 1 && other.ncols != 1) {
|
|
panic!("A and B should both be either a row or a column vector.");
|
|
}
|
|
if self.nrows * self.ncols != other.nrows * other.ncols {
|
|
panic!("A and B should have the same size");
|
|
}
|
|
|
|
let mut result = T::zero();
|
|
for i in 0..(self.nrows * self.ncols) {
|
|
result += self.values[i] * other.values[i];
|
|
}
|
|
|
|
result
|
|
}
|
|
|
|
fn slice(&self, rows: Range<usize>, cols: Range<usize>) -> Self {
|
|
let ncols = cols.len();
|
|
let nrows = rows.len();
|
|
|
|
let mut m = DenseMatrix::new(nrows, ncols, vec![T::zero(); nrows * ncols]);
|
|
|
|
for r in rows.start..rows.end {
|
|
for c in cols.start..cols.end {
|
|
m.set(r - rows.start, c - cols.start, self.get(r, c));
|
|
}
|
|
}
|
|
|
|
m
|
|
}
|
|
|
|
fn approximate_eq(&self, other: &Self, error: T) -> bool {
|
|
if self.ncols != other.ncols || self.nrows != other.nrows {
|
|
return false;
|
|
}
|
|
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
if (self.get(r, c) - other.get(r, c)).abs() > error {
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
|
|
true
|
|
}
|
|
|
|
fn fill(nrows: usize, ncols: usize, value: T) -> Self {
|
|
DenseMatrix::new(nrows, ncols, vec![value; ncols * nrows])
|
|
}
|
|
|
|
fn add_mut(&mut self, other: &Self) -> &Self {
|
|
if self.ncols != other.ncols || self.nrows != other.nrows {
|
|
panic!("A and B should have the same shape");
|
|
}
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
self.add_element_mut(r, c, other.get(r, c));
|
|
}
|
|
}
|
|
|
|
self
|
|
}
|
|
|
|
fn sub_mut(&mut self, other: &Self) -> &Self {
|
|
if self.ncols != other.ncols || self.nrows != other.nrows {
|
|
panic!("A and B should have the same shape");
|
|
}
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
self.sub_element_mut(r, c, other.get(r, c));
|
|
}
|
|
}
|
|
|
|
self
|
|
}
|
|
|
|
fn mul_mut(&mut self, other: &Self) -> &Self {
|
|
if self.ncols != other.ncols || self.nrows != other.nrows {
|
|
panic!("A and B should have the same shape");
|
|
}
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
self.mul_element_mut(r, c, other.get(r, c));
|
|
}
|
|
}
|
|
|
|
self
|
|
}
|
|
|
|
fn div_mut(&mut self, other: &Self) -> &Self {
|
|
if self.ncols != other.ncols || self.nrows != other.nrows {
|
|
panic!("A and B should have the same shape");
|
|
}
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
self.div_element_mut(r, c, other.get(r, c));
|
|
}
|
|
}
|
|
|
|
self
|
|
}
|
|
|
|
fn div_element_mut(&mut self, row: usize, col: usize, x: T) {
|
|
self.values[col * self.nrows + row] /= x;
|
|
}
|
|
|
|
fn mul_element_mut(&mut self, row: usize, col: usize, x: T) {
|
|
self.values[col * self.nrows + row] *= x;
|
|
}
|
|
|
|
fn add_element_mut(&mut self, row: usize, col: usize, x: T) {
|
|
self.values[col * self.nrows + row] += x
|
|
}
|
|
|
|
fn sub_element_mut(&mut self, row: usize, col: usize, x: T) {
|
|
self.values[col * self.nrows + row] -= x;
|
|
}
|
|
|
|
fn transpose(&self) -> Self {
|
|
let mut m = DenseMatrix {
|
|
ncols: self.nrows,
|
|
nrows: self.ncols,
|
|
values: vec![T::zero(); self.ncols * self.nrows],
|
|
};
|
|
for c in 0..self.ncols {
|
|
for r in 0..self.nrows {
|
|
m.set(c, r, self.get(r, c));
|
|
}
|
|
}
|
|
m
|
|
}
|
|
|
|
fn rand(nrows: usize, ncols: usize) -> Self {
|
|
let values: Vec<T> = (0..nrows * ncols).map(|_| T::rand()).collect();
|
|
DenseMatrix {
|
|
ncols,
|
|
nrows,
|
|
values,
|
|
}
|
|
}
|
|
|
|
fn norm2(&self) -> T {
|
|
let mut norm = T::zero();
|
|
|
|
for xi in self.values.iter() {
|
|
norm += *xi * *xi;
|
|
}
|
|
|
|
norm.sqrt()
|
|
}
|
|
|
|
fn norm(&self, p: T) -> T {
|
|
if p.is_infinite() && p.is_sign_positive() {
|
|
self.values
|
|
.iter()
|
|
.map(|x| x.abs())
|
|
.fold(T::neg_infinity(), |a, b| a.max(b))
|
|
} else if p.is_infinite() && p.is_sign_negative() {
|
|
self.values
|
|
.iter()
|
|
.map(|x| x.abs())
|
|
.fold(T::infinity(), |a, b| a.min(b))
|
|
} else {
|
|
let mut norm = T::zero();
|
|
|
|
for xi in self.values.iter() {
|
|
norm += xi.abs().powf(p);
|
|
}
|
|
|
|
norm.powf(T::one() / p)
|
|
}
|
|
}
|
|
|
|
fn column_mean(&self) -> Vec<T> {
|
|
let mut mean = vec![T::zero(); self.ncols];
|
|
|
|
for r in 0..self.nrows {
|
|
for (c, mean_c) in mean.iter_mut().enumerate().take(self.ncols) {
|
|
*mean_c += self.get(r, c);
|
|
}
|
|
}
|
|
|
|
for mean_i in mean.iter_mut() {
|
|
*mean_i /= T::from(self.nrows).unwrap();
|
|
}
|
|
|
|
mean
|
|
}
|
|
|
|
fn add_scalar_mut(&mut self, scalar: T) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] += scalar;
|
|
}
|
|
self
|
|
}
|
|
|
|
fn sub_scalar_mut(&mut self, scalar: T) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] -= scalar;
|
|
}
|
|
self
|
|
}
|
|
|
|
fn mul_scalar_mut(&mut self, scalar: T) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] *= scalar;
|
|
}
|
|
self
|
|
}
|
|
|
|
fn div_scalar_mut(&mut self, scalar: T) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] /= scalar;
|
|
}
|
|
self
|
|
}
|
|
|
|
fn negative_mut(&mut self) {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] = -self.values[i];
|
|
}
|
|
}
|
|
|
|
fn reshape(&self, nrows: usize, ncols: usize) -> Self {
|
|
if self.nrows * self.ncols != nrows * ncols {
|
|
panic!(
|
|
"Can't reshape {}x{} matrix into {}x{}.",
|
|
self.nrows, self.ncols, nrows, ncols
|
|
);
|
|
}
|
|
let mut dst = DenseMatrix::zeros(nrows, ncols);
|
|
let mut dst_r = 0;
|
|
let mut dst_c = 0;
|
|
for r in 0..self.nrows {
|
|
for c in 0..self.ncols {
|
|
dst.set(dst_r, dst_c, self.get(r, c));
|
|
if dst_c + 1 >= ncols {
|
|
dst_c = 0;
|
|
dst_r += 1;
|
|
} else {
|
|
dst_c += 1;
|
|
}
|
|
}
|
|
}
|
|
dst
|
|
}
|
|
|
|
fn copy_from(&mut self, other: &Self) {
|
|
if self.nrows != other.nrows || self.ncols != other.ncols {
|
|
panic!(
|
|
"Can't copy {}x{} matrix into {}x{}.",
|
|
self.nrows, self.ncols, other.nrows, other.ncols
|
|
);
|
|
}
|
|
|
|
self.values[..].clone_from_slice(&other.values[..]);
|
|
}
|
|
|
|
fn abs_mut(&mut self) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] = self.values[i].abs();
|
|
}
|
|
self
|
|
}
|
|
|
|
fn max_diff(&self, other: &Self) -> T {
|
|
let mut max_diff = T::zero();
|
|
for i in 0..self.values.len() {
|
|
max_diff = max_diff.max((self.values[i] - other.values[i]).abs());
|
|
}
|
|
max_diff
|
|
}
|
|
|
|
fn sum(&self) -> T {
|
|
let mut sum = T::zero();
|
|
for i in 0..self.values.len() {
|
|
sum += self.values[i];
|
|
}
|
|
sum
|
|
}
|
|
|
|
fn max(&self) -> T {
|
|
let mut max = T::neg_infinity();
|
|
for i in 0..self.values.len() {
|
|
max = T::max(max, self.values[i]);
|
|
}
|
|
max
|
|
}
|
|
|
|
fn min(&self) -> T {
|
|
let mut min = T::infinity();
|
|
for i in 0..self.values.len() {
|
|
min = T::min(min, self.values[i]);
|
|
}
|
|
min
|
|
}
|
|
|
|
fn softmax_mut(&mut self) {
|
|
let max = self
|
|
.values
|
|
.iter()
|
|
.map(|x| x.abs())
|
|
.fold(T::neg_infinity(), |a, b| a.max(b));
|
|
let mut z = T::zero();
|
|
for r in 0..self.nrows {
|
|
for c in 0..self.ncols {
|
|
let p = (self.get(r, c) - max).exp();
|
|
self.set(r, c, p);
|
|
z += p;
|
|
}
|
|
}
|
|
for r in 0..self.nrows {
|
|
for c in 0..self.ncols {
|
|
self.set(r, c, self.get(r, c) / z);
|
|
}
|
|
}
|
|
}
|
|
|
|
fn pow_mut(&mut self, p: T) -> &Self {
|
|
for i in 0..self.values.len() {
|
|
self.values[i] = self.values[i].powf(p);
|
|
}
|
|
self
|
|
}
|
|
|
|
fn argmax(&self) -> Vec<usize> {
|
|
let mut res = vec![0usize; self.nrows];
|
|
|
|
for (r, res_r) in res.iter_mut().enumerate().take(self.nrows) {
|
|
let mut max = T::neg_infinity();
|
|
let mut max_pos = 0usize;
|
|
for c in 0..self.ncols {
|
|
let v = self.get(r, c);
|
|
if max < v {
|
|
max = v;
|
|
max_pos = c;
|
|
}
|
|
}
|
|
*res_r = max_pos;
|
|
}
|
|
|
|
res
|
|
}
|
|
|
|
fn unique(&self) -> Vec<T> {
|
|
let mut result = self.values.clone();
|
|
result.sort_by(|a, b| a.partial_cmp(b).unwrap());
|
|
result.dedup();
|
|
result
|
|
}
|
|
|
|
fn cov(&self) -> Self {
|
|
let (m, n) = self.shape();
|
|
|
|
let mu = self.column_mean();
|
|
|
|
let mut cov = Self::zeros(n, n);
|
|
|
|
for k in 0..m {
|
|
for i in 0..n {
|
|
for j in 0..=i {
|
|
cov.add_element_mut(i, j, (self.get(k, i) - mu[i]) * (self.get(k, j) - mu[j]));
|
|
}
|
|
}
|
|
}
|
|
|
|
let m_t = T::from(m - 1).unwrap();
|
|
|
|
for i in 0..n {
|
|
for j in 0..=i {
|
|
cov.div_element_mut(i, j, m_t);
|
|
cov.set(j, i, cov.get(i, j));
|
|
}
|
|
}
|
|
|
|
cov
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use super::*;
|
|
|
|
#[test]
|
|
fn vec_dot() {
|
|
let v1 = vec![1., 2., 3.];
|
|
let v2 = vec![4., 5., 6.];
|
|
assert_eq!(32.0, BaseVector::dot(&v1, &v2));
|
|
}
|
|
|
|
#[test]
|
|
fn vec_copy_from() {
|
|
let mut v1 = vec![1., 2., 3.];
|
|
let v2 = vec![4., 5., 6.];
|
|
v1.copy_from(&v2);
|
|
assert_eq!(v1, v2);
|
|
}
|
|
|
|
#[test]
|
|
fn vec_approximate_eq() {
|
|
let a = vec![1., 2., 3.];
|
|
let b = vec![1. + 1e-5, 2. + 2e-5, 3. + 3e-5];
|
|
assert!(a.approximate_eq(&b, 1e-4));
|
|
assert!(!a.approximate_eq(&b, 1e-5));
|
|
}
|
|
|
|
#[test]
|
|
fn from_array() {
|
|
let vec = [1., 2., 3., 4., 5., 6.];
|
|
assert_eq!(
|
|
DenseMatrix::from_array(3, 2, &vec),
|
|
DenseMatrix::new(3, 2, vec![1., 3., 5., 2., 4., 6.])
|
|
);
|
|
assert_eq!(
|
|
DenseMatrix::from_array(2, 3, &vec),
|
|
DenseMatrix::new(2, 3, vec![1., 4., 2., 5., 3., 6.])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn row_column_vec_from_array() {
|
|
let vec = vec![1., 2., 3., 4., 5., 6.];
|
|
assert_eq!(
|
|
DenseMatrix::row_vector_from_array(&vec),
|
|
DenseMatrix::new(1, 6, vec![1., 2., 3., 4., 5., 6.])
|
|
);
|
|
assert_eq!(
|
|
DenseMatrix::column_vector_from_array(&vec),
|
|
DenseMatrix::new(6, 1, vec![1., 2., 3., 4., 5., 6.])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn from_to_row_vec() {
|
|
let vec = vec![1., 2., 3.];
|
|
assert_eq!(
|
|
DenseMatrix::from_row_vector(vec.clone()),
|
|
DenseMatrix::new(1, 3, vec![1., 2., 3.])
|
|
);
|
|
assert_eq!(
|
|
DenseMatrix::from_row_vector(vec).to_row_vector(),
|
|
vec![1., 2., 3.]
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn col_matrix_to_row_vector() {
|
|
let m: DenseMatrix<f64> = BaseMatrix::zeros(10, 1);
|
|
assert_eq!(m.to_row_vector().len(), 10)
|
|
}
|
|
|
|
#[test]
|
|
fn iter() {
|
|
let vec = vec![1., 2., 3., 4., 5., 6.];
|
|
let m = DenseMatrix::from_array(3, 2, &vec);
|
|
assert_eq!(vec, m.iter().collect::<Vec<f32>>());
|
|
}
|
|
|
|
#[test]
|
|
fn v_stack() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.], &[7., 8., 9.]]);
|
|
let b = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.]]);
|
|
let expected = DenseMatrix::from_2d_array(&[
|
|
&[1., 2., 3.],
|
|
&[4., 5., 6.],
|
|
&[7., 8., 9.],
|
|
&[1., 2., 3.],
|
|
&[4., 5., 6.],
|
|
]);
|
|
let result = a.v_stack(&b);
|
|
assert_eq!(result, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn h_stack() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.], &[7., 8., 9.]]);
|
|
let b = DenseMatrix::from_2d_array(&[&[1., 2.], &[3., 4.], &[5., 6.]]);
|
|
let expected = DenseMatrix::from_2d_array(&[
|
|
&[1., 2., 3., 1., 2.],
|
|
&[4., 5., 6., 3., 4.],
|
|
&[7., 8., 9., 5., 6.],
|
|
]);
|
|
let result = a.h_stack(&b);
|
|
assert_eq!(result, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn get_row() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.], &[7., 8., 9.]]);
|
|
assert_eq!(vec![4., 5., 6.], a.get_row(1));
|
|
}
|
|
|
|
#[test]
|
|
fn matmul() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.]]);
|
|
let b = DenseMatrix::from_2d_array(&[&[1., 2.], &[3., 4.], &[5., 6.]]);
|
|
let expected = DenseMatrix::from_2d_array(&[&[22., 28.], &[49., 64.]]);
|
|
let result = a.matmul(&b);
|
|
assert_eq!(result, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn ab() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.]]);
|
|
let b = DenseMatrix::from_2d_array(&[&[5., 6.], &[7., 8.], &[9., 10.]]);
|
|
let c = DenseMatrix::from_2d_array(&[&[1., 2.], &[3., 4.], &[5., 6.]]);
|
|
assert_eq!(
|
|
a.ab(false, &b, false),
|
|
DenseMatrix::from_2d_array(&[&[46., 52.], &[109., 124.]])
|
|
);
|
|
assert_eq!(
|
|
c.ab(true, &b, false),
|
|
DenseMatrix::from_2d_array(&[&[71., 80.], &[92., 104.]])
|
|
);
|
|
assert_eq!(
|
|
b.ab(false, &c, true),
|
|
DenseMatrix::from_2d_array(&[&[17., 39., 61.], &[23., 53., 83.,], &[29., 67., 105.]])
|
|
);
|
|
assert_eq!(
|
|
a.ab(true, &b, true),
|
|
DenseMatrix::from_2d_array(&[&[29., 39., 49.], &[40., 54., 68.,], &[51., 69., 87.]])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn dot() {
|
|
let a = DenseMatrix::from_array(1, 3, &[1., 2., 3.]);
|
|
let b = DenseMatrix::from_array(1, 3, &[4., 5., 6.]);
|
|
assert_eq!(a.dot(&b), 32.);
|
|
}
|
|
|
|
#[test]
|
|
fn copy_from() {
|
|
let mut a = DenseMatrix::from_2d_array(&[&[1., 2.], &[3., 4.], &[5., 6.]]);
|
|
let b = DenseMatrix::from_2d_array(&[&[7., 8.], &[9., 10.], &[11., 12.]]);
|
|
a.copy_from(&b);
|
|
assert_eq!(a, b);
|
|
}
|
|
|
|
#[test]
|
|
fn slice() {
|
|
let m = DenseMatrix::from_2d_array(&[
|
|
&[1., 2., 3., 1., 2.],
|
|
&[4., 5., 6., 3., 4.],
|
|
&[7., 8., 9., 5., 6.],
|
|
]);
|
|
let expected = DenseMatrix::from_2d_array(&[&[2., 3.], &[5., 6.]]);
|
|
let result = m.slice(0..2, 1..3);
|
|
assert_eq!(result, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn approximate_eq() {
|
|
let m = DenseMatrix::from_2d_array(&[&[2., 3.], &[5., 6.]]);
|
|
let m_eq = DenseMatrix::from_2d_array(&[&[2.5, 3.0], &[5., 5.5]]);
|
|
let m_neq = DenseMatrix::from_2d_array(&[&[3.0, 3.0], &[5., 6.5]]);
|
|
assert!(m.approximate_eq(&m_eq, 0.5));
|
|
assert!(!m.approximate_eq(&m_neq, 0.5));
|
|
}
|
|
|
|
#[test]
|
|
fn rand() {
|
|
let m: DenseMatrix<f64> = DenseMatrix::rand(3, 3);
|
|
for c in 0..3 {
|
|
for r in 0..3 {
|
|
assert!(m.get(r, c) != 0f64);
|
|
}
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn transpose() {
|
|
let m = DenseMatrix::from_2d_array(&[&[1.0, 3.0], &[2.0, 4.0]]);
|
|
let expected = DenseMatrix::from_2d_array(&[&[1.0, 2.0], &[3.0, 4.0]]);
|
|
let m_transposed = m.transpose();
|
|
for c in 0..2 {
|
|
for r in 0..2 {
|
|
assert!(m_transposed.get(r, c) == expected.get(r, c));
|
|
}
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn reshape() {
|
|
let m_orig = DenseMatrix::row_vector_from_array(&[1., 2., 3., 4., 5., 6.]);
|
|
let m_2_by_3 = m_orig.reshape(2, 3);
|
|
let m_result = m_2_by_3.reshape(1, 6);
|
|
assert_eq!(m_2_by_3.shape(), (2, 3));
|
|
assert_eq!(m_2_by_3.get(1, 1), 5.);
|
|
assert_eq!(m_result.get(0, 1), 2.);
|
|
assert_eq!(m_result.get(0, 3), 4.);
|
|
}
|
|
|
|
#[test]
|
|
fn norm() {
|
|
let v = DenseMatrix::row_vector_from_array(&[3., -2., 6.]);
|
|
assert_eq!(v.norm(1.), 11.);
|
|
assert_eq!(v.norm(2.), 7.);
|
|
assert_eq!(v.norm(std::f64::INFINITY), 6.);
|
|
assert_eq!(v.norm(std::f64::NEG_INFINITY), 2.);
|
|
}
|
|
|
|
#[test]
|
|
fn softmax_mut() {
|
|
let mut prob: DenseMatrix<f64> = DenseMatrix::row_vector_from_array(&[1., 2., 3.]);
|
|
prob.softmax_mut();
|
|
assert!((prob.get(0, 0) - 0.09).abs() < 0.01);
|
|
assert!((prob.get(0, 1) - 0.24).abs() < 0.01);
|
|
assert!((prob.get(0, 2) - 0.66).abs() < 0.01);
|
|
}
|
|
|
|
#[test]
|
|
fn col_mean() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.], &[7., 8., 9.]]);
|
|
let res = a.column_mean();
|
|
assert_eq!(res, vec![4., 5., 6.]);
|
|
}
|
|
|
|
#[test]
|
|
fn min_max_sum() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.]]);
|
|
assert_eq!(21., a.sum());
|
|
assert_eq!(1., a.min());
|
|
assert_eq!(6., a.max());
|
|
}
|
|
|
|
#[test]
|
|
fn eye() {
|
|
let a = DenseMatrix::from_2d_array(&[&[1., 0., 0.], &[0., 1., 0.], &[0., 0., 1.]]);
|
|
let res = DenseMatrix::eye(3);
|
|
assert_eq!(res, a);
|
|
}
|
|
|
|
#[test]
|
|
#[cfg(feature = "serde")]
|
|
fn to_from_json() {
|
|
let a = DenseMatrix::from_2d_array(&[&[0.9, 0.4, 0.7], &[0.4, 0.5, 0.3], &[0.7, 0.3, 0.8]]);
|
|
let deserialized_a: DenseMatrix<f64> =
|
|
serde_json::from_str(&serde_json::to_string(&a).unwrap()).unwrap();
|
|
assert_eq!(a, deserialized_a);
|
|
}
|
|
|
|
#[test]
|
|
#[cfg(feature = "serde")]
|
|
fn to_from_bincode() {
|
|
let a = DenseMatrix::from_2d_array(&[&[0.9, 0.4, 0.7], &[0.4, 0.5, 0.3], &[0.7, 0.3, 0.8]]);
|
|
let deserialized_a: DenseMatrix<f64> =
|
|
bincode::deserialize(&bincode::serialize(&a).unwrap()).unwrap();
|
|
assert_eq!(a, deserialized_a);
|
|
}
|
|
|
|
#[test]
|
|
fn to_string() {
|
|
let a = DenseMatrix::from_2d_array(&[&[0.9, 0.4, 0.7], &[0.4, 0.5, 0.3], &[0.7, 0.3, 0.8]]);
|
|
assert_eq!(
|
|
format!("{}", a),
|
|
"[[0.9, 0.4, 0.7], [0.4, 0.5, 0.3], [0.7, 0.3, 0.8]]"
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn cov() {
|
|
let a = DenseMatrix::from_2d_array(&[
|
|
&[64.0, 580.0, 29.0],
|
|
&[66.0, 570.0, 33.0],
|
|
&[68.0, 590.0, 37.0],
|
|
&[69.0, 660.0, 46.0],
|
|
&[73.0, 600.0, 55.0],
|
|
]);
|
|
let expected = DenseMatrix::from_2d_array(&[
|
|
&[11.5, 50.0, 34.75],
|
|
&[50.0, 1250.0, 205.0],
|
|
&[34.75, 205.0, 110.0],
|
|
]);
|
|
assert_eq!(a.cov(), expected);
|
|
}
|
|
}
|