nalgebra/src/linalg/solve.rs
2020-03-21 12:16:46 +01:00

435 lines
13 KiB
Rust

use simba::scalar::ComplexField;
use crate::base::allocator::Allocator;
use crate::base::constraint::{SameNumberOfRows, ShapeConstraint};
use crate::base::dimension::{Dim, U1};
use crate::base::storage::{Storage, StorageMut};
use crate::base::{DVectorSlice, DefaultAllocator, Matrix, MatrixMN, SquareMatrix, Vector};
impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
/// Computes the solution of the linear system `self . x = b` where `x` is the unknown and only
/// the lower-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.solve_lower_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Computes the solution of the linear system `self . x = b` where `x` is the unknown and only
/// the upper-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.solve_upper_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Solves the linear system `self . x = b` where `x` is the unknown and only the
/// lower-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.solve_lower_triangular_vector_mut(&mut b.column_mut(i)) {
return false;
}
}
true
}
fn solve_lower_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
where
S2: StorageMut<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.nrows();
for i in 0..dim {
let coeff;
unsafe {
let diag = *self.get_unchecked((i, i));
if diag.is_zero() {
return false;
}
coeff = *b.vget_unchecked(i) / diag;
*b.vget_unchecked_mut(i) = coeff;
}
b.rows_range_mut(i + 1..)
.axpy(-coeff, &self.slice_range(i + 1.., i), N::one());
}
true
}
// FIXME: add the same but for solving upper-triangular.
/// Solves the linear system `self . x = b` where `x` is the unknown and only the
/// lower-triangular part of `self` is considered not-zero. The diagonal is never read as it is
/// assumed to be equal to `diag`. Returns `false` and does not modify its inputs if `diag` is zero.
pub fn solve_lower_triangular_with_diag_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
diag: N,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
if diag.is_zero() {
return false;
}
let dim = self.nrows();
let cols = b.ncols();
for k in 0..cols {
let mut bcol = b.column_mut(k);
for i in 0..dim - 1 {
let coeff = unsafe { *bcol.vget_unchecked(i) } / diag;
bcol.rows_range_mut(i + 1..)
.axpy(-coeff, &self.slice_range(i + 1.., i), N::one());
}
}
true
}
/// Solves the linear system `self . x = b` where `x` is the unknown and only the
/// upper-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.solve_upper_triangular_vector_mut(&mut b.column_mut(i)) {
return false;
}
}
true
}
fn solve_upper_triangular_vector_mut<R2: Dim, S2>(&self, b: &mut Vector<N, R2, S2>) -> bool
where
S2: StorageMut<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.nrows();
for i in (0..dim).rev() {
let coeff;
unsafe {
let diag = *self.get_unchecked((i, i));
if diag.is_zero() {
return false;
}
coeff = *b.vget_unchecked(i) / diag;
*b.vget_unchecked_mut(i) = coeff;
}
b.rows_range_mut(..i)
.axpy(-coeff, &self.slice_range(..i, i), N::one());
}
true
}
/*
*
* Transpose and adjoint versions
*
*/
/// Computes the solution of the linear system `self.transpose() . x = b` where `x` is the unknown and only
/// the lower-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn tr_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.tr_solve_lower_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Computes the solution of the linear system `self.transpose() . x = b` where `x` is the unknown and only
/// the upper-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn tr_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.tr_solve_upper_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Solves the linear system `self.transpose() . x = b` where `x` is the unknown and only the
/// lower-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.xx_solve_lower_triangular_vector_mut(
&mut b.column_mut(i),
|e| e,
|a, b| a.dot(b),
) {
return false;
}
}
true
}
/// Solves the linear system `self.transpose() . x = b` where `x` is the unknown and only the
/// upper-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn tr_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.xx_solve_upper_triangular_vector_mut(
&mut b.column_mut(i),
|e| e,
|a, b| a.dot(b),
) {
return false;
}
}
true
}
/// Computes the solution of the linear system `self.adjoint() . x = b` where `x` is the unknown and only
/// the lower-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn ad_solve_lower_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.ad_solve_lower_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Computes the solution of the linear system `self.adjoint() . x = b` where `x` is the unknown and only
/// the upper-triangular part of `self` (including the diagonal) is considered not-zero.
#[inline]
pub fn ad_solve_upper_triangular<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
if self.ad_solve_upper_triangular_mut(&mut res) {
Some(res)
} else {
None
}
}
/// Solves the linear system `self.adjoint() . x = b` where `x` is the unknown and only the
/// lower-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn ad_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.xx_solve_lower_triangular_vector_mut(
&mut b.column_mut(i),
|e| e.conjugate(),
|a, b| a.dotc(b),
) {
return false;
}
}
true
}
/// Solves the linear system `self.adjoint() . x = b` where `x` is the unknown and only the
/// upper-triangular part of `self` (including the diagonal) is considered not-zero.
pub fn ad_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let cols = b.ncols();
for i in 0..cols {
if !self.xx_solve_upper_triangular_vector_mut(
&mut b.column_mut(i),
|e| e.conjugate(),
|a, b| a.dotc(b),
) {
return false;
}
}
true
}
#[inline(always)]
fn xx_solve_lower_triangular_vector_mut<R2: Dim, S2>(
&self,
b: &mut Vector<N, R2, S2>,
conjugate: impl Fn(N) -> N,
dot: impl Fn(
&DVectorSlice<N, S::RStride, S::CStride>,
&DVectorSlice<N, S2::RStride, S2::CStride>,
) -> N,
) -> bool
where
S2: StorageMut<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.nrows();
for i in (0..dim).rev() {
let dot = dot(&self.slice_range(i + 1.., i), &b.slice_range(i + 1.., 0));
unsafe {
let b_i = b.vget_unchecked_mut(i);
let diag = conjugate(*self.get_unchecked((i, i)));
if diag.is_zero() {
return false;
}
*b_i = (*b_i - dot) / diag;
}
}
true
}
#[inline(always)]
fn xx_solve_upper_triangular_vector_mut<R2: Dim, S2>(
&self,
b: &mut Vector<N, R2, S2>,
conjugate: impl Fn(N) -> N,
dot: impl Fn(
&DVectorSlice<N, S::RStride, S::CStride>,
&DVectorSlice<N, S2::RStride, S2::CStride>,
) -> N,
) -> bool
where
S2: StorageMut<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.nrows();
for i in 0..dim {
let dot = dot(&self.slice_range(..i, i), &b.slice_range(..i, 0));
unsafe {
let b_i = b.vget_unchecked_mut(i);
let diag = conjugate(*self.get_unchecked((i, i)));
if diag.is_zero() {
return false;
}
*b_i = (*b_i - dot) / diag;
}
}
true
}
}