forked from M-Labs/nalgebra
523 lines
15 KiB
Rust
523 lines
15 KiB
Rust
use crate::allocator::Allocator;
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use crate::storage::RawStorage;
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use crate::{Const, DefaultAllocator, Dim, Matrix, OVector, RowOVector, Scalar, VectorView, U1};
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use num::{One, Zero};
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use simba::scalar::{ClosedAdd, ClosedMul, Field, SupersetOf};
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use std::mem::MaybeUninit;
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/// # Folding on columns and rows
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impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
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/// Returns a row vector where each element is the result of the application of `f` on the
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/// corresponding column of the original matrix.
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#[inline]
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#[must_use]
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pub fn compress_rows(
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&self,
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f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T,
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) -> RowOVector<T, C>
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where
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DefaultAllocator: Allocator<T, U1, C>,
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{
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let ncols = self.shape_generic().1;
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let mut res = Matrix::uninit(Const::<1>, ncols);
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for i in 0..ncols.value() {
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// TODO: avoid bound checking of column.
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// Safety: all indices are in range.
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unsafe {
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*res.get_unchecked_mut((0, i)) = MaybeUninit::new(f(self.column(i)));
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}
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}
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// Safety: res is now fully initialized.
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unsafe { res.assume_init() }
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}
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/// Returns a column vector where each element is the result of the application of `f` on the
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/// corresponding column of the original matrix.
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///
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/// This is the same as `self.compress_rows(f).transpose()`.
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#[inline]
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#[must_use]
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pub fn compress_rows_tr(
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&self,
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f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T,
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) -> OVector<T, C>
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where
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DefaultAllocator: Allocator<T, C>,
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{
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let ncols = self.shape_generic().1;
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let mut res = Matrix::uninit(ncols, Const::<1>);
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for i in 0..ncols.value() {
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// TODO: avoid bound checking of column.
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// Safety: all indices are in range.
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unsafe {
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*res.vget_unchecked_mut(i) = MaybeUninit::new(f(self.column(i)));
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}
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}
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// Safety: res is now fully initialized.
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unsafe { res.assume_init() }
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}
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/// Returns a column vector resulting from the folding of `f` on each column of this matrix.
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#[inline]
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#[must_use]
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pub fn compress_columns(
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&self,
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init: OVector<T, R>,
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f: impl Fn(&mut OVector<T, R>, VectorView<'_, T, R, S::RStride, S::CStride>),
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) -> OVector<T, R>
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where
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DefaultAllocator: Allocator<T, R>,
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{
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let mut res = init;
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for i in 0..self.ncols() {
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f(&mut res, self.column(i))
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}
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res
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}
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}
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/// # Common statistics operations
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impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
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/*
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*
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* Sum computation.
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*
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*/
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/// The sum of all the elements of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::Matrix2x3;
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.sum(), 21.0);
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/// ```
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#[inline]
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#[must_use]
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pub fn sum(&self) -> T
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where
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T: ClosedAdd + Zero,
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{
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self.iter().cloned().fold(T::zero(), |a, b| a + b)
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}
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/// The sum of all the rows of this matrix.
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///
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/// Use `.row_sum_tr` if you need the result in a column vector instead.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{RowVector2, RowVector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_sum(), RowVector3::new(5.0, 7.0, 9.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.row_sum(), RowVector2::new(9,12));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_sum(&self) -> RowOVector<T, C>
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where
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T: ClosedAdd + Zero,
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DefaultAllocator: Allocator<T, U1, C>,
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{
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self.compress_rows(|col| col.sum())
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}
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/// The sum of all the rows of this matrix. The result is transposed and returned as a column vector.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{Vector2, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_sum_tr(), Vector3::new(5.0, 7.0, 9.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.row_sum_tr(), Vector2::new(9, 12));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_sum_tr(&self) -> OVector<T, C>
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where
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T: ClosedAdd + Zero,
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DefaultAllocator: Allocator<T, C>,
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{
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self.compress_rows_tr(|col| col.sum())
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}
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/// The sum of all the columns of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{Vector2, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.column_sum(), Vector2::new(6.0, 15.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.column_sum(), Vector3::new(3, 7, 11));
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/// ```
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#[inline]
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#[must_use]
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pub fn column_sum(&self) -> OVector<T, R>
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where
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T: ClosedAdd + Zero,
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DefaultAllocator: Allocator<T, R>,
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{
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let nrows = self.shape_generic().0;
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self.compress_columns(OVector::zeros_generic(nrows, Const::<1>), |out, col| {
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*out += col;
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})
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}
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/*
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*
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* Product computation.
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*
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*/
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/// The product of all the elements of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::Matrix2x3;
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.product(), 720.0);
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/// ```
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#[inline]
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#[must_use]
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pub fn product(&self) -> T
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where
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T: ClosedMul + One,
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{
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self.iter().cloned().fold(T::one(), |a, b| a * b)
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}
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/// The product of all the rows of this matrix.
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///
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/// Use `.row_sum_tr` if you need the result in a column vector instead.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{RowVector2, RowVector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_product(), RowVector3::new(4.0, 10.0, 18.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.row_product(), RowVector2::new(15, 48));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_product(&self) -> RowOVector<T, C>
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where
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T: ClosedMul + One,
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DefaultAllocator: Allocator<T, U1, C>,
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{
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self.compress_rows(|col| col.product())
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}
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/// The product of all the rows of this matrix. The result is transposed and returned as a column vector.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{Vector2, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_product_tr(), Vector3::new(4.0, 10.0, 18.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.row_product_tr(), Vector2::new(15, 48));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_product_tr(&self) -> OVector<T, C>
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where
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T: ClosedMul + One,
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DefaultAllocator: Allocator<T, C>,
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{
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self.compress_rows_tr(|col| col.product())
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}
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/// The product of all the columns of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Matrix3x2};
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/// # use nalgebra::{Vector2, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.column_product(), Vector2::new(6.0, 120.0));
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///
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/// let mint = Matrix3x2::new(1, 2,
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/// 3, 4,
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/// 5, 6);
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/// assert_eq!(mint.column_product(), Vector3::new(2, 12, 30));
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/// ```
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#[inline]
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#[must_use]
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pub fn column_product(&self) -> OVector<T, R>
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where
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T: ClosedMul + One,
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DefaultAllocator: Allocator<T, R>,
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{
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let nrows = self.shape_generic().0;
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self.compress_columns(
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OVector::repeat_generic(nrows, Const::<1>, T::one()),
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|out, col| {
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out.component_mul_assign(&col);
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},
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)
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}
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/*
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*
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* Variance computation.
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*
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*/
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/// The variance of all the elements of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::Matrix2x3;
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_relative_eq!(m.variance(), 35.0 / 12.0, epsilon = 1.0e-8);
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/// ```
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#[inline]
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#[must_use]
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pub fn variance(&self) -> T
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where
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T: Field + SupersetOf<f64>,
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{
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if self.is_empty() {
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T::zero()
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} else {
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let n_elements: T = crate::convert(self.len() as f64);
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let mean = self.mean();
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self.iter().cloned().fold(T::zero(), |acc, x| {
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acc + (x.clone() - mean.clone()) * (x - mean.clone())
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}) / n_elements
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}
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}
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/// The variance of all the rows of this matrix.
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///
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/// Use `.row_variance_tr` if you need the result in a column vector instead.
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, RowVector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_variance(), RowVector3::new(2.25, 2.25, 2.25));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_variance(&self) -> RowOVector<T, C>
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where
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T: Field + SupersetOf<f64>,
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DefaultAllocator: Allocator<T, U1, C>,
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{
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self.compress_rows(|col| col.variance())
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}
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/// The variance of all the rows of this matrix. The result is transposed and returned as a column vector.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_variance_tr(), Vector3::new(2.25, 2.25, 2.25));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_variance_tr(&self) -> OVector<T, C>
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where
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T: Field + SupersetOf<f64>,
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DefaultAllocator: Allocator<T, C>,
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{
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self.compress_rows_tr(|col| col.variance())
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}
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/// The variance of all the columns of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Matrix2x3, Vector2};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_relative_eq!(m.column_variance(), Vector2::new(2.0 / 3.0, 2.0 / 3.0), epsilon = 1.0e-8);
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/// ```
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#[inline]
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#[must_use]
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pub fn column_variance(&self) -> OVector<T, R>
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where
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T: Field + SupersetOf<f64>,
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DefaultAllocator: Allocator<T, R>,
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{
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let (nrows, ncols) = self.shape_generic();
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let mut mean = self.column_mean();
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mean.apply(|e| *e = -(e.clone() * e.clone()));
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let denom = T::one() / crate::convert::<_, T>(ncols.value() as f64);
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self.compress_columns(mean, |out, col| {
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for i in 0..nrows.value() {
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unsafe {
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let val = col.vget_unchecked(i);
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*out.vget_unchecked_mut(i) += denom.clone() * val.clone() * val.clone()
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}
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}
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})
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}
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/*
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*
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* Mean computation.
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*
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*/
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/// The mean of all the elements of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::Matrix2x3;
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.mean(), 3.5);
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/// ```
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#[inline]
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#[must_use]
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pub fn mean(&self) -> T
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where
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T: Field + SupersetOf<f64>,
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{
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if self.is_empty() {
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T::zero()
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} else {
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self.sum() / crate::convert(self.len() as f64)
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}
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}
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/// The mean of all the rows of this matrix.
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///
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/// Use `.row_mean_tr` if you need the result in a column vector instead.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, RowVector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_mean(), RowVector3::new(2.5, 3.5, 4.5));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_mean(&self) -> RowOVector<T, C>
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where
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T: Field + SupersetOf<f64>,
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DefaultAllocator: Allocator<T, U1, C>,
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{
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self.compress_rows(|col| col.mean())
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}
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/// The mean of all the rows of this matrix. The result is transposed and returned as a column vector.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Vector3};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.row_mean_tr(), Vector3::new(2.5, 3.5, 4.5));
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/// ```
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#[inline]
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#[must_use]
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pub fn row_mean_tr(&self) -> OVector<T, C>
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where
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T: Field + SupersetOf<f64>,
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DefaultAllocator: Allocator<T, C>,
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{
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self.compress_rows_tr(|col| col.mean())
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}
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/// The mean of all the columns of this matrix.
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///
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/// # Example
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///
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/// ```
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/// # use nalgebra::{Matrix2x3, Vector2};
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///
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/// let m = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// assert_eq!(m.column_mean(), Vector2::new(2.0, 5.0));
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/// ```
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#[inline]
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#[must_use]
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pub fn column_mean(&self) -> OVector<T, R>
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|
where
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|
T: Field + SupersetOf<f64>,
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|
DefaultAllocator: Allocator<T, R>,
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|
{
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|
let (nrows, ncols) = self.shape_generic();
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|
let denom = T::one() / crate::convert::<_, T>(ncols.value() as f64);
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|
self.compress_columns(OVector::zeros_generic(nrows, Const::<1>), |out, col| {
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|
out.axpy(denom.clone(), &col, T::one())
|
|
})
|
|
}
|
|
}
|