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Revise tests for least-square problems #227
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9cf8331
Move test of least_squares into tests/, and minor cleanup
termoshtt e51f966
Rewrite test cases
termoshtt a8a07fb
Test for F-continuous and complex cases
termoshtt 05a2bcd
Fix F-contiguous case
termoshtt 6bbe87d
Add tests for multi-column `b`
termoshtt b60cfc8
Comment out Unsupported C/F-mixed cases
termoshtt f6a9c2a
Fix memory layout for overdetermined case
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,129 @@ | ||
| /// Solve least square problem `|b - Ax|` | ||
| use approx::AbsDiffEq; | ||
| use ndarray::*; | ||
| use ndarray_linalg::*; | ||
|
|
||
| /// A is square. `x = A^{-1} b`, `|b - Ax| = 0` | ||
| fn test_exact<T: Scalar + Lapack>(a: Array2<T>) { | ||
| let b: Array1<T> = random(3); | ||
| let result = a.least_squares(&b).unwrap(); | ||
| // unpack result | ||
| let x = result.solution; | ||
| let residual_l2_square = result.residual_sum_of_squares.unwrap()[()]; | ||
|
|
||
| // must be full-rank | ||
| assert_eq!(result.rank, 3); | ||
|
|
||
| // |b - Ax| == 0 | ||
| assert!(residual_l2_square < T::real(1.0e-4)); | ||
|
|
||
| // b == Ax | ||
| let ax = a.dot(&x); | ||
| assert_close_l2!(&b, &ax, T::real(1.0e-4)); | ||
| } | ||
|
|
||
| macro_rules! impl_exact { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _exact>]() { | ||
| let a: Array2<f64> = random((3, 3)); | ||
| test_exact(a) | ||
| } | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _exact_t>]() { | ||
| let a: Array2<f64> = random((3, 3).f()); | ||
| test_exact(a) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_exact!(f32); | ||
| impl_exact!(f64); | ||
| impl_exact!(c32); | ||
| impl_exact!(c64); | ||
|
|
||
| /// #column < #row case. | ||
| /// Linear problem is overdetermined, `|b - Ax| > 0`. | ||
| fn test_overdetermined<T: Scalar + Lapack>(a: Array2<T>) | ||
| where | ||
| T::Real: AbsDiffEq<Epsilon = T::Real>, | ||
| { | ||
| let b: Array1<T> = random(4); | ||
| let result = a.least_squares(&b).unwrap(); | ||
| // unpack result | ||
| let x = result.solution; | ||
| let residual_l2_square = result.residual_sum_of_squares.unwrap()[()]; | ||
|
|
||
| // Must be full-rank | ||
| assert_eq!(result.rank, 3); | ||
|
|
||
| // eval `residual = b - Ax` | ||
| let residual = &b - &a.dot(&x); | ||
| assert!(residual_l2_square.abs_diff_eq(&residual.norm_l2().powi(2), T::real(1.0e-4))); | ||
|
|
||
| // `|residual| < |b|` | ||
| assert!(residual.norm_l2() < b.norm_l2()); | ||
| } | ||
|
|
||
| macro_rules! impl_overdetermined { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined>]() { | ||
| let a: Array2<f64> = random((4, 3)); | ||
| test_overdetermined(a) | ||
| } | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined_t>]() { | ||
| let a: Array2<f64> = random((4, 3).f()); | ||
| test_overdetermined(a) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_overdetermined!(f32); | ||
| impl_overdetermined!(f64); | ||
| impl_overdetermined!(c32); | ||
| impl_overdetermined!(c64); | ||
|
|
||
| /// #column > #row case. | ||
| /// Linear problem is underdetermined, `|b - Ax| = 0` and `x` is not unique | ||
| fn test_underdetermined<T: Scalar + Lapack>(a: Array2<T>) { | ||
| let b: Array1<T> = random(3); | ||
| let result = a.least_squares(&b).unwrap(); | ||
| assert_eq!(result.rank, 3); | ||
| assert!(result.residual_sum_of_squares.is_none()); | ||
|
|
||
| // b == Ax | ||
| let x = result.solution; | ||
| let ax = a.dot(&x); | ||
| assert_close_l2!(&b, &ax, T::real(1.0e-4)); | ||
| } | ||
|
|
||
| macro_rules! impl_underdetermined { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined>]() { | ||
| let a: Array2<f64> = random((3, 4)); | ||
| test_underdetermined(a) | ||
| } | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined_t>]() { | ||
| let a: Array2<f64> = random((3, 4).f()); | ||
| test_underdetermined(a) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_underdetermined!(f32); | ||
| impl_underdetermined!(f64); | ||
| impl_underdetermined!(c32); | ||
| impl_underdetermined!(c64); | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,201 @@ | ||
| /// Solve least square problem `|b - Ax|` with multi-column `b` | ||
| use approx::AbsDiffEq; | ||
| use ndarray::*; | ||
| use ndarray_linalg::*; | ||
|
|
||
| /// A is square. `x = A^{-1} b`, `|b - Ax| = 0` | ||
| fn test_exact<T: Scalar + Lapack>(a: Array2<T>, b: Array2<T>) { | ||
| assert_eq!(a.layout().unwrap().size(), (3, 3)); | ||
| assert_eq!(b.layout().unwrap().size(), (3, 2)); | ||
|
|
||
| let result = a.least_squares(&b).unwrap(); | ||
| // unpack result | ||
| let x: Array2<T> = result.solution; | ||
| let residual_l2_square: Array1<T::Real> = result.residual_sum_of_squares.unwrap(); | ||
|
|
||
| // must be full-rank | ||
| assert_eq!(result.rank, 3); | ||
|
|
||
| // |b - Ax| == 0 | ||
| for &residual in &residual_l2_square { | ||
| assert!(residual < T::real(1.0e-4)); | ||
| } | ||
|
|
||
| // b == Ax | ||
| let ax = a.dot(&x); | ||
| assert_close_l2!(&b, &ax, T::real(1.0e-4)); | ||
| } | ||
|
|
||
| macro_rules! impl_exact { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _exact_ac_bc>]() { | ||
| let a: Array2<f64> = random((3, 3)); | ||
| let b: Array2<f64> = random((3, 2)); | ||
| test_exact(a, b) | ||
| } | ||
|
|
||
| /* Unsupported currently. See https://github.com/rust-ndarray/ndarray-linalg/issues/234 | ||
| #[test] | ||
| fn [<least_squares_ $scalar _exact_ac_bf>]() { | ||
| let a: Array2<f64> = random((3, 3)); | ||
| let b: Array2<f64> = random((3, 2).f()); | ||
| test_exact(a, b) | ||
| } | ||
| #[test] | ||
| fn [<least_squares_ $scalar _exact_af_bc>]() { | ||
| let a: Array2<f64> = random((3, 3).f()); | ||
| let b: Array2<f64> = random((3, 2)); | ||
| test_exact(a, b) | ||
| } | ||
| */ | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _exact_af_bf>]() { | ||
| let a: Array2<f64> = random((3, 3).f()); | ||
| let b: Array2<f64> = random((3, 2).f()); | ||
| test_exact(a, b) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_exact!(f32); | ||
| impl_exact!(f64); | ||
| impl_exact!(c32); | ||
| impl_exact!(c64); | ||
|
|
||
| /// #column < #row case. | ||
| /// Linear problem is overdetermined, `|b - Ax| > 0`. | ||
| fn test_overdetermined<T: Scalar + Lapack>(a: Array2<T>, bs: Array2<T>) | ||
| where | ||
| T::Real: AbsDiffEq<Epsilon = T::Real>, | ||
| { | ||
| assert_eq!(a.layout().unwrap().size(), (4, 3)); | ||
| assert_eq!(bs.layout().unwrap().size(), (4, 2)); | ||
|
|
||
| let result = a.least_squares(&bs).unwrap(); | ||
| // unpack result | ||
| let xs = result.solution; | ||
| let residual_l2_square = result.residual_sum_of_squares.unwrap(); | ||
|
|
||
| // Must be full-rank | ||
| assert_eq!(result.rank, 3); | ||
|
|
||
| for j in 0..2 { | ||
| let b = bs.index_axis(Axis(1), j); | ||
| let x = xs.index_axis(Axis(1), j); | ||
| let residual = &b - &a.dot(&x); | ||
| let residual_l2_sq = residual_l2_square[j]; | ||
| assert!(residual_l2_sq.abs_diff_eq(&residual.norm_l2().powi(2), T::real(1.0e-4))); | ||
|
|
||
| // `|residual| < |b|` | ||
| assert!(residual.norm_l2() < b.norm_l2()); | ||
| } | ||
| } | ||
|
|
||
| macro_rules! impl_overdetermined { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined_ac_bc>]() { | ||
| let a: Array2<f64> = random((4, 3)); | ||
| let b: Array2<f64> = random((4, 2)); | ||
| test_overdetermined(a, b) | ||
| } | ||
|
|
||
| /* Unsupported currently. See https://github.com/rust-ndarray/ndarray-linalg/issues/234 | ||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined_af_bc>]() { | ||
| let a: Array2<f64> = random((4, 3).f()); | ||
| let b: Array2<f64> = random((4, 2)); | ||
| test_overdetermined(a, b) | ||
| } | ||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined_ac_bf>]() { | ||
| let a: Array2<f64> = random((4, 3)); | ||
| let b: Array2<f64> = random((4, 2).f()); | ||
| test_overdetermined(a, b) | ||
| } | ||
| */ | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _overdetermined_af_bf>]() { | ||
| let a: Array2<f64> = random((4, 3).f()); | ||
| let b: Array2<f64> = random((4, 2).f()); | ||
| test_overdetermined(a, b) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_overdetermined!(f32); | ||
| impl_overdetermined!(f64); | ||
| impl_overdetermined!(c32); | ||
| impl_overdetermined!(c64); | ||
|
|
||
| /// #column > #row case. | ||
| /// Linear problem is underdetermined, `|b - Ax| = 0` and `x` is not unique | ||
| fn test_underdetermined<T: Scalar + Lapack>(a: Array2<T>, b: Array2<T>) { | ||
| assert_eq!(a.layout().unwrap().size(), (3, 4)); | ||
| assert_eq!(b.layout().unwrap().size(), (3, 2)); | ||
|
|
||
| let result = a.least_squares(&b).unwrap(); | ||
| assert_eq!(result.rank, 3); | ||
| assert!(result.residual_sum_of_squares.is_none()); | ||
|
|
||
| // b == Ax | ||
| let x = result.solution; | ||
| let ax = a.dot(&x); | ||
| assert_close_l2!(&b, &ax, T::real(1.0e-4)); | ||
| } | ||
|
|
||
| macro_rules! impl_underdetermined { | ||
| ($scalar:ty) => { | ||
| paste::item! { | ||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined_ac_bc>]() { | ||
| let a: Array2<f64> = random((3, 4)); | ||
| let b: Array2<f64> = random((3, 2)); | ||
| test_underdetermined(a, b) | ||
| } | ||
|
|
||
| /* Unsupported currently. See https://github.com/rust-ndarray/ndarray-linalg/issues/234 | ||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined_af_bc>]() { | ||
| let a: Array2<f64> = random((3, 4).f()); | ||
| let b: Array2<f64> = random((3, 2)); | ||
| test_underdetermined(a, b) | ||
| } | ||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined_ac_bf>]() { | ||
| let a: Array2<f64> = random((3, 4)); | ||
| let b: Array2<f64> = random((3, 2).f()); | ||
| test_underdetermined(a, b) | ||
| } | ||
| */ | ||
|
|
||
| #[test] | ||
| fn [<least_squares_ $scalar _underdetermined_af_bf>]() { | ||
| let a: Array2<f64> = random((3, 4).f()); | ||
| let b: Array2<f64> = random((3, 2).f()); | ||
| test_underdetermined(a, b) | ||
| } | ||
| } | ||
| }; | ||
| } | ||
|
|
||
| impl_underdetermined!(f32); | ||
| impl_underdetermined!(f64); | ||
| impl_underdetermined!(c32); | ||
| impl_underdetermined!(c64); |
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s/f64/$scalar/g