Merge branch 'dev' into master-public
# Conflicts: # src/linalg/svd.rs
This commit is contained in:
commit
82106caa9e
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@ -484,90 +484,94 @@ where
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/// Rebuild the original matrix.
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///
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/// This is useful if some of the singular values have been manually modified. Panics if the
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/// right- and left- singular vectors have not been computed at construction-time.
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pub fn recompose(self) -> MatrixMN<N, R, C> {
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let mut u = self.u.expect("SVD recomposition: U has not been computed.");
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let v_t = self
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.v_t
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.expect("SVD recomposition: V^t has not been computed.");
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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u.column_mut(i).mul_assign(val);
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/// This is useful if some of the singular values have been manually modified.
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/// Returns `Err` if the right- and left- singular vectors have not been
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/// computed at construction-time.
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pub fn recompose(self) -> Result<MatrixMN<N, R, C>, &'static str> {
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match (self.u, self.v_t) {
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(Some(mut u), Some(v_t)) => {
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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u.column_mut(i).mul_assign(val);
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}
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Ok(u * v_t)
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}
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(None, None) => Err("SVD recomposition: U and V^t have not been computed."),
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(None, _) => Err("SVD recomposition: U has not been computed."),
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(_, None) => Err("SVD recomposition: V^t has not been computed.")
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}
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u * v_t
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}
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/// Computes the pseudo-inverse of the decomposed matrix.
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///
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/// Any singular value smaller than `eps` is assumed to be zero.
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/// Panics if the right- and left- singular vectors have not been computed at
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/// construction-time.
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pub fn pseudo_inverse(mut self, eps: N) -> MatrixMN<N, C, R>
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where DefaultAllocator: Allocator<N, C, R> {
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assert!(
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eps >= N::zero(),
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"SVD pseudo inverse: the epsilon must be non-negative."
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);
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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if val > eps {
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self.singular_values[i] = N::one() / val;
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} else {
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self.singular_values[i] = N::zero();
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}
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/// Returns `Err` if the right- and left- singular vectors have not
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/// been computed at construction-time.
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pub fn pseudo_inverse(mut self, eps: N) -> Result<MatrixMN<N, C, R>, &'static str>
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where
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DefaultAllocator: Allocator<N, C, R>,
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{
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if eps < N::zero() {
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Err("SVD pseudo inverse: the epsilon must be non-negative.")
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}
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else {
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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self.recompose().transpose()
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if val > eps {
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self.singular_values[i] = N::one() / val;
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} else {
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self.singular_values[i] = N::zero();
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}
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}
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self.recompose().map(|m| m.transpose())
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}
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}
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/// Solves the system `self * x = b` where `self` is the decomposed matrix and `x` the unknown.
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///
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/// Any singular value smaller than `eps` is assumed to be zero.
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/// Returns `None` if the singular vectors `U` and `V` have not been computed.
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/// Returns `Err` if the singular vectors `U` and `V` have not been computed.
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// FIXME: make this more generic wrt the storage types and the dimensions for `b`.
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pub fn solve<R2: Dim, C2: Dim, S2>(
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&self,
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b: &Matrix<N, R2, C2, S2>,
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eps: N,
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) -> MatrixMN<N, C, C2>
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) -> Result<MatrixMN<N, C, C2>, &'static str>
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where
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S2: Storage<N, R2, C2>,
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DefaultAllocator: Allocator<N, C, C2> + Allocator<N, DimMinimum<R, C>, C2>,
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ShapeConstraint: SameNumberOfRows<R, R2>,
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{
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assert!(
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eps >= N::zero(),
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"SVD solve: the epsilon must be non-negative."
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);
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let u = self
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.u
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.as_ref()
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.expect("SVD solve: U has not been computed.");
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let v_t = self
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.v_t
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.as_ref()
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.expect("SVD solve: V^t has not been computed.");
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if eps < N::zero() {
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Err("SVD solve: the epsilon must be non-negative.")
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}
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else {
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match (&self.u, &self.v_t) {
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(Some(u), Some(v_t)) => {
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let mut ut_b = u.tr_mul(b);
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let mut ut_b = u.tr_mul(b);
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for j in 0..ut_b.ncols() {
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let mut col = ut_b.column_mut(j);
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for j in 0..ut_b.ncols() {
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let mut col = ut_b.column_mut(j);
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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if val > eps {
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col[i] /= val;
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} else {
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col[i] = N::zero();
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}
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}
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}
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for i in 0..self.singular_values.len() {
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let val = self.singular_values[i];
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if val > eps {
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col[i] /= val;
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} else {
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col[i] = N::zero();
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Ok(v_t.tr_mul(&ut_b))
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}
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(None, None) => Err("SVD solve: U and V^t have not been computed."),
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(None, _) => Err("SVD solve: U has not been computed."),
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(_, None) => Err("SVD solve: V^t has not been computed.")
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}
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}
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v_t.tr_mul(&ut_b)
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}
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}
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@ -624,8 +628,10 @@ where
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/// Computes the pseudo-inverse of this matrix.
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///
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/// All singular values below `eps` are considered equal to 0.
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pub fn pseudo_inverse(self, eps: N) -> MatrixMN<N, C, R>
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where DefaultAllocator: Allocator<N, C, R> {
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pub fn pseudo_inverse(self, eps: N) -> Result<MatrixMN<N, C, R>, &'static str>
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where
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DefaultAllocator: Allocator<N, C, R>,
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{
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SVD::new(self.clone_owned(), true, true).pseudo_inverse(eps)
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}
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}
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@ -10,7 +10,7 @@ mod quickcheck_tests {
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fn svd(m: DMatrix<f64>) -> bool {
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if m.len() > 0 {
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let svd = m.clone().svd(true, true);
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let recomp_m = svd.clone().recompose();
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let recomp_m = svd.clone().recompose().unwrap();
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let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
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let ds = DMatrix::from_diagonal(&s);
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@ -91,7 +91,7 @@ mod quickcheck_tests {
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fn svd_pseudo_inverse(m: DMatrix<f64>) -> bool {
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if m.len() > 0 {
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let svd = m.clone().svd(true, true);
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let pinv = svd.pseudo_inverse(1.0e-10);
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let pinv = svd.pseudo_inverse(1.0e-10).unwrap();
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if m.nrows() > m.ncols() {
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println!("{}", &pinv * &m);
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@ -118,10 +118,10 @@ mod quickcheck_tests {
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let b1 = DVector::new_random(n);
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let b2 = DMatrix::new_random(n, nb);
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let sol1 = svd.solve(&b1, 1.0e-7);
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let sol2 = svd.solve(&b2, 1.0e-7);
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let sol1 = svd.solve(&b1, 1.0e-7).unwrap();
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let sol2 = svd.solve(&b2, 1.0e-7).unwrap();
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let recomp = svd.recompose();
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let recomp = svd.recompose().unwrap();
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if !relative_eq!(m, recomp, epsilon = 1.0e-6) {
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println!("{}{}", m, recomp);
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}
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fn svd_zeros() {
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let m = DMatrix::from_element(10, 10, 0.0);
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let svd = m.clone().svd(true, true);
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assert_eq!(m, svd.recompose());
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assert_eq!(Ok(m), svd.recompose());
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}
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#[test]
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fn svd_identity() {
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let m = DMatrix::<f64>::identity(10, 10);
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let svd = m.clone().svd(true, true);
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assert_eq!(m, svd.recompose());
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assert_eq!(Ok(m), svd.recompose());
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let m = DMatrix::<f64>::identity(10, 15);
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let svd = m.clone().svd(true, true);
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assert_eq!(m, svd.recompose());
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assert_eq!(Ok(m), svd.recompose());
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let m = DMatrix::<f64>::identity(15, 10);
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let svd = m.clone().svd(true, true);
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assert_eq!(m, svd.recompose());
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assert_eq!(Ok(m), svd.recompose());
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}
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#[test]
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m[(8,8)] = 16.0; m[(3,9)] = 17.0;
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m[(9,9)] = 18.0;
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let svd = m.clone().svd(true, true);
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assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
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assert!(relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7));
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// Rectangular versions.
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let mut m = DMatrix::<f64>::from_element(15, 10, 0.0);
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@ -310,10 +310,10 @@ fn svd_with_delimited_subproblem() {
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m[(8,8)] = 16.0; m[(3,9)] = 17.0;
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m[(9,9)] = 18.0;
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let svd = m.clone().svd(true, true);
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assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
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assert!(relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7));
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let svd = m.transpose().svd(true, true);
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assert!(relative_eq!(m.transpose(), svd.recompose(), epsilon = 1.0e-7));
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assert!(relative_eq!(m.transpose(), svd.recompose().unwrap(), epsilon = 1.0e-7));
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}
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#[test]
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println!("Singular values: {}", svd.singular_values);
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println!("u: {:.5}", svd.u.unwrap());
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println!("v: {:.5}", svd.v_t.unwrap());
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let recomp = svd.recompose();
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let recomp = svd.recompose().unwrap();
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println!("{:.5}{:.5}", m, recomp);
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assert!(relative_eq!(m, recomp, epsilon = 1.0e-5));
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}
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#[test]
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fn svd_err() {
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let m = DMatrix::from_element(10, 10, 0.0);
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let svd = m.clone().svd(false, false);
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assert_eq!(Err("SVD recomposition: U and V^t have not been computed."), svd.clone().recompose());
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assert_eq!(Err("SVD pseudo inverse: the epsilon must be non-negative."), svd.clone().pseudo_inverse(-1.0));
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}
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