274 lines
9.2 KiB
Rust
274 lines
9.2 KiB
Rust
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use alga::general::Real;
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use core::{DefaultAllocator, Matrix, SquareMatrix, Vector, MatrixMN};
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use core::dimension::{Dim, U1};
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use core::storage::{Storage, StorageMut};
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use core::allocator::Allocator;
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use core::constraint::{ShapeConstraint, SameNumberOfRows};
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impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
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/// Computes the solution of the linear system `self . x = b` where `x` is the unknown and only
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/// the lower-triangular part of `self` (including the diagonal) is concidered not-zero.
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#[inline]
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pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
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-> Option<MatrixMN<N, R2, C2>>
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where S2: StorageMut<N, R2, C2>,
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DefaultAllocator: Allocator<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let mut res = b.clone_owned();
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if self.solve_lower_triangular_mut(&mut res) {
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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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/// Computes the solution of the linear system `self . x = b` where `x` is the unknown and only
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/// the upper-triangular part of `self` (including the diagonal) is concidered not-zero.
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#[inline]
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pub fn solve_upper_triangular<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
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-> Option<MatrixMN<N, R2, C2>>
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where S2: StorageMut<N, R2, C2>,
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DefaultAllocator: Allocator<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let mut res = b.clone_owned();
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if self.solve_upper_triangular_mut(&mut res) {
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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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/// Solves the linear system `self . x = b` where `x` is the unknown and only the
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/// lower-triangular part of `self` (including the diagonal) is concidered not-zero.
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pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>) -> bool
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where S2: StorageMut<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let cols = b.ncols();
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for i in 0 .. cols {
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if !self.solve_lower_triangular_vector_mut(&mut b.column_mut(i)) {
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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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fn solve_lower_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
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where S2: StorageMut<N, R2, U1>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let dim = self.nrows();
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for i in 0 .. dim {
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let coeff;
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unsafe {
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let diag = *self.get_unchecked(i, i);
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if diag.is_zero() {
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return false;
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}
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coeff = *b.vget_unchecked(i) / diag;
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*b.vget_unchecked_mut(i) = coeff;
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}
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b.rows_range_mut(i + 1 ..).axpy(-coeff, &self.slice_range(i + 1 .., i), N::one());
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}
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true
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}
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// FIXME: add the same but for solving upper-triangular.
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/// Solves the linear system `self . x = b` where `x` is the unknown and only the
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/// lower-triangular part of `self` is concidered not-zero. The diagonal is never read as it is
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/// assumed to be equal to `diag`. Returns `false` and does not modify its inputs if `diag` is zero.
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pub fn solve_lower_triangular_with_diag_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>, diag: N)
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-> bool
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where S2: StorageMut<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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if diag.is_zero() {
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return false;
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}
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let dim = self.nrows();
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let cols = b.ncols();
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for k in 0 .. cols {
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let mut bcol = b.column_mut(k);
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for i in 0 .. dim - 1 {
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let coeff = unsafe { *bcol.vget_unchecked(i) } / diag;
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bcol.rows_range_mut(i + 1 ..).axpy(-coeff, &self.slice_range(i + 1 .., i), N::one());
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}
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}
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true
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}
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/// Solves the linear system `self . x = b` where `x` is the unknown and only the
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/// upper-triangular part of `self` (including the diagonal) is concidered not-zero.
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pub fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>) -> bool
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where S2: StorageMut<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let cols = b.ncols();
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for i in 0 .. cols {
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if !self.solve_upper_triangular_vector_mut(&mut b.column_mut(i)) {
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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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fn solve_upper_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
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where S2: StorageMut<N, R2, U1>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let dim = self.nrows();
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for i in (0 .. dim).rev() {
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let coeff;
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unsafe {
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let diag = *self.get_unchecked(i, i);
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if diag.is_zero() {
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return false;
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}
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coeff = *b.vget_unchecked(i) / diag;
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*b.vget_unchecked_mut(i) = coeff;
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}
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b.rows_range_mut(.. i).axpy(-coeff, &self.slice_range(.. i, i), N::one());
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}
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true
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}
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/*
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*
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* Transpose versions
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*
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*/
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/// Computes the solution of the linear system `self.transpose() . x = b` where `x` is the unknown and only
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/// the lower-triangular part of `self` (including the diagonal) is concidered not-zero.
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#[inline]
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pub fn tr_solve_lower_triangular<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
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-> Option<MatrixMN<N, R2, C2>>
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where S2: StorageMut<N, R2, C2>,
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DefaultAllocator: Allocator<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let mut res = b.clone_owned();
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if self.tr_solve_lower_triangular_mut(&mut res) {
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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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/// Computes the solution of the linear system `self.transpose() . x = b` where `x` is the unknown and only
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/// the upper-triangular part of `self` (including the diagonal) is concidered not-zero.
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#[inline]
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pub fn tr_solve_upper_triangular<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
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-> Option<MatrixMN<N, R2, C2>>
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where S2: StorageMut<N, R2, C2>,
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DefaultAllocator: Allocator<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let mut res = b.clone_owned();
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if self.tr_solve_upper_triangular_mut(&mut res) {
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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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/// Solves the linear system `self.transpose() . x = b` where `x` is the unknown and only the
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/// lower-triangular part of `self` (including the diagonal) is concidered not-zero.
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pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>) -> bool
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where S2: StorageMut<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let cols = b.ncols();
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for i in 0 .. cols {
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if !self.tr_solve_lower_triangular_vector_mut(&mut b.column_mut(i)) {
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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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fn tr_solve_lower_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
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where S2: StorageMut<N, R2, U1>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let dim = self.nrows();
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for i in (0 .. dim).rev() {
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let dot = self.slice_range(i + 1 .., i).dot(&b.slice_range(i + 1 .., 0));
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unsafe {
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let b_i = b.vget_unchecked_mut(i);
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let diag = *self.get_unchecked(i, i);
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if diag.is_zero() {
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return false;
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}
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*b_i = (*b_i - dot) / diag;
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}
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}
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true
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}
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/// Solves the linear system `self.transpose() . x = b` where `x` is the unknown and only the
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/// upper-triangular part of `self` (including the diagonal) is concidered not-zero.
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pub fn tr_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>) -> bool
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where S2: StorageMut<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let cols = b.ncols();
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for i in 0 .. cols {
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if !self.tr_solve_upper_triangular_vector_mut(&mut b.column_mut(i)) {
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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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fn tr_solve_upper_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
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where S2: StorageMut<N, R2, U1>,
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ShapeConstraint: SameNumberOfRows<R2, D> {
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let dim = self.nrows();
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for i in 0 .. dim {
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let dot = self.slice_range(.. i, i).dot(&b.slice_range(.. i, 0));
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unsafe {
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let b_i = b.vget_unchecked_mut(i);
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let diag = *self.get_unchecked(i, i);
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if diag.is_zero() {
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return false;
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}
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*b_i = (*b_i - dot) / diag;
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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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