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Merge branch 'dev' into master-public 

# Conflicts:
#	src/linalg/svd.rs
This commit is contained in:
sebcrozet 2018-12-29 14:39:32 +01:00
parent 564246ec1c 7a95644a21
commit 82106caa9e
2 changed files with 84 additions and 70 deletions
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120
src/linalg/svd.rs
View File

@ -484,90 +484,94 @@ where
/// Rebuild the original matrix.
///
/// This is useful if some of the singular values have been manually modified. Panics if the
/// right- and left- singular vectors have not been computed at construction-time.
pub fn recompose(self) -> MatrixMN<N, R, C> {
let mut u = self.u.expect("SVD recomposition: U has not been computed.");
let v_t = self
.v_t
.expect("SVD recomposition: V^t has not been computed.");
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
u.column_mut(i).mul_assign(val);
/// This is useful if some of the singular values have been manually modified.
/// Returns `Err` if the right- and left- singular vectors have not been
/// computed at construction-time.
pub fn recompose(self) -> Result<MatrixMN<N, R, C>, &'static str> {
match (self.u, self.v_t) {
(Some(mut u), Some(v_t)) => {
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
u.column_mut(i).mul_assign(val);
}
Ok(u * v_t)
}
(None, None) => Err("SVD recomposition: U and V^t have not been computed."),
(None, _) => Err("SVD recomposition: U has not been computed."),
(_, None) => Err("SVD recomposition: V^t has not been computed.")
}
u * v_t
}
/// Computes the pseudo-inverse of the decomposed matrix.
///
/// Any singular value smaller than `eps` is assumed to be zero.
/// Panics if the right- and left- singular vectors have not been computed at
/// construction-time.
pub fn pseudo_inverse(mut self, eps: N) -> MatrixMN<N, C, R>
where DefaultAllocator: Allocator<N, C, R> {
assert!(
eps >= N::zero(),
"SVD pseudo inverse: the epsilon must be non-negative."
);
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
if val > eps {
self.singular_values[i] = N::one() / val;
} else {
self.singular_values[i] = N::zero();
}
/// Returns `Err` if the right- and left- singular vectors have not
/// been computed at construction-time.
pub fn pseudo_inverse(mut self, eps: N) -> Result<MatrixMN<N, C, R>, &'static str>
where
DefaultAllocator: Allocator<N, C, R>,
{
if eps < N::zero() {
Err("SVD pseudo inverse: the epsilon must be non-negative.")
}
else {
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
self.recompose().transpose()
if val > eps {
self.singular_values[i] = N::one() / val;
} else {
self.singular_values[i] = N::zero();
}
}
self.recompose().map(|m| m.transpose())
}
}
/// Solves the system `self * x = b` where `self` is the decomposed matrix and `x` the unknown.
///
/// Any singular value smaller than `eps` is assumed to be zero.
/// Returns `None` if the singular vectors `U` and `V` have not been computed.
/// Returns `Err` if the singular vectors `U` and `V` have not been computed.
// FIXME: make this more generic wrt the storage types and the dimensions for `b`.
pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
eps: N,
) -> MatrixMN<N, C, C2>
) -> Result<MatrixMN<N, C, C2>, &'static str>
where
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, C, C2> + Allocator<N, DimMinimum<R, C>, C2>,
ShapeConstraint: SameNumberOfRows<R, R2>,
{
assert!(
eps >= N::zero(),
"SVD solve: the epsilon must be non-negative."
);
let u = self
.u
.as_ref()
.expect("SVD solve: U has not been computed.");
let v_t = self
.v_t
.as_ref()
.expect("SVD solve: V^t has not been computed.");
if eps < N::zero() {
Err("SVD solve: the epsilon must be non-negative.")
}
else {
match (&self.u, &self.v_t) {
(Some(u), Some(v_t)) => {
let mut ut_b = u.tr_mul(b);
let mut ut_b = u.tr_mul(b);
for j in 0..ut_b.ncols() {
let mut col = ut_b.column_mut(j);
for j in 0..ut_b.ncols() {
let mut col = ut_b.column_mut(j);
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
if val > eps {
col[i] /= val;
} else {
col[i] = N::zero();
}
}
}
for i in 0..self.singular_values.len() {
let val = self.singular_values[i];
if val > eps {
col[i] /= val;
} else {
col[i] = N::zero();
Ok(v_t.tr_mul(&ut_b))
}
(None, None) => Err("SVD solve: U and V^t have not been computed."),
(None, _) => Err("SVD solve: U has not been computed."),
(_, None) => Err("SVD solve: V^t has not been computed.")
}
}
v_t.tr_mul(&ut_b)
}
}
@ -624,8 +628,10 @@ where
/// Computes the pseudo-inverse of this matrix.
///
/// All singular values below `eps` are considered equal to 0.
pub fn pseudo_inverse(self, eps: N) -> MatrixMN<N, C, R>
where DefaultAllocator: Allocator<N, C, R> {
pub fn pseudo_inverse(self, eps: N) -> Result<MatrixMN<N, C, R>, &'static str>
where
DefaultAllocator: Allocator<N, C, R>,
{
SVD::new(self.clone_owned(), true, true).pseudo_inverse(eps)
}
}

34
tests/linalg/svd.rs
View File

@ -10,7 +10,7 @@ mod quickcheck_tests {
fn svd(m: DMatrix<f64>) -> bool {
if m.len() > 0 {
let svd = m.clone().svd(true, true);
let recomp_m = svd.clone().recompose();
let recomp_m = svd.clone().recompose().unwrap();
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
@ -91,7 +91,7 @@ mod quickcheck_tests {
fn svd_pseudo_inverse(m: DMatrix<f64>) -> bool {
if m.len() > 0 {
let svd = m.clone().svd(true, true);
let pinv = svd.pseudo_inverse(1.0e-10);
let pinv = svd.pseudo_inverse(1.0e-10).unwrap();
if m.nrows() > m.ncols() {
println!("{}", &pinv * &m);
@ -118,10 +118,10 @@ mod quickcheck_tests {
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
let sol1 = svd.solve(&b1, 1.0e-7);
let sol2 = svd.solve(&b2, 1.0e-7);
let sol1 = svd.solve(&b1, 1.0e-7).unwrap();
let sol2 = svd.solve(&b2, 1.0e-7).unwrap();
let recomp = svd.recompose();
let recomp = svd.recompose().unwrap();
if !relative_eq!(m, recomp, epsilon = 1.0e-6) {
println!("{}{}", m, recomp);
}
@ -263,22 +263,22 @@ fn svd_singular_horizontal() {
fn svd_zeros() {
let m = DMatrix::from_element(10, 10, 0.0);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
assert_eq!(Ok(m), svd.recompose());
}
#[test]
fn svd_identity() {
let m = DMatrix::<f64>::identity(10, 10);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
assert_eq!(Ok(m), svd.recompose());
let m = DMatrix::<f64>::identity(10, 15);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
assert_eq!(Ok(m), svd.recompose());
let m = DMatrix::<f64>::identity(15, 10);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
assert_eq!(Ok(m), svd.recompose());
}
#[test]
@ -295,7 +295,7 @@ fn svd_with_delimited_subproblem() {
m[(8,8)] = 16.0; m[(3,9)] = 17.0;
m[(9,9)] = 18.0;
let svd = m.clone().svd(true, true);
assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
assert!(relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7));
// Rectangular versions.
let mut m = DMatrix::<f64>::from_element(15, 10, 0.0);
@ -310,10 +310,10 @@ fn svd_with_delimited_subproblem() {
m[(8,8)] = 16.0; m[(3,9)] = 17.0;
m[(9,9)] = 18.0;
let svd = m.clone().svd(true, true);
assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
assert!(relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7));
let svd = m.transpose().svd(true, true);
assert!(relative_eq!(m.transpose(), svd.recompose(), epsilon = 1.0e-7));
assert!(relative_eq!(m.transpose(), svd.recompose().unwrap(), epsilon = 1.0e-7));
}
#[test]
@ -329,7 +329,15 @@ fn svd_fail() {
println!("Singular values: {}", svd.singular_values);
println!("u: {:.5}", svd.u.unwrap());
println!("v: {:.5}", svd.v_t.unwrap());
let recomp = svd.recompose();
let recomp = svd.recompose().unwrap();
println!("{:.5}{:.5}", m, recomp);
assert!(relative_eq!(m, recomp, epsilon = 1.0e-5));
}
#[test]
fn svd_err() {
let m = DMatrix::from_element(10, 10, 0.0);
let svd = m.clone().svd(false, false);
assert_eq!(Err("SVD recomposition: U and V^t have not been computed."), svd.clone().recompose());
assert_eq!(Err("SVD pseudo inverse: the epsilon must be non-negative."), svd.clone().pseudo_inverse(-1.0));
}