import pytest import numpy as np from scipy._lib._array_api import ( xp_assert_close, xp_assert_equal, xp_swapaxes, is_torch, make_xp_test_case, _xp_copy_to_numpy ) from scipy.ndimage import convolve1d # type: ignore[attr-defined] from scipy.signal import savgol_coeffs, savgol_filter from scipy.signal._savitzky_golay import _polyder skip_xp_backends = pytest.mark.skip_xp_backends xfail_xp_backends = pytest.mark.xfail_xp_backends pytestmark = pytest.mark.skip_xp_backends( "dask.array", reason="linalg.lstsq is missing rcond" ) def check_polyder(p, m, expected, xp): dp = _polyder(p, m, xp=xp) xp_assert_equal(dp, expected) def test_polyder(xp): cases = [ ([5], 0, [5]), ([5], 1, [0]), ([3, 2, 1], 0, [3, 2, 1]), ([3, 2, 1], 1, [6, 2]), ([3, 2, 1], 2, [6]), ([3, 2, 1], 3, [0]), ([[3, 2, 1], [5, 6, 7]], 0, [[3, 2, 1], [5, 6, 7]]), ([[3, 2, 1], [5, 6, 7]], 1, [[6, 2], [10, 6]]), ([[3, 2, 1], [5, 6, 7]], 2, [[6], [10]]), ([[3, 2, 1], [5, 6, 7]], 3, [[0], [0]]), ] for p, m, expected in cases: pp = xp.asarray(p) ee = xp.asarray(expected) check_polyder( pp.T if pp.ndim == 2 else pp, m, ee.T if ee.ndim ==2 else ee, xp ) #-------------------------------------------------------------------- # savgol_coeffs tests #-------------------------------------------------------------------- def alt_sg_coeffs(window_length, polyorder, pos, xp): """This is an alternative implementation of the SG coefficients. It uses numpy.polyfit and numpy.polyval. The results should be equivalent to those of savgol_coeffs(), but this implementation is slower. window_length should be odd. """ if pos is None: pos = window_length // 2 t = np.arange(window_length) unit = (t == pos).astype(int) h = np.polyval(np.polyfit(t, unit, polyorder), t) return xp.asarray(h) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_trivial(xp): # Test a trivial case of savgol_coeffs: polyorder = window_length - 1 h = savgol_coeffs(1, 0, xp=xp) xp_assert_close(h, xp.asarray([1.0], dtype=xp.float64)) h = savgol_coeffs(3, 2, xp=xp) xp_assert_close(h, xp.asarray([0.0, 1, 0], dtype=xp.float64), atol=1e-10) h = savgol_coeffs(5, 4, xp=xp) xp_assert_close(h, xp.asarray([0.0, 0, 1, 0, 0], dtype=xp.float64), atol=1e-10) h = savgol_coeffs(5, 4, pos=1, xp=xp) xp_assert_close(h, xp.asarray([0.0, 0, 0, 1, 0], dtype=xp.float64), atol=1e-10) h = savgol_coeffs(5, 4, pos=1, use='dot', xp=xp) xp_assert_close(h, xp.asarray([0.0, 1, 0, 0, 0], dtype=xp.float64), atol=1e-10) def compare_coeffs_to_alt(window_length, order, xp): # For the given window_length and order, compare the results # of savgol_coeffs and alt_sg_coeffs for pos from 0 to window_length - 1. # Also include pos=None. for pos in [None] + list(range(window_length)): h1 = savgol_coeffs(window_length, order, pos=pos, use='dot', xp=xp) h2 = alt_sg_coeffs(window_length, order, pos=pos, xp=xp) xp_assert_close( h1, h2, atol=2e-10, err_msg=f"window_length = {window_length}, order = {order}, pos = {pos}" ) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_compare(xp): # Compare savgol_coeffs() to alt_sg_coeffs(). for window_length in range(1, 8, 2): for order in range(window_length): compare_coeffs_to_alt(window_length, order, xp=xp) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_exact(xp): polyorder = 4 window_length = 9 halflen = window_length // 2 x = xp.linspace(0, 21, 43) delta = x[1] - x[0] # The data is a cubic polynomial. We'll use an order 4 # SG filter, so the filtered values should equal the input data # (except within half window_length of the edges). y = 0.5 * x ** 3 - x h = savgol_coeffs(window_length, polyorder, xp=xp) y0 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h))) xp_assert_close(y0[halflen:-halflen], y[halflen:-halflen]) # Check the same input, but use deriv=1. dy is the exact result. dy = 1.5 * x ** 2 - 1 h = savgol_coeffs(window_length, polyorder, deriv=1, delta=delta, xp=xp) y1 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h))) xp_assert_close(y1[halflen:-halflen], dy[halflen:-halflen]) # Check the same input, but use deriv=2. d2y is the exact result. d2y = 3.0 * x h = savgol_coeffs(window_length, polyorder, deriv=2, delta=delta, xp=xp) y2 = xp.asarray(convolve1d(_xp_copy_to_numpy(y), _xp_copy_to_numpy(h))) xp_assert_close(y2[halflen:-halflen], d2y[halflen:-halflen]) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_deriv(xp): # The data in `x` is a sampled parabola, so using savgol_coeffs with an # order 2 or higher polynomial should give exact results. i = xp.asarray([-2.0, 0.0, 2.0, 4.0, 6.0], dtype=xp.float64) x = i ** 2 / 4 dx = i / 2 d2x = xp.full_like(i, 0.5) for pos in range(x.shape[0]): coeffs0 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', xp=xp) xp_assert_close(coeffs0 @ x, x[pos], atol=1e-10) coeffs1 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=1, xp=xp) xp_assert_close(coeffs1 @ x, dx[pos], atol=1e-10) coeffs2 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=2, xp=xp) xp_assert_close(coeffs2 @ x , d2x[pos], atol=1e-10) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_deriv_gt_polyorder(xp): """ If deriv > polyorder, the coefficients should be all 0. This is a regression test for a bug where, e.g., savgol_coeffs(5, polyorder=1, deriv=2) raised an error. """ coeffs = savgol_coeffs(5, polyorder=1, deriv=2, xp=xp) xp_assert_equal(coeffs, xp.zeros(5, dtype=xp.float64)) coeffs = savgol_coeffs(7, polyorder=4, deriv=6, xp=xp) xp_assert_equal(coeffs, xp.zeros(7, dtype=xp.float64)) @xfail_xp_backends( "torch", reason="torch loses precision (worse with f32 default dtype)" ) @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_large(xp): # Test that for large values of window_length and polyorder the array of # coefficients returned is symmetric. The aim is to ensure that # no potential numeric overflow occurs. coeffs0 = savgol_coeffs(31, 9, xp=xp) xp_assert_close( coeffs0, xp.flip(coeffs0), atol=5e-4 if is_torch(xp) else 1.5e-6 ) coeffs1 = savgol_coeffs(31, 9, deriv=1, xp=xp) xp_assert_close( coeffs1, -xp.flip(coeffs1), atol=1.2e-2 if is_torch(xp) else 1.5e-6 ) # -------------------------------------------------------------------- # savgol_coeffs tests for even window length # -------------------------------------------------------------------- @make_xp_test_case(savgol_coeffs) def test_sg_coeffs_even_window_length(xp): # Simple case - deriv=0, polyorder=0, 1 window_lengths = [4, 6, 8, 10, 12, 14, 16] for length in window_lengths: h_p_d = savgol_coeffs(length, 0, 0, xp=xp) xp_assert_close(h_p_d, xp.ones_like(h_p_d) / length) # Verify with closed forms # deriv=1, polyorder=1, 2 def h_p_d_closed_form_1(k, m): return 6*(k - 0.5)/((2*m + 1)*m*(2*m - 1)) # deriv=2, polyorder=2 def h_p_d_closed_form_2(k, m): numer = 15*(-4*m**2 + 1 + 12*(k - 0.5)**2) denom = 4*(2*m + 1)*(m + 1)*m*(m - 1)*(2*m - 1) return numer/denom for length in window_lengths: m = length//2 expected_output = [h_p_d_closed_form_1(k, m) for k in range(-m + 1, m + 1)][::-1] expected_output = xp.asarray(expected_output, dtype=xp.float64) actual_output = savgol_coeffs(length, 1, 1, xp=xp) xp_assert_close(actual_output, expected_output) actual_output = savgol_coeffs(length, 2, 1, xp=xp) xp_assert_close(actual_output, expected_output) expected_output = [h_p_d_closed_form_2(k, m) for k in range(-m + 1, m + 1)][::-1] expected_output = xp.asarray(expected_output, dtype=xp.float64) actual_output = savgol_coeffs(length, 2, 2, xp=xp) xp_assert_close(actual_output, expected_output) actual_output = savgol_coeffs(length, 3, 2, xp=xp) xp_assert_close(actual_output, expected_output) #-------------------------------------------------------------------- # savgol_filter tests #-------------------------------------------------------------------- @make_xp_test_case(savgol_filter) def test_sg_filter_trivial(xp): """ Test some trivial edge cases for savgol_filter().""" x = xp.asarray([1.0]) y = savgol_filter(x, 1, 0) xp_assert_equal(y, xp.asarray([1.0])) # Input is a single value. With a window length of 3 and polyorder 1, # the value in y is from the straight-line fit of (-1,0), (0,3) and # (1, 0) at 0. This is just the average of the three values, hence 1.0. x = xp.asarray([3.0]) y = savgol_filter(x, 3, 1, mode='constant') xp_assert_close(y, xp.asarray([1.0]), atol=1.5e-15) x = xp.asarray([3.0]) y = savgol_filter(x, 3, 1, mode='nearest') xp_assert_close(y, xp.asarray([3.0]), atol=1.5e-15) x = xp.asarray([1.0] * 3) y = savgol_filter(x, 3, 1, mode='wrap') xp_assert_close(y, xp.asarray([1.0, 1.0, 1.0]), atol=1.5e-15) @make_xp_test_case(savgol_filter) def test_sg_filter_basic(xp): # Some basic test cases for savgol_filter(). x = xp.asarray([1.0, 2.0, 1.0]) y = savgol_filter(x, 3, 1, mode='constant') xp_assert_close(y, xp.asarray([1.0, 4.0 / 3, 1.0])) y = savgol_filter(x, 3, 1, mode='mirror') xp_assert_close(y, xp.asarray([5.0 / 3, 4.0 / 3, 5.0 / 3])) y = savgol_filter(x, 3, 1, mode='wrap') xp_assert_close(y, xp.asarray([4.0 / 3, 4.0 / 3, 4.0 / 3])) @make_xp_test_case(savgol_filter) def test_sg_filter_2d(xp): x = xp.asarray([[1.0, 2.0, 1.0], [2.0, 4.0, 2.0]]) expected = xp.asarray([[1.0, 4.0 / 3, 1.0], [2.0, 8.0 / 3, 2.0]]) y = savgol_filter(x, 3, 1, mode='constant') xp_assert_close(y, expected) y = savgol_filter(x.T, 3, 1, mode='constant', axis=0) xp_assert_close(y, expected.T) @make_xp_test_case(savgol_filter) def test_sg_filter_interp_edges(xp): # Another test with low degree polynomial data, for which we can easily # give the exact results. In this test, we use mode='interp', so # savgol_filter should match the exact solution for the entire data set, # including the edges. t = xp.linspace(-5, 5, 21, dtype=xp.float64) delta = t[1] - t[0] # Polynomial test data. x = xp.stack([t, 3 * t ** 2, t ** 3 - t]) dx = xp.stack([xp.ones_like(t), 6 * t, 3 * t ** 2 - 1.0]) d2x = xp.stack([xp.zeros_like(t), xp.full_like(t, 6), 6 * t]) window_length = 7 y = savgol_filter(x, window_length, 3, axis=-1, mode='interp') xp_assert_close(y, x, atol=1e-12) y1 = savgol_filter(x, window_length, 3, axis=-1, mode='interp', deriv=1, delta=delta) xp_assert_close(y1, dx, atol=1e-12) y2 = savgol_filter(x, window_length, 3, axis=-1, mode='interp', deriv=2, delta=delta) xp_assert_close(y2, d2x, atol=1e-12) # Transpose everything, and test again with axis=0. x = x.T dx = dx.T d2x = d2x.T y = savgol_filter(x, window_length, 3, axis=0, mode='interp') xp_assert_close(y, x, atol=1e-12) y1 = savgol_filter(x, window_length, 3, axis=0, mode='interp', deriv=1, delta=delta) xp_assert_close(y1, dx, atol=1e-12) y2 = savgol_filter(x, window_length, 3, axis=0, mode='interp', deriv=2, delta=delta) xp_assert_close(y2, d2x, atol=1e-12) @make_xp_test_case(savgol_filter) def test_sg_filter_interp_edges_3d(xp): # Test mode='interp' with a 3-D array. t = xp.linspace(-5, 5, 21) delta = t[1] - t[0] x1 = xp.stack([t, -t]) x2 = xp.stack([t ** 2, 3 * t ** 2 + 5]) x3 = xp.stack([t ** 3, 2 * t ** 3 + t ** 2 - 0.5 * t]) dx1 = xp.stack([xp.ones_like(t), -xp.ones_like(t)]) dx2 = xp.stack([2 * t, 6 * t]) dx3 = xp.stack([3 * t ** 2, 6 * t ** 2 + 2 * t - 0.5]) # z has shape (3, 2, 21) z = xp.stack([x1, x2, x3]) dz = xp.stack([dx1, dx2, dx3]) y = savgol_filter(z, 7, 3, axis=-1, mode='interp', delta=delta) xp_assert_close(y, z, atol=1e-10) dy = savgol_filter(z, 7, 3, axis=-1, mode='interp', deriv=1, delta=delta) xp_assert_close(dy, dz, atol=1e-10) # z has shape (3, 21, 2) z = xp.stack([x1.T, x2.T, x3.T]) dz = xp.stack([dx1.T, dx2.T, dx3.T]) y = savgol_filter(z, 7, 3, axis=1, mode='interp', delta=delta) xp_assert_close(y, z, atol=1e-10) dy = savgol_filter(z, 7, 3, axis=1, mode='interp', deriv=1, delta=delta) xp_assert_close(dy, dz, atol=1e-10) # z has shape (21, 3, 2) z = xp.asarray(xp_swapaxes(z, 0, 1, xp=xp), copy=True) dz = xp.asarray(xp_swapaxes(dz, 0, 1, xp=xp), copy=True) y = savgol_filter(z, 7, 3, axis=0, mode='interp', delta=delta) xp_assert_close(y, z, atol=1e-10) dy = savgol_filter(z, 7, 3, axis=0, mode='interp', deriv=1, delta=delta) xp_assert_close(dy, dz, atol=1e-10) @make_xp_test_case(savgol_filter) def test_sg_filter_valid_window_length_3d(xp): """Tests that the window_length check is using the correct axis.""" x = xp.ones((10, 20, 30)) savgol_filter(x, window_length=29, polyorder=3, mode='interp') with pytest.raises(ValueError, match='window_length must be less than'): # window_length is more than x.shape[-1]. savgol_filter(x, window_length=31, polyorder=3, mode='interp') savgol_filter(x, window_length=9, polyorder=3, axis=0, mode='interp') with pytest.raises(ValueError, match='window_length must be less than'): # window_length is more than x.shape[0]. savgol_filter(x, window_length=11, polyorder=3, axis=0, mode='interp')