698 lines
19 KiB
Rust
698 lines
19 KiB
Rust
//! Matrix with dimensions unknown at compile-time.
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#![allow(missing_doc)] // we hide doc to not have to document the $trhs double dispatch trait.
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use rand::Rand;
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use rand;
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use std::num::{One, Zero};
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use traits::operations::ApproxEq;
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use std::mem;
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use structs::dvec::{DVec, DVecMulRhs};
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use traits::operations::{Inv, Transpose, Mean, Cov};
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use traits::structure::{Cast, ColSlice, RowSlice, Eye, Indexable};
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use std::fmt::{Show, Formatter, Result};
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#[doc(hidden)]
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mod metal;
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/// Matrix with dimensions unknown at compile-time.
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#[deriving(TotalEq, Eq, Clone)]
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pub struct DMat<N> {
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nrows: uint,
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ncols: uint,
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mij: Vec<N>
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}
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double_dispatch_binop_decl_trait!(DMat, DMatMulRhs)
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double_dispatch_binop_decl_trait!(DMat, DMatDivRhs)
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double_dispatch_binop_decl_trait!(DMat, DMatAddRhs)
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double_dispatch_binop_decl_trait!(DMat, DMatSubRhs)
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mul_redispatch_impl!(DMat, DMatMulRhs)
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div_redispatch_impl!(DMat, DMatDivRhs)
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add_redispatch_impl!(DMat, DMatAddRhs)
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sub_redispatch_impl!(DMat, DMatSubRhs)
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impl<N> DMat<N> {
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/// Creates an uninitialized matrix.
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#[inline]
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pub unsafe fn new_uninitialized(nrows: uint, ncols: uint) -> DMat<N> {
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let mut vec = Vec::with_capacity(nrows * ncols);
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vec.set_len(nrows * ncols);
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DMat {
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nrows: nrows,
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ncols: ncols,
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mij: vec
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}
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}
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}
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impl<N: Zero + Clone> DMat<N> {
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/// Builds a matrix filled with zeros.
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///
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/// # Arguments
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/// * `dim` - The dimension of the matrix. A `dim`-dimensional matrix contains `dim * dim`
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/// components.
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#[inline]
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pub fn new_zeros(nrows: uint, ncols: uint) -> DMat<N> {
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DMat::from_elem(nrows, ncols, Zero::zero())
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}
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/// Tests if all components of the matrix are zeroes.
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#[inline]
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pub fn is_zero(&self) -> bool {
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self.mij.iter().all(|e| e.is_zero())
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}
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#[inline]
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pub fn reset(&mut self) {
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for mij in self.mij.mut_iter() {
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*mij = Zero::zero();
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}
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}
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}
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impl<N: Rand> DMat<N> {
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/// Builds a matrix filled with random values.
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#[inline]
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pub fn new_random(nrows: uint, ncols: uint) -> DMat<N> {
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DMat::from_fn(nrows, ncols, |_, _| rand::random())
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}
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}
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impl<N: One + Clone> DMat<N> {
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/// Builds a matrix filled with a given constant.
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#[inline]
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pub fn new_ones(nrows: uint, ncols: uint) -> DMat<N> {
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DMat::from_elem(nrows, ncols, One::one())
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}
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}
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impl<N: Clone> DMat<N> {
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/// Builds a matrix filled with a given constant.
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#[inline]
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pub fn from_elem(nrows: uint, ncols: uint, val: N) -> DMat<N> {
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DMat {
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nrows: nrows,
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ncols: ncols,
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mij: Vec::from_elem(nrows * ncols, val)
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}
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}
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/// Builds a matrix filled with the components provided by a vector.
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/// The vector contains the matrix data in row-major order.
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/// Note that `from_col_vec` is a lot faster than `from_row_vec` since a `DMat` stores its data
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/// in column-major order.
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///
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/// The vector must have at least `nrows * ncols` elements.
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#[inline]
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pub fn from_row_vec(nrows: uint, ncols: uint, vec: &[N]) -> DMat<N> {
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let mut res = DMat::from_col_vec(ncols, nrows, vec);
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// we transpose because the buffer is row_major
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res.transpose();
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res
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}
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/// Builds a matrix filled with the components provided by a vector.
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/// The vector contains the matrix data in column-major order.
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/// Note that `from_col_vec` is a lot faster than `from_row_vec` since a `DMat` stores its data
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/// in column-major order.
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///
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/// The vector must have at least `nrows * ncols` elements.
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#[inline]
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pub fn from_col_vec(nrows: uint, ncols: uint, vec: &[N]) -> DMat<N> {
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assert!(nrows * ncols == vec.len());
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DMat {
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nrows: nrows,
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ncols: ncols,
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mij: Vec::from_slice(vec)
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}
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}
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}
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impl<N> DMat<N> {
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/// Builds a matrix filled with a given constant.
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#[inline(always)]
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pub fn from_fn(nrows: uint, ncols: uint, f: |uint, uint| -> N) -> DMat<N> {
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DMat {
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nrows: nrows,
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ncols: ncols,
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mij: Vec::from_fn(nrows * ncols, |i| { let m = i % ncols; f(m, m - i * ncols) })
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}
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}
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/// The number of row on the matrix.
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#[inline]
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pub fn nrows(&self) -> uint {
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self.nrows
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}
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/// The number of columns on the matrix.
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#[inline]
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pub fn ncols(&self) -> uint {
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self.ncols
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}
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/// Transforms this matrix into an array. This consumes the matrix and is O(1).
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/// The returned vector contains the matrix data in column-major order.
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#[inline]
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pub fn to_vec(self) -> Vec<N> {
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self.mij
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}
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/// Gets a reference to this matrix data.
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/// The returned vector contains the matrix data in column-major order.
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#[inline]
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pub fn as_vec<'r>(&'r self) -> &'r [N] {
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self.mij.as_slice()
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}
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/// Gets a mutable reference to this matrix data.
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/// The returned vector contains the matrix data in column-major order.
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#[inline]
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pub fn as_mut_vec<'r>(&'r mut self) -> &'r mut [N] {
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self.mij.as_mut_slice()
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}
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}
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// FIXME: add a function to modify the dimension (to avoid useless allocations)?
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impl<N: One + Zero + Clone> Eye for DMat<N> {
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/// Builds an identity matrix.
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///
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/// # Arguments
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/// * `dim` - The dimension of the matrix. A `dim`-dimensional matrix contains `dim * dim`
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/// components.
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#[inline]
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fn new_identity(dim: uint) -> DMat<N> {
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let mut res = DMat::new_zeros(dim, dim);
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for i in range(0u, dim) {
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let _1: N = One::one();
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res.set((i, i), _1);
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}
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res
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}
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}
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impl<N: Clone> DMat<N> {
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#[inline(always)]
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fn offset(&self, i: uint, j: uint) -> uint {
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i + j * self.nrows
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}
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}
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impl<N: Clone> Indexable<(uint, uint), N> for DMat<N> {
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/// Changes the value of a component of the matrix.
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///
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/// # Arguments
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/// * `rowcol` - 0-based tuple (row, col) to be changed
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#[inline]
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fn set(&mut self, rowcol: (uint, uint), val: N) {
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let (row, col) = rowcol;
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assert!(row < self.nrows);
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assert!(col < self.ncols);
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let offset = self.offset(row, col);
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*self.mij.get_mut(offset) = val
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}
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/// Just like `set` without bounds checking.
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#[inline]
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unsafe fn unsafe_set(&mut self, rowcol: (uint, uint), val: N) {
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let (row, col) = rowcol;
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let offset = self.offset(row, col);
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*self.mij.as_mut_slice().unsafe_mut_ref(offset) = val
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}
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/// Reads the value of a component of the matrix.
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///
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/// # Arguments
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/// * `rowcol` - 0-based tuple (row, col) to be read
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#[inline]
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fn at(&self, rowcol: (uint, uint)) -> N {
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let (row, col) = rowcol;
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assert!(row < self.nrows);
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assert!(col < self.ncols);
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unsafe { self.unsafe_at((row, col)) }
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}
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/// Just like `at` without bounds checking.
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#[inline]
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unsafe fn unsafe_at(&self, rowcol: (uint, uint)) -> N {
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let (row, col) = rowcol;
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(*self.mij.as_slice().unsafe_ref(self.offset(row, col))).clone()
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}
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#[inline]
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fn swap(&mut self, rowcol1: (uint, uint), rowcol2: (uint, uint)) {
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let (row1, col1) = rowcol1;
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let (row2, col2) = rowcol2;
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let offset1 = self.offset(row1, col1);
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let offset2 = self.offset(row2, col2);
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let count = self.mij.len();
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assert!(offset1 < count);
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assert!(offset2 < count);
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self.mij.as_mut_slice().swap(offset1, offset2);
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}
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fn shape(&self) -> (uint, uint) {
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(self.nrows, self.ncols)
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}
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}
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impl<N: Clone + Mul<N, N> + Add<N, N> + Zero> DMatMulRhs<N, DMat<N>> for DMat<N> {
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fn binop(left: &DMat<N>, right: &DMat<N>) -> DMat<N> {
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assert!(left.ncols == right.nrows);
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let mut res = unsafe { DMat::new_uninitialized(left.nrows, right.ncols) };
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for i in range(0u, left.nrows) {
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for j in range(0u, right.ncols) {
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let mut acc: N = Zero::zero();
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unsafe {
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for k in range(0u, left.ncols) {
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acc = acc
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+ left.unsafe_at((i, k)) * right.unsafe_at((k, j));
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}
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res.unsafe_set((i, j), acc);
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}
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}
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}
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res
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}
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}
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impl<N: Clone + Add<N, N> + Mul<N, N> + Zero>
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DMatMulRhs<N, DVec<N>> for DVec<N> {
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fn binop(left: &DMat<N>, right: &DVec<N>) -> DVec<N> {
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assert!(left.ncols == right.at.len());
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let mut res : DVec<N> = unsafe { DVec::new_uninitialized(left.nrows) };
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for i in range(0u, left.nrows) {
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let mut acc: N = Zero::zero();
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for j in range(0u, left.ncols) {
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unsafe {
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acc = acc + left.unsafe_at((i, j)) * right.unsafe_at(j);
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}
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}
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*res.at.get_mut(i) = acc;
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}
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res
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}
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}
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impl<N: Clone + Add<N, N> + Mul<N, N> + Zero>
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DVecMulRhs<N, DVec<N>> for DMat<N> {
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fn binop(left: &DVec<N>, right: &DMat<N>) -> DVec<N> {
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assert!(right.nrows == left.at.len());
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let mut res : DVec<N> = unsafe { DVec::new_uninitialized(right.ncols) };
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for i in range(0u, right.ncols) {
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let mut acc: N = Zero::zero();
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for j in range(0u, right.nrows) {
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unsafe {
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acc = acc + left.unsafe_at(j) * right.unsafe_at((j, i));
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}
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}
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*res.at.get_mut(i) = acc;
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}
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res
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}
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}
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impl<N: Clone + Num>
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Inv for DMat<N> {
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#[inline]
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fn inv_cpy(m: &DMat<N>) -> Option<DMat<N>> {
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let mut res : DMat<N> = m.clone();
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if res.inv() {
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Some(res)
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}
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else {
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None
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}
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}
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fn inv(&mut self) -> bool {
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assert!(self.nrows == self.ncols);
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let dim = self.nrows;
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let mut res: DMat<N> = Eye::new_identity(dim);
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let _0T: N = Zero::zero();
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// inversion using Gauss-Jordan elimination
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for k in range(0u, dim) {
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// search a non-zero value on the k-th column
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// FIXME: would it be worth it to spend some more time searching for the
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// max instead?
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let mut n0 = k; // index of a non-zero entry
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while n0 != dim {
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if unsafe { self.unsafe_at((n0, k)) } != _0T {
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break;
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}
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n0 = n0 + 1;
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}
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if n0 == dim {
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return false
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}
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// swap pivot line
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if n0 != k {
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for j in range(0u, dim) {
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let off_n0_j = self.offset(n0, j);
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let off_k_j = self.offset(k, j);
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self.mij.as_mut_slice().swap(off_n0_j, off_k_j);
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res.mij.as_mut_slice().swap(off_n0_j, off_k_j);
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}
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}
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unsafe {
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let pivot = self.unsafe_at((k, k));
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for j in range(k, dim) {
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let selfval = self.unsafe_at((k, j)) / pivot;
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self.unsafe_set((k, j), selfval);
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}
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for j in range(0u, dim) {
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let resval = res.unsafe_at((k, j)) / pivot;
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res.unsafe_set((k, j), resval);
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}
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for l in range(0u, dim) {
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if l != k {
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let normalizer = self.unsafe_at((l, k));
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for j in range(k, dim) {
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let selfval = self.unsafe_at((l, j)) - self.unsafe_at((k, j)) * normalizer;
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self.unsafe_set((l, j), selfval);
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}
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for j in range(0u, dim) {
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let resval = res.unsafe_at((l, j)) - res.unsafe_at((k, j)) * normalizer;
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res.unsafe_set((l, j), resval);
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}
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}
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}
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}
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}
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*self = res;
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true
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}
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}
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impl<N: Clone> Transpose for DMat<N> {
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#[inline]
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fn transpose_cpy(m: &DMat<N>) -> DMat<N> {
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if m.nrows == m.ncols {
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let mut res = m.clone();
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res.transpose();
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res
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}
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else {
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let mut res = unsafe { DMat::new_uninitialized(m.ncols, m.nrows) };
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for i in range(0u, m.nrows) {
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for j in range(0u, m.ncols) {
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unsafe {
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res.unsafe_set((j, i), m.unsafe_at((i, j)))
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}
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}
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}
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res
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}
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}
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#[inline]
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fn transpose(&mut self) {
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if self.nrows == self.ncols {
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for i in range(1u, self.nrows) {
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for j in range(0u, self.ncols - 1) {
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let off_i_j = self.offset(i, j);
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let off_j_i = self.offset(j, i);
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self.mij.as_mut_slice().swap(off_i_j, off_j_i);
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}
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}
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mem::swap(&mut self.nrows, &mut self.ncols);
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}
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else {
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// FIXME: implement a better algorithm which does that in-place.
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*self = Transpose::transpose_cpy(self);
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}
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}
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}
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impl<N: Num + Cast<f32> + Clone> Mean<DVec<N>> for DMat<N> {
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fn mean(m: &DMat<N>) -> DVec<N> {
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let mut res: DVec<N> = DVec::new_zeros(m.ncols);
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let normalizer: N = Cast::from(1.0f32 / Cast::from(m.nrows));
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for i in range(0u, m.nrows) {
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for j in range(0u, m.ncols) {
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unsafe {
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let acc = res.unsafe_at(j) + m.unsafe_at((i, j)) * normalizer;
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res.unsafe_set(j, acc);
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}
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}
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}
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res
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}
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}
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impl<N: Clone + Num + Cast<f32> + DMatDivRhs<N, DMat<N>> + ToStr > Cov<DMat<N>> for DMat<N> {
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// FIXME: this could be heavily optimized, removing all temporaries by merging loops.
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fn cov(m: &DMat<N>) -> DMat<N> {
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assert!(m.nrows > 1);
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let mut centered = unsafe { DMat::new_uninitialized(m.nrows, m.ncols) };
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let mean = Mean::mean(m);
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// FIXME: use the rows iterator when available
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for i in range(0u, m.nrows) {
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for j in range(0u, m.ncols) {
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unsafe {
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centered.unsafe_set((i, j), m.unsafe_at((i, j)) - mean.unsafe_at(j));
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}
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}
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}
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// FIXME: return a triangular matrix?
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let fnormalizer: f32 = Cast::from(m.nrows() - 1);
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let normalizer: N = Cast::from(fnormalizer);
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// FIXME: this will do 2 allocations for temporaries!
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(Transpose::transpose_cpy(¢ered) * centered) / normalizer
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}
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||
}
|
||
|
||
impl<N: Clone> ColSlice<DVec<N>> for DMat<N> {
|
||
fn col_slice(&self, col_id :uint, row_start: uint, row_end: uint) -> DVec<N> {
|
||
assert!(col_id < self.ncols);
|
||
assert!(row_start < row_end);
|
||
assert!(row_end <= self.nrows);
|
||
// we can init from slice thanks to the matrix being column major
|
||
let start= self.offset(row_start, col_id);
|
||
let stop = self.offset(row_end, col_id);
|
||
let slice = DVec::from_vec(
|
||
row_end - row_start, self.mij.slice(start, stop));
|
||
slice
|
||
}
|
||
}
|
||
|
||
impl<N: Clone> RowSlice<DVec<N>> for DMat<N> {
|
||
fn row_slice(&self, row_id :uint, col_start: uint, col_end: uint) -> DVec<N> {
|
||
assert!(row_id < self.nrows);
|
||
assert!(col_start < col_end);
|
||
assert!(col_end <= self.ncols);
|
||
let mut slice : DVec<N> = unsafe {
|
||
DVec::new_uninitialized(self.nrows)
|
||
};
|
||
let mut slice_idx = 0u;
|
||
for col_id in range(col_start, col_end) {
|
||
unsafe {
|
||
slice.unsafe_set(slice_idx, self.unsafe_at((row_id, col_id)));
|
||
}
|
||
slice_idx += 1;
|
||
}
|
||
slice
|
||
}
|
||
}
|
||
|
||
impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
|
||
#[inline]
|
||
fn approx_epsilon(_: Option<DMat<N>>) -> N {
|
||
ApproxEq::approx_epsilon(None::<N>)
|
||
}
|
||
|
||
#[inline]
|
||
fn approx_eq(a: &DMat<N>, b: &DMat<N>) -> bool {
|
||
let mut zip = a.mij.iter().zip(b.mij.iter());
|
||
|
||
zip.all(|(a, b)| ApproxEq::approx_eq(a, b))
|
||
}
|
||
|
||
#[inline]
|
||
fn approx_eq_eps(a: &DMat<N>, b: &DMat<N>, epsilon: &N) -> bool {
|
||
let mut zip = a.mij.iter().zip(b.mij.iter());
|
||
|
||
zip.all(|(a, b)| ApproxEq::approx_eq_eps(a, b, epsilon))
|
||
}
|
||
}
|
||
|
||
impl<N: Show + Clone> Show for DMat<N> {
|
||
fn fmt(&self, form:&mut Formatter) -> Result {
|
||
for i in range(0u, self.nrows()) {
|
||
for j in range(0u, self.ncols()) {
|
||
let _ = write!(form, "{} ", self.at((i, j)));
|
||
}
|
||
let _ = write!(form, "\n");
|
||
}
|
||
write!(form, "\n")
|
||
}
|
||
}
|
||
|
||
macro_rules! scalar_mul_impl (
|
||
($n: ident) => (
|
||
impl DMatMulRhs<$n, DMat<$n>> for $n {
|
||
#[inline]
|
||
fn binop(left: &DMat<$n>, right: &$n) -> DMat<$n> {
|
||
DMat {
|
||
nrows: left.nrows,
|
||
ncols: left.ncols,
|
||
mij: left.mij.iter().map(|a| a * *right).collect()
|
||
}
|
||
}
|
||
}
|
||
)
|
||
)
|
||
|
||
macro_rules! scalar_div_impl (
|
||
($n: ident) => (
|
||
impl DMatDivRhs<$n, DMat<$n>> for $n {
|
||
#[inline]
|
||
fn binop(left: &DMat<$n>, right: &$n) -> DMat<$n> {
|
||
DMat {
|
||
nrows: left.nrows,
|
||
ncols: left.ncols,
|
||
mij: left.mij.iter().map(|a| a / *right).collect()
|
||
}
|
||
}
|
||
}
|
||
)
|
||
)
|
||
|
||
macro_rules! scalar_add_impl (
|
||
($n: ident) => (
|
||
impl DMatAddRhs<$n, DMat<$n>> for $n {
|
||
#[inline]
|
||
fn binop(left: &DMat<$n>, right: &$n) -> DMat<$n> {
|
||
DMat {
|
||
nrows: left.nrows,
|
||
ncols: left.ncols,
|
||
mij: left.mij.iter().map(|a| a + *right).collect()
|
||
}
|
||
}
|
||
}
|
||
)
|
||
)
|
||
|
||
macro_rules! scalar_sub_impl (
|
||
($n: ident) => (
|
||
impl DMatSubRhs<$n, DMat<$n>> for $n {
|
||
#[inline]
|
||
fn binop(left: &DMat<$n>, right: &$n) -> DMat<$n> {
|
||
DMat {
|
||
nrows: left.nrows,
|
||
ncols: left.ncols,
|
||
mij: left.mij.iter().map(|a| a - *right).collect()
|
||
}
|
||
}
|
||
}
|
||
)
|
||
)
|
||
|
||
scalar_mul_impl!(f64)
|
||
scalar_mul_impl!(f32)
|
||
scalar_mul_impl!(u64)
|
||
scalar_mul_impl!(u32)
|
||
scalar_mul_impl!(u16)
|
||
scalar_mul_impl!(u8)
|
||
scalar_mul_impl!(i64)
|
||
scalar_mul_impl!(i32)
|
||
scalar_mul_impl!(i16)
|
||
scalar_mul_impl!(i8)
|
||
scalar_mul_impl!(uint)
|
||
scalar_mul_impl!(int)
|
||
|
||
scalar_div_impl!(f64)
|
||
scalar_div_impl!(f32)
|
||
scalar_div_impl!(u64)
|
||
scalar_div_impl!(u32)
|
||
scalar_div_impl!(u16)
|
||
scalar_div_impl!(u8)
|
||
scalar_div_impl!(i64)
|
||
scalar_div_impl!(i32)
|
||
scalar_div_impl!(i16)
|
||
scalar_div_impl!(i8)
|
||
scalar_div_impl!(uint)
|
||
scalar_div_impl!(int)
|
||
|
||
scalar_add_impl!(f64)
|
||
scalar_add_impl!(f32)
|
||
scalar_add_impl!(u64)
|
||
scalar_add_impl!(u32)
|
||
scalar_add_impl!(u16)
|
||
scalar_add_impl!(u8)
|
||
scalar_add_impl!(i64)
|
||
scalar_add_impl!(i32)
|
||
scalar_add_impl!(i16)
|
||
scalar_add_impl!(i8)
|
||
scalar_add_impl!(uint)
|
||
scalar_add_impl!(int)
|
||
|
||
scalar_sub_impl!(f64)
|
||
scalar_sub_impl!(f32)
|
||
scalar_sub_impl!(u64)
|
||
scalar_sub_impl!(u32)
|
||
scalar_sub_impl!(u16)
|
||
scalar_sub_impl!(u8)
|
||
scalar_sub_impl!(i64)
|
||
scalar_sub_impl!(i32)
|
||
scalar_sub_impl!(i16)
|
||
scalar_sub_impl!(i8)
|
||
scalar_sub_impl!(uint)
|
||
scalar_sub_impl!(int)
|