From 3bc4fa33c3ec9272fed565260677518dcf5957fe Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 03:34:42 +0300 Subject: [PATCH 01/32] change version to 0.10.0.dev0 --- csaps/_version.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/csaps/_version.py b/csaps/_version.py index d452437..829ff4e 100644 --- a/csaps/_version.py +++ b/csaps/_version.py @@ -1,3 +1,3 @@ # -*- coding: utf-8 -*- -__version__ = '0.9.0' +__version__ = '0.10.0.dev0' From ce64a92598a7b2f430d9827c06e0edc4e401cdd4 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 03:46:08 +0300 Subject: [PATCH 02/32] compute coeffs without heavy reshape 'F' --- csaps/_sspumv.py | 16 +++++++--------- 1 file changed, 7 insertions(+), 9 deletions(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index 0e1581a..a738cda 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -235,6 +235,7 @@ def trace(m: sp.dia_matrix): return 1. / (1. + trace(a) / (6. * trace(b))) + @profile def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, float]: pcount = self._xdata.size dx = np.diff(self._xdata) @@ -286,15 +287,12 @@ def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, flo c3 = np.vstack((d_pad, p * u, d_pad)) c2 = np.diff(yi, axis=0) / dx - dx * (2. * c3[:-1, :] + c3[1:, :]) - coeffs = np.hstack(( - (np.diff(c3, axis=0) / dx).T, - 3. * c3[:-1, :].T, - c2.T, - yi[:-1, :].T - )) - - cf_shape = ((pcount - 1) * self._ydim, 4) - coeffs = coeffs.reshape(cf_shape, order='F') + coeffs = np.stack(( + (np.diff(c3, axis=0) / dx).ravel(), + 3. * c3[:-1, :].ravel(), + c2.ravel(), + yi[:-1, :].ravel() + ), axis=1) else: p = 1. yi = self._ydata[:, 0][:, np.newaxis] From 075ffbfb2ae9b18d1a02b034efb1cda8d910a8a5 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 11:14:26 +0300 Subject: [PATCH 03/32] remove 'profile' decorator --- csaps/_sspumv.py | 1 - 1 file changed, 1 deletion(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index a738cda..631583b 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -235,7 +235,6 @@ def trace(m: sp.dia_matrix): return 1. / (1. + trace(a) / (6. * trace(b))) - @profile def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, float]: pcount = self._xdata.size dx = np.diff(self._xdata) From 07d15d771cebfe5714c620496d8b51c5f3ee71c3 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 12:45:03 +0300 Subject: [PATCH 04/32] use numpy.pad instead of vstack --- csaps/_sspumv.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index 631583b..beaadf2 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -277,13 +277,13 @@ def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, flo u = u.T dx = dx[:, np.newaxis] - d_pad = np.zeros((1, self._ydim)) - d1 = np.diff(np.vstack((d_pad, u, d_pad)), axis=0) / dx - d2 = np.diff(np.vstack((d_pad, d1, d_pad)), axis=0) + pad_width = [(1, 1), (0, 0)] + d1 = np.diff(np.pad(u, pad_width), axis=0) / dx + d2 = np.diff(np.pad(d1, pad_width), axis=0) yi = self._ydata.T - ((6. * (1. - p)) * w) @ d2 - c3 = np.vstack((d_pad, p * u, d_pad)) + c3 = np.pad(p * u, pad_width) c2 = np.diff(yi, axis=0) / dx - dx * (2. * c3[:-1, :] + c3[1:, :]) coeffs = np.stack(( From c20a447280fce41651ad16be205d9703837f5871 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 12:55:37 +0300 Subject: [PATCH 05/32] update deps --- setup.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/setup.py b/setup.py index e3c8830..aa87feb 100644 --- a/setup.py +++ b/setup.py @@ -29,8 +29,8 @@ def _get_long_description(): packages=['csaps'], python_requires='>=3.6, <4', install_requires=[ - 'numpy >=0.12.1, <1.20.0', - 'scipy >=0.19.1, <1.6.0', + 'numpy >=1.11.0, <1.20.0', + 'scipy >=1.0.0, <1.6.0', ], extras_require={ 'docs': [ From baaceed26b14a544fb9cbe2cc083e295530fa52e Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 8 Feb 2020 21:53:19 +0300 Subject: [PATCH 06/32] a slight changes of error messages --- csaps/_sspumv.py | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index beaadf2..b2c86b6 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -165,7 +165,7 @@ def __call__(self, xi: UnivariateDataType) -> np.ndarray: xi = ty.cast(np.ndarray, np.asarray(xi, dtype=np.float64)) if xi.ndim > 1: # pragma: no cover - raise ValueError('"xi" data must be a 1-d array.') + raise ValueError("'xi' data must be a 1-d array.") return self._spline.evaluate(xi) @@ -197,16 +197,16 @@ def _prepare_data(xdata, ydata, weights, axis): ydata = np.asarray(ydata, dtype=np.float64) if xdata.ndim > 1: - raise ValueError('xdata must be a vector') + raise ValueError("'xdata' must be a vector") if xdata.size < 2: - raise ValueError('xdata must contain at least 2 data points.') + raise ValueError("'xdata' must contain at least 2 data points.") yshape = list(ydata.shape) if yshape[axis] != xdata.size: raise ValueError( - f'"ydata" data must be a 1-D or N-D array with shape[{axis}] ' - f'that is equal to "xdata" size ({xdata.size})') + f"'ydata' data must be a 1-D or N-D array with shape[{axis}] " + f"that is equal to 'xdata' size ({xdata.size})") # Reshape ydata N-D array to 2-D NxM array where N is the data # dimension and M is the number of data points. @@ -240,7 +240,8 @@ def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, flo dx = np.diff(self._xdata) if not all(dx > 0): # pragma: no cover - raise ValueError('Items of xdata vector must satisfy the condition: x1 < x2 < ... < xN') + raise ValueError( + "Items of 'xdata' vector must satisfy the condition: x1 < x2 < ... < xN") dy = np.diff(self._ydata, axis=1) dy_dx = dy / dx From 8e6f8023aa7c34c877093b6ea33cce75e0c4c564 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sun, 9 Feb 2020 01:57:38 +0300 Subject: [PATCH 07/32] refactoring SplinePPForm evaluate code - remove superfluous array operations --- csaps/_sspumv.py | 16 ++++++---------- 1 file changed, 6 insertions(+), 10 deletions(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index b2c86b6..33ce9d0 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -89,23 +89,19 @@ def evaluate(self, xi: np.ndarray) -> np.ndarray: lx = len(xi) if d > 1: - xi_shape = (1, d * lx) - xi_ndm = np.array(xi, ndmin=2) - xi = np.reshape(np.repeat(xi_ndm, d, axis=0), xi_shape, order='F') - - index_rep = (np.repeat(np.array(1 + d * index, ndmin=2), d, axis=0) - + np.repeat(np.array(np.r_[-d:0], ndmin=2).T, lx, axis=1)) - index = np.reshape(index_rep, (d * lx, 1), order='F') + xi = np.repeat(xi, d, axis=0).T.flatten() + index_mat = (1 + d * index)[np.newaxis] + np.r_[-d:0][np.newaxis].T + index = index_mat.T.flatten() index -= 1 # Apply nested multiplication - values = self._coeffs[index, 0].T + values = self._coeffs[index, 0] for i in range(1, self._coeffs.shape[1]): - values = xi * values + self._coeffs[index, i].T + values = xi * values + self._coeffs[index, i] - values = values.reshape((d, lx), order='F').squeeze() + values = values.reshape((lx, d)).T if values.shape != shape: # Reshape values 2-D NxM array to N-D array with original shape From 93738a9af5096e75f1d6d31d2617c381c8ee882d Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sun, 9 Feb 2020 02:27:23 +0300 Subject: [PATCH 08/32] remove superfluous array operations --- csaps/_sspumv.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index 33ce9d0..0203cb1 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -89,7 +89,7 @@ def evaluate(self, xi: np.ndarray) -> np.ndarray: lx = len(xi) if d > 1: - xi = np.repeat(xi, d, axis=0).T.flatten() + xi = np.repeat(xi, d) index_mat = (1 + d * index)[np.newaxis] + np.r_[-d:0][np.newaxis].T index = index_mat.T.flatten() From 959184121907e9a3e171ae61dc63d1bb690f46c6 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sun, 9 Feb 2020 19:06:04 +0300 Subject: [PATCH 09/32] remove superfluous dimension in nd-grid spline coeffs - currently, we do not support vectorization for nd-grid case and we do not need additional dimension in coefficients array --- csaps/_sspndg.py | 32 +++++++++++++++++--------------- tests/test_ndgrid.py | 16 ++++++++++++++++ 2 files changed, 33 insertions(+), 15 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index c0948d4..2443636 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -47,7 +47,7 @@ def __init__(self, breaks: ty.Sequence[np.ndarray], coeffs: np.ndarray) -> None: self._breaks = breaks self._coeffs = coeffs self._pieces = tuple(x.size - 1 for x in breaks) - self._order = tuple(s // p for s, p in zip(coeffs.shape[1:], self._pieces)) + self._order = tuple(s // p for s, p in zip(coeffs.shape, self._pieces)) self._ndim = len(breaks) @property @@ -75,15 +75,17 @@ def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: sizey = list(yi.shape) nsize = tuple(x.size for x in xi) + d = self.ndim - 1 + for i in reversed(range(self.ndim)): - ndim = int(np.prod(sizey[:self.ndim])) + ndim = int(np.prod(sizey[:d])) coeffs = yi.reshape((ndim * self.pieces[i], self.order[i]), order='F') spp = SplinePPForm(self.breaks[i], coeffs, ndim=ndim, shape=(ndim, xi[i].size)) yi = spp.evaluate(xi[i]) - yi = yi.reshape((*sizey[:self.ndim], nsize[i]), order='F') - axes = (0, self.ndim, *range(1, self.ndim)) + yi = yi.reshape((*sizey[:d], nsize[i]), order='F') + axes = (d, *range(d)) yi = yi.transpose(axes) sizey = list(yi.shape) @@ -209,25 +211,25 @@ def __call__(self, xi: NdGridDataType) -> np.ndarray: return self._spline.evaluate(xi) def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSplinePPForm, ty.Tuple[float, ...]]: - sizey = [1] + list(self._ydata.shape) - ydata = self._ydata.reshape(sizey, order='F').copy() - _smooth = [] + sizey = list(self._ydata.shape) + coeffs = self._ydata.reshape(sizey, order='F').copy() + smooths = [] - # Perform coordinatewise smoothing spline computing + # computing coordinatewise smoothing spline for i in reversed(range(self._ndim)): shape_i = (np.prod(sizey[:-1]), sizey[-1]) - ydata_i = ydata.reshape(shape_i, order='F') + ydata_i = coeffs.reshape(shape_i, order='F') s = CubicSmoothingSpline( self._xdata[i], ydata_i, weights=self._weights[i], smooth=smooth[i]) - _smooth.append(s.smooth) + smooths.append(s.smooth) sizey[-1] = s.spline.pieces * s.spline.order - ydata = s.spline.coeffs.reshape(sizey, order='F') + coeffs = s.spline.coeffs.reshape(sizey, order='F') if self._ndim > 1: - axes = (0, self._ndim, *range(1, self._ndim)) - ydata = ydata.transpose(axes) - sizey = list(ydata.shape) + axes = (self._ndim - 1, *range(self._ndim - 1)) + coeffs = coeffs.transpose(axes) + sizey = list(coeffs.shape) - return NdGridSplinePPForm(self._xdata, ydata), tuple(_smooth) + return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(smooths) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index 075fb9a..d418eab 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -41,3 +41,19 @@ def test_surface(): assert len(sp.smooth) == 2 assert isinstance(sp.spline, csaps.NdGridSplinePPForm) assert noisy_s.shape == noisy.shape + + +def test_volume(): + xdata = [ + np.linspace(-3, 3, 21), + np.linspace(-3.5, 3.5, 31), + np.linspace(-2.5, 2.5, 41), + ] + + np.random.seed(12345) + ydata = np.random.randn(21, 31, 41) + + sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata) + ydata_s = sp(xdata) + + assert ydata_s.shape == ydata.shape From 93205bc0794a108d646aecddeee11ced0aff049c Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sun, 9 Feb 2020 19:14:11 +0300 Subject: [PATCH 10/32] a slight refactoring --- csaps/_sspndg.py | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 2443636..845055c 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -76,6 +76,7 @@ def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: nsize = tuple(x.size for x in xi) d = self.ndim - 1 + permute_axes = (d, *range(d)) for i in reversed(range(self.ndim)): ndim = int(np.prod(sizey[:d])) @@ -85,8 +86,7 @@ def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: yi = spp.evaluate(xi[i]) yi = yi.reshape((*sizey[:d], nsize[i]), order='F') - axes = (d, *range(d)) - yi = yi.transpose(axes) + yi = yi.transpose(permute_axes) sizey = list(yi.shape) return yi.reshape(nsize, order='F') @@ -215,6 +215,8 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp coeffs = self._ydata.reshape(sizey, order='F').copy() smooths = [] + permute_axes = (self._ndim - 1, *range(self._ndim - 1)) + # computing coordinatewise smoothing spline for i in reversed(range(self._ndim)): shape_i = (np.prod(sizey[:-1]), sizey[-1]) @@ -228,8 +230,7 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp coeffs = s.spline.coeffs.reshape(sizey, order='F') if self._ndim > 1: - axes = (self._ndim - 1, *range(self._ndim - 1)) - coeffs = coeffs.transpose(axes) + coeffs = coeffs.transpose(permute_axes) sizey = list(coeffs.shape) return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(smooths) From a48085bc8a84f417fad4ae5c358a71dfa0d0570b Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Mon, 10 Feb 2020 12:48:53 +0300 Subject: [PATCH 11/32] remove extra reshape --- csaps/_sspndg.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 845055c..8339e91 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -212,7 +212,7 @@ def __call__(self, xi: NdGridDataType) -> np.ndarray: def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSplinePPForm, ty.Tuple[float, ...]]: sizey = list(self._ydata.shape) - coeffs = self._ydata.reshape(sizey, order='F').copy() + coeffs = self._ydata.copy() smooths = [] permute_axes = (self._ndim - 1, *range(self._ndim - 1)) From a818adcd143c570d0eac173f22a60a1831f03847 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Mon, 10 Feb 2020 14:20:54 +0300 Subject: [PATCH 12/32] use to_2d for higher performance --- csaps/_sspndg.py | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 8339e91..c77632c 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -13,6 +13,7 @@ from ._base import SplinePPFormBase, ISmoothingSpline from ._types import UnivariateDataType, NdGridDataType from ._sspumv import SplinePPForm, CubicSmoothingSpline +from ._reshape import to_2d def ndgrid_prepare_data_sites(data, name) -> ty.Tuple[np.ndarray, ...]: @@ -85,11 +86,10 @@ def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: spp = SplinePPForm(self.breaks[i], coeffs, ndim=ndim, shape=(ndim, xi[i].size)) yi = spp.evaluate(xi[i]) - yi = yi.reshape((*sizey[:d], nsize[i]), order='F') - yi = yi.transpose(permute_axes) + yi = yi.reshape((*sizey[:d], nsize[i]), order='F').transpose(permute_axes) sizey = list(yi.shape) - return yi.reshape(nsize, order='F') + return yi.reshape(nsize) class NdGridCubicSmoothingSpline(ISmoothingSpline[NdGridSplinePPForm, ty.Tuple[float, ...], NdGridDataType]): @@ -211,7 +211,7 @@ def __call__(self, xi: NdGridDataType) -> np.ndarray: return self._spline.evaluate(xi) def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSplinePPForm, ty.Tuple[float, ...]]: - sizey = list(self._ydata.shape) + shapey = list(self._ydata.shape) coeffs = self._ydata.copy() smooths = [] @@ -219,18 +219,17 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp # computing coordinatewise smoothing spline for i in reversed(range(self._ndim)): - shape_i = (np.prod(sizey[:-1]), sizey[-1]) - ydata_i = coeffs.reshape(shape_i, order='F') + ydata_i = to_2d(coeffs.T, axis=0) s = CubicSmoothingSpline( self._xdata[i], ydata_i, weights=self._weights[i], smooth=smooth[i]) smooths.append(s.smooth) - sizey[-1] = s.spline.pieces * s.spline.order - coeffs = s.spline.coeffs.reshape(sizey, order='F') + shapey[-1] = s.spline.pieces * s.spline.order + coeffs = s.spline.coeffs.reshape(shapey, order='F') if self._ndim > 1: coeffs = coeffs.transpose(permute_axes) - sizey = list(coeffs.shape) + shapey = list(coeffs.shape) return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(smooths) From 35280a42d0655b977c52bc686db37b1a6419151c Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Mon, 10 Feb 2020 15:39:58 +0300 Subject: [PATCH 13/32] add additional test for nd-grid --- tests/test_ndgrid.py | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index d418eab..e8eb8fc 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -57,3 +57,20 @@ def test_volume(): ydata_s = sp(xdata) assert ydata_s.shape == ydata.shape + + +@pytest.mark.parametrize('shape', [ + (3, 4), + (3, 4, 5), + (3, 4, 5, 6), + (3, 4, 5, 6, 7), +], ids=['2d', '3d', '4d', '5d']) +def test_nd_array(shape: tuple): + xdata = [np.arange(s) for s in shape] + ydata = np.arange(0, np.prod(shape)).reshape(shape) + + sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata, smooth=1.0) + ydata_s = sp(xdata) + + assert ydata_s.shape == ydata.shape + assert ydata_s == pytest.approx(ydata) From 2ba672922456a770c36d97b3af65cc7ee4dac1c0 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Mon, 10 Feb 2020 15:42:05 +0300 Subject: [PATCH 14/32] a slight refactoring --- csaps/_sspndg.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index c77632c..4d996d0 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -13,7 +13,7 @@ from ._base import SplinePPFormBase, ISmoothingSpline from ._types import UnivariateDataType, NdGridDataType from ._sspumv import SplinePPForm, CubicSmoothingSpline -from ._reshape import to_2d +from ._reshape import to_2d, from_2d def ndgrid_prepare_data_sites(data, name) -> ty.Tuple[np.ndarray, ...]: @@ -211,10 +211,10 @@ def __call__(self, xi: NdGridDataType) -> np.ndarray: return self._spline.evaluate(xi) def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSplinePPForm, ty.Tuple[float, ...]]: - shapey = list(self._ydata.shape) coeffs = self._ydata.copy() - smooths = [] + shapey = list(coeffs.shape) + smooths = [] permute_axes = (self._ndim - 1, *range(self._ndim - 1)) # computing coordinatewise smoothing spline From c80225be41c83d1f965e96f510e42fcdf2f5b7e4 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Mon, 10 Feb 2020 18:47:17 +0300 Subject: [PATCH 15/32] remove extra test --- tests/test_ndgrid.py | 16 ---------------- 1 file changed, 16 deletions(-) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index e8eb8fc..4f1909b 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -43,22 +43,6 @@ def test_surface(): assert noisy_s.shape == noisy.shape -def test_volume(): - xdata = [ - np.linspace(-3, 3, 21), - np.linspace(-3.5, 3.5, 31), - np.linspace(-2.5, 2.5, 41), - ] - - np.random.seed(12345) - ydata = np.random.randn(21, 31, 41) - - sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata) - ydata_s = sp(xdata) - - assert ydata_s.shape == ydata.shape - - @pytest.mark.parametrize('shape', [ (3, 4), (3, 4, 5), From 005de5f7d6ed8c580ce9980fb40c77ff8a2d9cbc Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Tue, 11 Feb 2020 18:27:06 +0300 Subject: [PATCH 16/32] add 1d test to nd-grid tests --- tests/test_ndgrid.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index e8eb8fc..ff2a484 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -60,11 +60,12 @@ def test_volume(): @pytest.mark.parametrize('shape', [ + (3,), (3, 4), (3, 4, 5), (3, 4, 5, 6), (3, 4, 5, 6, 7), -], ids=['2d', '3d', '4d', '5d']) +], ids=['1d', '2d', '3d', '4d', '5d']) def test_nd_array(shape: tuple): xdata = [np.arange(s) for s in shape] ydata = np.arange(0, np.prod(shape)).reshape(shape) From bde062bfcccec5a559a38cd78c5a5f9e50ed2d55 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Wed, 12 Feb 2020 01:57:39 +0300 Subject: [PATCH 17/32] refactoring --- csaps/_sspndg.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 4d996d0..5d088c8 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -211,8 +211,8 @@ def __call__(self, xi: NdGridDataType) -> np.ndarray: return self._spline.evaluate(xi) def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSplinePPForm, ty.Tuple[float, ...]]: - coeffs = self._ydata.copy() - shapey = list(coeffs.shape) + coeffs = self._ydata + coeffs_shape = list(coeffs.shape) smooths = [] permute_axes = (self._ndim - 1, *range(self._ndim - 1)) @@ -225,11 +225,11 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp self._xdata[i], ydata_i, weights=self._weights[i], smooth=smooth[i]) smooths.append(s.smooth) - shapey[-1] = s.spline.pieces * s.spline.order - coeffs = s.spline.coeffs.reshape(shapey, order='F') + coeffs_shape[-1] = s.spline.pieces * s.spline.order + coeffs = s.spline.coeffs.reshape(coeffs_shape, order='F') if self._ndim > 1: coeffs = coeffs.transpose(permute_axes) - shapey = list(coeffs.shape) + coeffs_shape = list(coeffs.shape) return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(smooths) From 94f23c63035f30ef1dc70bfcf6e1a00ed8a74e1b Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 13:03:56 +0300 Subject: [PATCH 18/32] remove unused import --- csaps/_sspndg.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 5d088c8..897c110 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -13,7 +13,7 @@ from ._base import SplinePPFormBase, ISmoothingSpline from ._types import UnivariateDataType, NdGridDataType from ._sspumv import SplinePPForm, CubicSmoothingSpline -from ._reshape import to_2d, from_2d +from ._reshape import to_2d def ndgrid_prepare_data_sites(data, name) -> ty.Tuple[np.ndarray, ...]: From 11d90bb9a357ba9dd8c86685604fef848f07d537 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 19:12:21 +0300 Subject: [PATCH 19/32] a slight tests changes --- tests/test_univariate.py | 21 +++++++++++++-------- 1 file changed, 13 insertions(+), 8 deletions(-) diff --git a/tests/test_univariate.py b/tests/test_univariate.py index 947fcde..09004de 100644 --- a/tests/test_univariate.py +++ b/tests/test_univariate.py @@ -28,7 +28,7 @@ def test_invalid_data(x, y, w): @pytest.mark.parametrize('y', [ # 1D (2, ) - np.array([2, 4]), + [2, 4], # 2D (2, 2) [(2, 4), (3, 5)], @@ -37,14 +37,14 @@ def test_invalid_data(x, y, w): [(2, 4), (3, 5), (4, 6)], # 3D (2, 2, 2) - [[(2, 4), (3, 5)], - [(2, 4), (3, 5)]], + [[(1, 2), (3, 4)], + [(5, 6), (7, 8)]], # 1D (3, ) [2, 4, 6], - # 2D (2, 3) - [(2, 4, 6), (3, 5, 7)], + # 2D (2, 5) + [(1, 2, 3, 4, 5), (3, 4, 5, 6, 7)], # 2D (3, 3) [(2, 4, 6), (3, 5, 7), (4, 6, 8)], @@ -95,11 +95,16 @@ def test_invalid_data(x, y, w): [[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)]]], # 4D (3, 3, 3, 4) - [[[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + [[[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)]], - [[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + + [[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)]], - [[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + + [[(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], + [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)], [(2, 4, 6, 8), (3, 5, 7, 9), (4, 6, 8, 10)]]], ]) From a0ba837a92a625bcbb0e3632c829bf3db1203f70 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 19:12:40 +0300 Subject: [PATCH 20/32] add nd-grid tests for corner case with 2 points --- tests/test_ndgrid.py | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index b6cd038..b73bfd6 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -43,6 +43,38 @@ def test_surface(): assert noisy_s.shape == noisy.shape +@pytest.mark.parametrize('shape', [ + (2,), + + (2, 3), + (2, 2), + + (2, 3, 4), + (2, 2, 3), + (2, 2, 2), + + (2, 3, 4, 5), + (2, 2, 3, 4), + (2, 2, 2, 3), + (2, 2, 2, 2), + + (2, 3, 4, 5, 6), + (2, 2, 3, 4, 5), + (2, 2, 2, 3, 4), + (2, 2, 2, 2, 3), + (2, 2, 2, 2, 2), +]) +def test_nd_2pt_array(shape: tuple): + xdata = [np.arange(s) for s in shape] + ydata = np.arange(0, np.prod(shape)).reshape(shape) + + sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata, smooth=1.0) + ydata_s = sp(xdata) + + assert ydata_s.shape == ydata.shape + assert ydata_s == pytest.approx(ydata) + + @pytest.mark.parametrize('shape', [ (3,), (3, 4), From 2ed1a2972b2b4ba1f081bb4ed81e7e291e6089ac Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 19:17:24 +0300 Subject: [PATCH 21/32] re-design storing spline coefficients and improve performance - improve performance of all make/evaluate operations by deleting superfluous reshapes and other array manipulations with spline coefficients --- csaps/_base.py | 16 ++++++------ csaps/_sspndg.py | 67 ++++++++++++++++++++++++++++++++---------------- csaps/_sspumv.py | 64 ++++++++++++++++++++++----------------------- 3 files changed, 85 insertions(+), 62 deletions(-) diff --git a/csaps/_base.py b/csaps/_base.py index f6e8b21..cb5f83e 100644 --- a/csaps/_base.py +++ b/csaps/_base.py @@ -41,24 +41,24 @@ def coeffs(self) -> np.ndarray: @property @abc.abstractmethod - def pieces(self) -> TProps: - """Returns a spline pieces data + def order(self) -> TProps: + """Returns a spline order Returns ------- - pieces : ty.Union[int, ty.Tuple[int, ...]] - Returns a spline pieces data + order : ty.Union[int, ty.Tuple[int, ...]] + Returns a spline order """ @property @abc.abstractmethod - def order(self) -> TProps: - """Returns a spline order + def pieces(self) -> TProps: + """Returns a spline pieces data Returns ------- - order : ty.Union[int, ty.Tuple[int, ...]] - Returns a spline order + pieces : ty.Union[int, ty.Tuple[int, ...]] + Returns a spline pieces data """ @property diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 897c110..2ed2b42 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -13,7 +13,6 @@ from ._base import SplinePPFormBase, ISmoothingSpline from ._types import UnivariateDataType, NdGridDataType from ._sspumv import SplinePPForm, CubicSmoothingSpline -from ._reshape import to_2d def ndgrid_prepare_data_sites(data, name) -> ty.Tuple[np.ndarray, ...]: @@ -41,16 +40,21 @@ class NdGridSplinePPForm(SplinePPFormBase[ty.Sequence[np.ndarray], ty.Tuple[int, breaks : np.ndarray Breaks values 1-D array coeffs : np.ndarray - Spline coefficients 2-D array + Spline coefficients N-D array """ def __init__(self, breaks: ty.Sequence[np.ndarray], coeffs: np.ndarray) -> None: self._breaks = breaks self._coeffs = coeffs self._pieces = tuple(x.size - 1 for x in breaks) - self._order = tuple(s // p for s, p in zip(coeffs.shape, self._pieces)) self._ndim = len(breaks) + if self._ndim > 1: + self._order = tuple(s // p for s, p in zip(coeffs.shape, self._pieces)) + else: + # the corner case for univariate spline that is represented as 1d-grid + self._order = (coeffs.shape[1] // self._pieces[0], ) + @property def breaks(self) -> ty.Sequence[np.ndarray]: return self._breaks @@ -59,37 +63,52 @@ def breaks(self) -> ty.Sequence[np.ndarray]: def coeffs(self) -> np.ndarray: return self._coeffs - @property - def pieces(self) -> ty.Tuple[int, ...]: - return self._pieces - @property def order(self) -> ty.Tuple[int, ...]: return self._order + @property + def pieces(self) -> ty.Tuple[int, ...]: + return self._pieces + @property def ndim(self) -> int: return self._ndim def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: - yi = self.coeffs.copy() - sizey = list(yi.shape) - nsize = tuple(x.size for x in xi) + shape = tuple(x.size for x in xi) + + coeffs = self.coeffs + coeffs_shape = list(coeffs.shape) d = self.ndim - 1 - permute_axes = (d, *range(d)) + permuted_axes = (d, *range(d)) for i in reversed(range(self.ndim)): - ndim = int(np.prod(sizey[:d])) - coeffs = yi.reshape((ndim * self.pieces[i], self.order[i]), order='F') + xii = xi[i] + ndim = int(np.prod(coeffs_shape[:d])) + + if self.ndim > 2: + coeffs = coeffs.reshape((ndim, self.pieces[i] * self.order[i])) - spp = SplinePPForm(self.breaks[i], coeffs, ndim=ndim, shape=(ndim, xi[i].size)) - yi = spp.evaluate(xi[i]) + spp = SplinePPForm( + breaks=self.breaks[i], + coeffs=coeffs, + pieces=self.pieces[i], + order=self.order[i], + shape=(ndim, xii.size) + ) - yi = yi.reshape((*sizey[:d], nsize[i]), order='F').transpose(permute_axes) - sizey = list(yi.shape) + coeffs = spp.evaluate(xii) - return yi.reshape(nsize) + if self.ndim > 2: + coeffs = coeffs.reshape((*coeffs_shape[:d], shape[i])) + + if self.ndim > 1: + coeffs = coeffs.transpose(permuted_axes) + coeffs_shape = list(coeffs.shape) + + return coeffs.reshape(shape) class NdGridCubicSmoothingSpline(ISmoothingSpline[NdGridSplinePPForm, ty.Tuple[float, ...], NdGridDataType]): @@ -219,14 +238,18 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp # computing coordinatewise smoothing spline for i in reversed(range(self._ndim)): - ydata_i = to_2d(coeffs.T, axis=0) + if self._ndim > 2: + coeffs = coeffs.reshape(np.prod(coeffs.shape[:-1]), coeffs.shape[-1]) s = CubicSmoothingSpline( - self._xdata[i], ydata_i, weights=self._weights[i], smooth=smooth[i]) + self._xdata[i], coeffs, weights=self._weights[i], smooth=smooth[i]) smooths.append(s.smooth) - coeffs_shape[-1] = s.spline.pieces * s.spline.order - coeffs = s.spline.coeffs.reshape(coeffs_shape, order='F') + coeffs = s.spline.coeffs + + if self._ndim > 2: + coeffs_shape[-1] = s.spline.pieces * s.spline.order + coeffs = coeffs.reshape(coeffs_shape) if self._ndim > 1: coeffs = coeffs.transpose(permute_axes) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index 0203cb1..ed24673 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -38,13 +38,13 @@ class SplinePPForm(SplinePPFormBase[np.ndarray, int]): Axis along which values are assumed to be varying """ - def __init__(self, breaks: np.ndarray, coeffs: np.ndarray, ndim: int, + def __init__(self, breaks: np.ndarray, coeffs: np.ndarray, order: int, pieces: int, shape: ty.Sequence[int], axis: int = -1) -> None: self._breaks = breaks self._coeffs = coeffs - self._pieces = np.prod(coeffs.shape[:-1]) // ndim - self._order = coeffs.shape[-1] - self._ndim = ndim + self._order = order + self._pieces = pieces + self._ndim = coeffs.shape[0] self._shape = shape self._axis = axis @@ -57,14 +57,14 @@ def breaks(self) -> np.ndarray: def coeffs(self) -> np.ndarray: return self._coeffs - @property - def pieces(self) -> int: - return self._pieces - @property def order(self) -> int: return self._order + @property + def pieces(self) -> int: + return self._pieces + @property def ndim(self) -> int: return self._ndim @@ -82,26 +82,17 @@ def evaluate(self, xi: np.ndarray) -> np.ndarray: nanx = np.flatnonzero(index == 0) index = np.fmin(index, mesh.size + 1) index[nanx] = 1 + index -= 1 # Go to local coordinates - xi = xi - self.breaks[index - 1] - d = self.ndim - lx = len(xi) - - if d > 1: - xi = np.repeat(xi, d) - index_mat = (1 + d * index)[np.newaxis] + np.r_[-d:0][np.newaxis].T - index = index_mat.T.flatten() - - index -= 1 + xi = xi - self.breaks[index] # Apply nested multiplication - values = self._coeffs[index, 0] + values = self._coeffs[:, index] - for i in range(1, self._coeffs.shape[1]): - values = xi * values + self._coeffs[index, i] - - values = values.reshape((lx, d)).T + for i in range(1, self._order): + index += self._pieces + values = xi * values + self._coeffs[:, index] if values.shape != shape: # Reshape values 2-D NxM array to N-D array with original shape @@ -283,21 +274,30 @@ def _make_spline(self, smooth: ty.Optional[float]) -> ty.Tuple[SplinePPForm, flo c3 = np.pad(p * u, pad_width) c2 = np.diff(yi, axis=0) / dx - dx * (2. * c3[:-1, :] + c3[1:, :]) - coeffs = np.stack(( - (np.diff(c3, axis=0) / dx).ravel(), - 3. * c3[:-1, :].ravel(), - c2.ravel(), - yi[:-1, :].ravel() - ), axis=1) + coeffs = np.vstack(( + np.diff(c3, axis=0) / dx, + 3. * c3[:-1, :], + c2, + yi[:-1, :], + )).T + + order = 4 + pieces = coeffs.shape[1] // order else: - p = 1. + # The corner case for the data with 2 points. yi = self._ydata[:, 0][:, np.newaxis] - coeffs = np.array(np.hstack((dy_dx, yi)), ndmin=2) + coeffs = np.hstack((dy_dx, yi)) + + order = 2 + pieces = 1 + + p = 1. spline = SplinePPForm( breaks=self._xdata, coeffs=coeffs, - ndim=self._ydim, + order=order, + pieces=pieces, shape=self._shape, axis=self._axis ) From 3fb06f9d0f363ca2adb6e3b278a76c11a1b24451 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 23:34:09 +0300 Subject: [PATCH 22/32] add properties shape and axis to spline classes --- csaps/_sspndg.py | 6 ++++++ csaps/_sspumv.py | 28 ++++++++++++++++++++-------- tests/test_ndgrid.py | 2 +- tests/test_univariate.py | 27 ++++++++++++++++++++++++++- 4 files changed, 53 insertions(+), 10 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index 2ed2b42..a8ce048 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -75,6 +75,12 @@ def pieces(self) -> ty.Tuple[int, ...]: def ndim(self) -> int: return self._ndim + @property + def shape(self) -> ty.Tuple[int, ...]: + """Returns the original data shape + """ + return tuple(x.size for x in self.breaks) + def evaluate(self, xi: ty.Sequence[np.ndarray]) -> np.ndarray: shape = tuple(x.size for x in xi) diff --git a/csaps/_sspumv.py b/csaps/_sspumv.py index ed24673..3c0e00d 100644 --- a/csaps/_sspumv.py +++ b/csaps/_sspumv.py @@ -46,7 +46,7 @@ def __init__(self, breaks: np.ndarray, coeffs: np.ndarray, order: int, pieces: i self._pieces = pieces self._ndim = coeffs.shape[0] - self._shape = shape + self._shape = tuple(shape) self._axis = axis @property @@ -69,9 +69,21 @@ def pieces(self) -> int: def ndim(self) -> int: return self._ndim + @property + def shape(self) -> ty.Tuple[int, ...]: + """Returns the original data shape + """ + return self._shape + + @property + def axis(self) -> int: + """Returns the data axis along the spline will be evaluated + """ + return self._axis + def evaluate(self, xi: np.ndarray) -> np.ndarray: - shape = list(self._shape) - shape[self._axis] = xi.size + shape = list(self.shape) + shape[self.axis] = xi.size # For each data site, compute its break interval mesh = self.breaks[1:-1] @@ -88,15 +100,15 @@ def evaluate(self, xi: np.ndarray) -> np.ndarray: xi = xi - self.breaks[index] # Apply nested multiplication - values = self._coeffs[:, index] + values = self.coeffs[:, index] - for i in range(1, self._order): - index += self._pieces - values = xi * values + self._coeffs[:, index] + for i in range(1, self.order): + index += self.pieces + values = xi * values + self.coeffs[:, index] if values.shape != shape: # Reshape values 2-D NxM array to N-D array with original shape - values = from_2d(values, shape, self._axis) + values = from_2d(values, shape, self.axis) return values diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index b73bfd6..8ab1536 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -89,5 +89,5 @@ def test_nd_array(shape: tuple): sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata, smooth=1.0) ydata_s = sp(xdata) - assert ydata_s.shape == ydata.shape + assert sp.spline.shape == ydata.shape assert ydata_s == pytest.approx(ydata) diff --git a/tests/test_univariate.py b/tests/test_univariate.py index 09004de..654a899 100644 --- a/tests/test_univariate.py +++ b/tests/test_univariate.py @@ -115,6 +115,26 @@ def test_vectorize(y): np.testing.assert_allclose(ys, y) +@pytest.mark.parametrize('y, order, pieces, ndim', [ + ([1, 2], 2, 1, 1), + ([[1, 2], [1, 2]], 2, 1, 2), + ([1, 2, 3], 4, 2, 1), + ([[1, 2, 3], [1, 2, 3]], 4, 2, 2), + ([1, 2, 3, 4, 5, 6, 7], 4, 6, 1), + ([[1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]], 4, 6, 2), +]) +def test_vectorize(y, order, pieces, ndim): + x = np.arange(np.array(y).shape[-1]) + y = np.array(y) + + s = csaps.UnivariateCubicSmoothingSpline(x, y).spline + + assert s.order == order + assert s.pieces == pieces + assert s.ndim == ndim + assert s.shape == y.shape + + @pytest.mark.parametrize('shape, axis', chain( *map(product, [ # shape @@ -134,7 +154,12 @@ def test_axis(shape, axis): y = np.arange(int(np.prod(shape))).reshape(shape) x = np.arange(np.array(y).shape[axis]) - ys = csaps.UnivariateCubicSmoothingSpline(x, y, axis=axis)(x) + s = csaps.UnivariateCubicSmoothingSpline(x, y, axis=axis) + ys = s(x) + + assert s.spline.shape == y.shape + assert s.spline.axis == axis + np.testing.assert_allclose(ys, y) From e85db5f8a7084cfc2b32d126e73b83ae8b024e8d Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 23:37:06 +0300 Subject: [PATCH 23/32] fix func name --- tests/test_univariate.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_univariate.py b/tests/test_univariate.py index 654a899..45ff972 100644 --- a/tests/test_univariate.py +++ b/tests/test_univariate.py @@ -123,7 +123,7 @@ def test_vectorize(y): ([1, 2, 3, 4, 5, 6, 7], 4, 6, 1), ([[1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]], 4, 6, 2), ]) -def test_vectorize(y, order, pieces, ndim): +def test_splineppform(y, order, pieces, ndim): x = np.arange(np.array(y).shape[-1]) y = np.array(y) From 83c9ef688ab446a78189b498ff937f22dc826ce8 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Fri, 14 Feb 2020 23:44:20 +0300 Subject: [PATCH 24/32] Bump version to 0.10.0 --- CHANGELOG.md | 6 ++++++ csaps/_version.py | 2 +- 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index 60d23ff..c3673d6 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,5 +1,11 @@ # Changelog +## v0.10.0 + +* Significant performance improvements for make/evaluate splines +* Change format for storing spline coefficients (reshape coeffs array) to improve performance +* Add shape property to `SplinePPForm`/`NdGridSplinePPForm` and axis property to `SplinePPForm` + ## v0.9.0 * Drop support of Python 3.5 diff --git a/csaps/_version.py b/csaps/_version.py index 829ff4e..a8cad44 100644 --- a/csaps/_version.py +++ b/csaps/_version.py @@ -1,3 +1,3 @@ # -*- coding: utf-8 -*- -__version__ = '0.10.0.dev0' +__version__ = '0.10.0' From 5374e4afcf38594e74d4d7d73f77c19d9cc9f012 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 18:59:48 +0300 Subject: [PATCH 25/32] a slight change print output for spline repr --- csaps/_base.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/csaps/_base.py b/csaps/_base.py index cb5f83e..dedff20 100644 --- a/csaps/_base.py +++ b/csaps/_base.py @@ -91,7 +91,7 @@ def __repr__(self): # pragma: no cover return ( f'{type(self).__name__}\n' f' breaks: {self.breaks}\n' - f' coeffs: {self.coeffs.shape} shape\n' + f' coeffs: shape {self.coeffs.shape}\n' f' pieces: {self.pieces}\n' f' order: {self.order}\n' f' ndim: {self.ndim}\n' From bdd9488f619bf17d4af39ac4e200af8fae61ce4d Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 19:01:47 +0300 Subject: [PATCH 26/32] update docs - add "internals" section - add a slight clarification to manual --- docs/index.rst | 1 + docs/internals.rst | 57 ++++++++++++++++++++++++++++++++++++++++++++++ docs/manual.rst | 6 ++--- 3 files changed, 61 insertions(+), 3 deletions(-) create mode 100644 docs/internals.rst diff --git a/docs/index.rst b/docs/index.rst index 37c5f37..a8311ed 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -51,6 +51,7 @@ Content formulation manual + internals benchmarks api changelog diff --git a/docs/internals.rst b/docs/internals.rst new file mode 100644 index 0000000..707fead --- /dev/null +++ b/docs/internals.rst @@ -0,0 +1,57 @@ +.. _internals: + +.. currentmodule:: csaps + +Internals +========= + +Spline Representation +--------------------- + +The computed splines are represented by classes :class:`SplinePPForm` for univariate/multivariate +and :class:`NdGridSplinePPForm` for nd-gridded data. + +The spline coefficients are stored in the numpy array. It is 2D 1xM array for univariate data, +2D NxM array for multivariate data and 2D/ND array (tensor-product of univariate spline coefficients) +for nd-gridded data. + +Let's look at a simple example. + +The multivariate data:: + + x = [1, 2, 3, 4] + y = [(1, 2, 3, 4), (5, 6, 7, 8)] + +Compute the spline: + +.. code-block:: python + + >>> s = csaps(x, y).spline + +And print the spline info and coefficients array: + +.. code-block:: python + + >>> print(s) + + SplinePPForm + breaks: [1. 2. 3. 4.] + coeffs: shape (2, 12) + pieces: 3 + order: 4 + ndim: 2 + + >>> print(s.coeffs) + + [[0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 2. 3.] + [0. 0. 0. 0. 0. 0. 1. 1. 1. 5. 6. 7.]] + +Each row in the array contain coefficients for all spline pieces for corresponding data. +In our case we have 2D Y-data with shape (2, 4) and have the coefficients array with shape (2, 12) + + - 2 rows: 2 dimensions in the data + - 12 columns: 3 pieces of the cubic spline (4-order) + +The spline pieces for each dimension are composed sequentially in the one row. +Such representation allows us to compute tensor-product for nd-grid data and evaluate splines +without superfluous manipulations and reshapes of the coefficients array. diff --git a/docs/manual.rst b/docs/manual.rst index 3fc4349..18e9df6 100644 --- a/docs/manual.rst +++ b/docs/manual.rst @@ -197,8 +197,8 @@ where - ``y`` -- the data values. For univariate case it is vector with the same size as ``x``, for multivariate case it is a sequence of vectors or nd-array, and for nd-gridded data it is nd-array - - ``xi`` -- the data sites for smoothed data. It is shape-like ``x`` data and in the same - range as ``x``, but usually has more interpolated points + - ``xi`` -- the data sites for smoothed data (output mesh). It is shape-like ``x`` and in the same + range as ``x``, but usually it has more interpolated points - ``smooth`` -- the smoothing parameter in the range ``[0, 1]`` @@ -384,7 +384,7 @@ The example for univariate data: Spline smoothing parameter: 0.8999999999999999 Spline description: SplinePPForm breaks: [-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.] - coeffs: (10, 4) shape + coeffs: shape (1, 40) pieces: 10 order: 4 ndim: 1 From cdfd33c8bec8bd46c516b4ea2a95866880df7791 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 19:20:18 +0300 Subject: [PATCH 27/32] docs: add a slight clarification --- docs/internals.rst | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/docs/internals.rst b/docs/internals.rst index 707fead..972f09a 100644 --- a/docs/internals.rst +++ b/docs/internals.rst @@ -9,11 +9,12 @@ Spline Representation --------------------- The computed splines are represented by classes :class:`SplinePPForm` for univariate/multivariate -and :class:`NdGridSplinePPForm` for nd-gridded data. +and :class:`NdGridSplinePPForm` for nd-gridded data. This representation can be named as "PP-form" +(piecewise-polynomial form). -The spline coefficients are stored in the numpy array. It is 2D 1xM array for univariate data, -2D NxM array for multivariate data and 2D/ND array (tensor-product of univariate spline coefficients) -for nd-gridded data. +The polynom coefficients for each piece of spline are stored in the numpy array. +It is 2D 1xM array for univariate data, 2D NxM array for multivariate data and 2D/ND array +(tensor-product of univariate spline coefficients) for nd-gridded data. Let's look at a simple example. From 227534eb4e95dcfd310a1deab574c89e571442ad Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 19:53:12 +0300 Subject: [PATCH 28/32] add info about memory optimization to changelog --- CHANGELOG.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index c3673d6..eb86034 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,7 +2,7 @@ ## v0.10.0 -* Significant performance improvements for make/evaluate splines +* Significant performance improvements for make/evaluate splines and memory consumption optimization * Change format for storing spline coefficients (reshape coeffs array) to improve performance * Add shape property to `SplinePPForm`/`NdGridSplinePPForm` and axis property to `SplinePPForm` From 7b2639b3fb22e70e131ea371d7bee109b85b764a Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 20:46:40 +0300 Subject: [PATCH 29/32] fix bugs with smooth factor for nd-gridded data - fix zero smooth check (we could not use zero smooth factor) - fix smooth factors inverted order --- csaps/_sspndg.py | 4 ++-- tests/test_ndgrid.py | 54 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 56 insertions(+), 2 deletions(-) diff --git a/csaps/_sspndg.py b/csaps/_sspndg.py index a8ce048..c275d37 100644 --- a/csaps/_sspndg.py +++ b/csaps/_sspndg.py @@ -210,7 +210,7 @@ def _prepare_data(cls, xdata, ydata, weights, smooth): if w.size != x.size: raise ValueError(f'weights ({w}) and xdata ({x}) dimension size mismatch') - if not smooth: + if smooth is None: smooth = [None] * data_ndim if not isinstance(smooth, c_abc.Sequence): @@ -261,4 +261,4 @@ def _make_spline(self, smooth: ty.List[ty.Optional[float]]) -> ty.Tuple[NdGridSp coeffs = coeffs.transpose(permute_axes) coeffs_shape = list(coeffs.shape) - return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(smooths) + return NdGridSplinePPForm(breaks=self._xdata, coeffs=coeffs), tuple(reversed(smooths)) diff --git a/tests/test_ndgrid.py b/tests/test_ndgrid.py index 8ab1536..36aa88f 100644 --- a/tests/test_ndgrid.py +++ b/tests/test_ndgrid.py @@ -43,6 +43,60 @@ def test_surface(): assert noisy_s.shape == noisy.shape +@pytest.mark.parametrize('shape, smooth', [ + ((4,), 0.0), + ((4,), 0.5), + ((4,), 1.0), + + ((4,), (0.0,)), + ((4,), (0.5,)), + ((4,), (1.0,)), + + ((4, 5), 0.0), + ((4, 5), 0.5), + ((4, 5), 1.0), + ((4, 5), (0.0, 0.0)), + ((4, 5), (0.0, 0.5)), + ((4, 5), (0.5, 0.0)), + ((4, 5), (0.5, 0.7)), + ((4, 5), (1.0, 0.0)), + ((4, 5), (0.0, 1.0)), + ((4, 5), (1.0, 1.0)), + + ((4, 5, 6), 0.0), + ((4, 5, 6), 0.5), + ((4, 5, 6), 1.0), + ((4, 5, 6), (0.0, 0.0, 0.0)), + ((4, 5, 6), (0.5, 0.0, 0.0)), + ((4, 5, 6), (0.5, 0.6, 0.0)), + ((4, 5, 6), (0.0, 0.5, 0.6)), + ((4, 5, 6), (0.4, 0.5, 0.6)), + + ((4, 5, 6, 7), 0.0), + ((4, 5, 6, 7), 0.5), + ((4, 5, 6, 7), 1.0), + ((4, 5, 6, 7), (0.0, 0.0, 0.0, 0.0)), + ((4, 5, 6, 7), (0.5, 0.0, 0.0, 0.0)), + ((4, 5, 6, 7), (0.0, 0.5, 0.0, 0.0)), + ((4, 5, 6, 7), (0.5, 0.6, 0.0, 0.0)), + ((4, 5, 6, 7), (0.0, 0.5, 0.6, 0.0)), + ((4, 5, 6, 7), (0.0, 0.5, 0.6, 0.7)), + ((4, 5, 6, 7), (0.4, 0.5, 0.6, 0.7)), +]) +def test_smooth_factor(shape, smooth): + x = [np.arange(s) for s in shape] + y = np.arange(0, np.prod(shape)).reshape(shape) + + sp = csaps.NdGridCubicSmoothingSpline(x, y, smooth=smooth) + + if isinstance(smooth, tuple): + expected_smooth = smooth + else: + expected_smooth = tuple([smooth] * len(shape)) + + assert sp.smooth == pytest.approx(expected_smooth) + + @pytest.mark.parametrize('shape', [ (2,), From 2671ac56880b5420df8376db6da1a25bd7e5074d Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Sat, 15 Feb 2020 20:48:52 +0300 Subject: [PATCH 30/32] update changelog --- CHANGELOG.md | 1 + 1 file changed, 1 insertion(+) diff --git a/CHANGELOG.md b/CHANGELOG.md index eb86034..68af13e 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -5,6 +5,7 @@ * Significant performance improvements for make/evaluate splines and memory consumption optimization * Change format for storing spline coefficients (reshape coeffs array) to improve performance * Add shape property to `SplinePPForm`/`NdGridSplinePPForm` and axis property to `SplinePPForm` +* Fix issues with the smoothing factor in nd-grid case: inverted ordering and unnable to use 0.0 value ## v0.9.0 From f8ef10521e626e7e60bbfa58e859cfbae0c5e2e9 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Tue, 18 Feb 2020 13:18:11 +0300 Subject: [PATCH 31/32] docs: update benchmarks --- .../benchmarks/multivariate-evaluate.png | Bin 81375 -> 83689 bytes docs/_static/benchmarks/multivariate-make.png | Bin 31714 -> 32598 bytes .../benchmarks/ndgrid-evaluate-ndim2.png | Bin 0 -> 98306 bytes .../benchmarks/ndgrid-evaluate-ndim3.png | Bin 0 -> 50517 bytes docs/_static/benchmarks/ndgrid-evaluate.png | Bin 93752 -> 0 bytes docs/_static/benchmarks/ndgrid-make-ndim2.png | Bin 0 -> 22494 bytes docs/_static/benchmarks/ndgrid-make-ndim3.png | Bin 0 -> 21975 bytes 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zyW!_p;x%k-@Aqqfo5chN-*S&%*uzm0A+N-ZOxP(1es-`5f7)nvHX?MG-O~+sn~{e5 zEJSUdAEa+O{g8+&45<5vC6_C;zUYJ0Q|wlOPVKtyc`_m;!Ws~N6RsP3U8WhvC1h9v zJS#ulVK#P1qrSL)DFp$v`rSCfbs}>43wotFb951vj;1G7TArGmyxl8FcA&9wT{vp8 zHRt;4vQ)fDh#znp^j4^B--t1>A8xqM3e?arJq8XJ$qI%r`a@1{B|Uo2SKS57zA~qIp*~> zHESRh*;ZWam@OhDS@Oc3sj8BpaZ7UPQ@k8R zk%*a~EGTYlP2}M7z2d8wOb&F<3K^gQV4YZwpsOe=25GxOCsdGevQvTyRro+>QfG>N z|E@NbLKJ$qu#vR#`JH2nD35xYH}2ZmIB)dx?N;$+vHkjQd&xf-X8-SxJzp+oAdRongvRT`H3 diff --git a/docs/benchmarks.rst b/docs/benchmarks.rst index d886d43..4a7e385 100644 --- a/docs/benchmarks.rst +++ b/docs/benchmarks.rst @@ -71,9 +71,13 @@ ND-Grid Make Spline ~~~~~~~~~~~ -.. image:: _static/benchmarks/ndgrid-make.png +.. image:: _static/benchmarks/ndgrid-make-ndim2.png + +.. image:: _static/benchmarks/ndgrid-make-ndim3.png Evaluate Spline ~~~~~~~~~~~~~~~ -.. image:: _static/benchmarks/ndgrid-evaluate.png +.. image:: _static/benchmarks/ndgrid-evaluate-ndim2.png + +.. image:: _static/benchmarks/ndgrid-evaluate-ndim3.png From 42d1161302ddb4e5455b45cf80e5ec68bec3c326 Mon Sep 17 00:00:00 2001 From: Eugene Prilepin Date: Tue, 18 Feb 2020 13:18:52 +0300 Subject: [PATCH 32/32] update changelog --- CHANGELOG.md | 1 + 1 file changed, 1 insertion(+) diff --git a/CHANGELOG.md b/CHANGELOG.md index 68af13e..973a55e 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -6,6 +6,7 @@ * Change format for storing spline coefficients (reshape coeffs array) to improve performance * Add shape property to `SplinePPForm`/`NdGridSplinePPForm` and axis property to `SplinePPForm` * Fix issues with the smoothing factor in nd-grid case: inverted ordering and unnable to use 0.0 value +* Update documentation ## v0.9.0

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