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