From 58612e40ad225ce4ca30757904e5f7836b3202bc Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 17:59:26 +0200 Subject: [PATCH 1/8] feat: add MCA base class --- xeofs/models/_base_mca.py | 493 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 493 insertions(+) create mode 100644 xeofs/models/_base_mca.py diff --git a/xeofs/models/_base_mca.py b/xeofs/models/_base_mca.py new file mode 100644 index 0000000..b6e88e6 --- /dev/null +++ b/xeofs/models/_base_mca.py @@ -0,0 +1,493 @@ +from typing import Optional, Tuple, List, Union + +import numpy as np +import scipy as sc +from sklearn.utils.extmath import randomized_svd + +from ..utils.tools import get_mode_selector + + +class _BaseMCA(): + '''Base class for Maximum Covariance Analysis (MCA). + + Parameters + ---------- + X : np.ndarray + 2D data matrix ``X`` with samples as rows and features as columns. + NaN entries will raise an error. + Y : np.ndarray + 2D data matrix ``Y`` with samples as rows and features as columns. + NaN entries will raise an error. + n_modes : Optional[int] + Number of modes to be retrieved. If None, then all possible modes will + be computed. Reducing ``n_modes`` can greatly speed up computational + (the default is None). + norm : bool + Normalize each feature by its standard deviation (the default is False). + weights_X : Optional[np.ndarray] + Apply `weights` to features of ``X``. Weights must be a 1D array with the same + length as number of features. No NaN entries are allowed + (the default is None). + weights_y : Optional[np.ndarray] + Apply `weights_Y` to features of ``Y``. Weights must be a 1D array with the same + length as number of features. No NaN entries are allowed + (the default is None). + + Attributes + ---------- + n_samples : int + Number of samples (rows of data matrix). + n_features : int + Number of features (columns of data matrix). + n_modes : int + Number of modes. + + ''' + + def __init__( + self, + X: np.ndarray, + Y: np.ndarray, + n_modes: Optional[int] = None, + norm: bool = False, + weights_X: Optional[np.ndarray] = None, + weights_Y: Optional[np.ndarray] = None + ): + # Remove mean for each feature + self._X_mean = X.mean(axis=0) + self._Y_mean = Y.mean(axis=0) + X -= self._X_mean + Y -= self._Y_mean + + # Weights are applied to features, not samples. + self._weights_X = weights_X + self._weights_Y = weights_Y + # Use int type to ensure that there won't be rounding errors + # when applying trivial weighting (= all weights equal 1) + if self._weights_X is None: + self._weights_X = np.ones(X.shape[1], dtype=int) + if self._weights_Y is None: + self._weights_Y = np.ones(Y.shape[1], dtype=int) + + # Standardization is included as weights + if norm: + stdev_X = X.std(axis=0) + stdev_Y = Y.std(axis=0) + eps = 1e-8 + if (stdev_X < eps).any() or (stdev_Y < eps).any(): + err_msg = ( + 'Standard deviation of one ore more features is zero, ' + 'normalization not possible.' + ) + raise ValueError(err_msg) + self._weights_X = self._weights_X / stdev_X + self._weights_Y = self._weights_Y / stdev_Y + X = X * self._weights_X + Y = Y * self._weights_Y + + n_samples_X = X.shape[0] + n_samples_Y = Y.shape[0] + if n_samples_X != n_samples_Y: + msg = ( + 'X and Y must have same number of samples but ' + 'got {:} and {:}' + ) + msg = msg.format(n_samples_X, n_samples_Y) + raise ValueError(msg) + + self.n_samples = X.shape[0] + self.n_features_X = X.shape[1] + self.n_features_Y = Y.shape[1] + + self.n_modes = n_modes + if n_modes is None: + self.n_modes = min(self.n_features_X - 1, self.n_features_Y - 1) + + self.X = X + self.Y = Y + + def solve(self) -> None: + ''' + Perform MCA (aka SVD analysis). + + To boost performance, the standard solver is based on + the truncated randomized SVD implementation of scikit-learn [1]_ . + + + References + ---------- + .. [1] https://scikit-learn.org/stable/modules/generated/sklearn.utils.extmath.randomized_svd.html + + ''' + C = self.X.T @ self.Y / (self.n_samples - 1) + self._squared_total_variance = np.power(C, 2).sum() + + Vx, svalues, Vy = randomized_svd( + C, n_components=self.n_modes, n_iter=5, random_state=None + ) + Vy = Vy.T + self._Vx = Vx + self._Vy = Vy + # Note: + # - explained variance is given by the singular values of the SVD; + # - We use the term singular_values_X as used in the context of PCA: + # Considering X = Y, MCA is the same as PCA. In this case, + # singular_values_X is equivalent to the singular values obtained + # when performing PCA of X + self._singular_values = svalues + self._explained_covariance = svalues + self._squared_covariance_fraction = np.power(svalues, 2) / self._squared_total_variance + self._singular_values_X = np.sqrt(svalues * (self.n_samples - 1)) + self._norm_X = np.sqrt(svalues) + self._norm_Y = np.sqrt(svalues) + + # Ensure consistent signs for deterministic output + maxidx = [abs(self._Vx).argmax(axis=0)] + flip_signs = np.sign(self._Vx[maxidx, range(self._Vx.shape[1])]) + self._Vx *= flip_signs + self._Vy *= flip_signs + + # Project data onto the singular vectors + sqrt_expvar = np.sqrt(self._explained_covariance) + self._Ux = self.X @ self._Vx / sqrt_expvar + self._Uy = self.Y @ self._Vy / sqrt_expvar + + def singular_values(self) -> np.ndarray: + '''Get the singular values of the covariance matrix. + + ''' + return self._singular_values + + def explained_covariance(self) -> np.ndarray: + '''Get the explained covariance. + + The explained covariance is simply given by the individual singular + values of the covariance matrix. + + ''' + return self._explained_covariance + + def squared_covariance_fraction(self) -> np.ndarray: + '''Get the squared covariance fraction. + + The squared covariance fraction (SCF) is the fraction of total covariance + explained by a given mode `i` and is calculated by + + .. math:: + SCF_i = \frac{\sigma_i**2}{\sum_{i=1}^{m} \sigma_i**2} + + where `m` is the total number of modes and :math:`\sigma_i` denotes the + `ith` singular value of the covariance matrix. + + ''' + return self._squared_covariance_fraction + + def singular_vectors( + self, scaling : int = 0 + ) -> Tuple[np.ndarray, np.ndarray]: + '''Get the singular vectors of the covariance matrix. + + Parameters + ---------- + scaling : [0, 1, 2] + Singular vectors are scaled (i) to be orthonormal (``scaling=0``), + (ii) by the square root of the singular values (``scaling=1``) or + (iii) by the singular values (``scaling=2``) (the default is 0). + + ''' + if scaling == 0: + Vx = self._Vx + Vy = self._Vy + elif scaling == 1: + Vx = self._Vx * np.sqrt(self._explained_covariance) + Vy = self._Vy * np.sqrt(self._explained_covariance) + elif scaling == 2: + Vx = self._Vx * self._explained_covariance + Vy = self._Vy * self._explained_covariance + else: + msg = ( + 'The scaling option {:} is not valid. Please choose one ' + 'of the following: [0, 1, 2]' + ) + msg = msg.format(scaling) + raise ValueError(msg) + return Vx, Vy + + def pcs(self, scaling : int = 0) -> Tuple[np.ndarray, np.ndarray]: + '''Get the PCs. + + The principal components (PCs) in MCA are defined as the projection of + the data matrices ``X`` and ``Y`` onto the singular vectors. + There is one set of PCs for each data field. + + Parameters + ---------- + scaling : [0, 1, 2] + PCs are scaled (i) to be orthonormal (``scaling=0``), (ii) by the + square root of the singular values (``scaling=1``) or (iii) by the + singular values (``scaling=2``) (the default is 0). + + ''' + if scaling == 0: + Ux = self._Ux + Uy = self._Uy + elif scaling == 1: + Ux = self._Ux * np.sqrt(self._explained_covariance) + Uy = self._Uy * np.sqrt(self._explained_covariance) + elif scaling == 2: + Ux = self._Ux * self._explained_covariance + Uy = self._Uy * self._explained_covariance + else: + msg = ( + 'The scaling option {:} is not valid. Please choose one ' + 'of the following: [0, 1, 2]' + ) + msg = msg.format(scaling) + raise ValueError(msg) + return Ux, Uy + + def _corr_coef(self, A, B): + # Columnwise mean of input arrays & subtract from input arrays + # themeselves + A_mA = A - A.mean(0) + B_mB = B - B.mean(0) + + # Sum of squares across rows + ssA = (A_mA**2).sum(0) + ssB = (B_mB**2).sum(0) + + # Finally get corr coeff + return np.dot(A_mA.T, B_mB) / np.sqrt(np.dot(ssA[:, None], ssB[None])) + + + def homogeneous_patterns(self) -> Tuple[np.ndarray, np.ndarray]: + '''Correlation coefficients between PCs and their associated input data. + + More precisely, the homogeneous patterns `r_{hom}` are defined as + + .. math:: + r_{hom, x} = \corr \left(X, PC_x \right) \\ + r_{hom, y} = \corr \left(Y, PC_y \right) + + Returns + ------- + Tuple[np.ndarray, np.ndarry] + Homogeneous patterns for ``X`` and ``Y`` (n_features x n_modes). + + Tuple[np.ndarray, np.ndarry] + coefficients and associated + Two-sided p-values for ``X and ``Y`` (n_features x n_modes). + ''' + + # Compute correlation matrix + corr_X = self._corr_coef(self.X, self._Ux) + corr_Y = self._corr_coef(self.Y, self._Uy) + + # Compute two-sided p-values + # Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html#r8c6348c62346-1 + a = self.n_samples / 2 - 1 + dist = sc.stats.beta(a, a, loc=-1, scale=2) + pvals_X = 2 * dist.cdf(-abs(corr_X)) + pvals_Y = 2 * dist.cdf(-abs(corr_Y)) + return (corr_X, corr_Y), (pvals_X, pvals_Y) + + def heterogeneous_patterns(self) -> Tuple[np.ndarray, np.ndarray]: + '''Correlation coefficients between PCs and the opposite input data. + + More precisely, the heterogenous patterns `r_{het}` are defined as + + .. math:: + r_{het, x} = \corr \left(X, PC_y \right) \\ + r_{het, y} = \corr \left(Y, PC_x \right) + + Returns + ------- + Tuple[np.ndarray, np.ndarry] + Heterogenous patterns for ``X`` and ``Y`` (n_features x n_modes). + + Tuple[np.ndarray, np.ndarry] + coefficients and associated + Two-sided p-values for ``X and ``Y`` (n_features x n_modes). + ''' + + # Compute correlation matrix + corr_X = self._corr_coef(self.X, self._Uy) + corr_Y = self._corr_coef(self.Y, self._Ux) + + # Compute two-sided p-values + # Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html#r8c6348c62346-1 + a = self.n_samples / 2 - 1 + dist = sc.stats.beta(a, a, loc=-1, scale=2) + pvals_X = 2 * dist.cdf(-abs(corr_X)) + pvals_Y = 2 * dist.cdf(-abs(corr_Y)) + return (corr_X, corr_Y), (pvals_X, pvals_Y) + + def reconstruct_XY( + self, + mode : Optional[Union[int, List[int], slice]] = None + ) -> Tuple[np.ndarray, np.ndarray]: + '''Reconstruct original data fields ``X`` and ``Y``. + + If weights were applied, ``X`` and ``Y`` will be automatically + rescaled. + + Parameters + ---------- + mode : Optional[Union[int, List[int], slice]] + Mode(s) based on which ``X`` will be reconstructed. If ``mode`` is + an int, a single mode is used. If a list of integers is provided, + use all specified modes for reconstruction. Alternatively, you may + want to select a slice to reconstruct. The first mode is denoted + by 1 (and not by 0). If None then ``X`` is recontructed using all + available modes (the default is None). + + Examples + -------- + + Perform an analysis using some data ``X``: + + >>> model = MCA(X, Y, norm=True) + >>> model.solve() + + Reconstruct ``X`` and ``Y`` using all modes: + + >>> model.reconstruct_XY() + + Reconstruct ``X`` and ``Y`` using the first mode only: + + >>> model.reconstruct_XY(1) + + Reconstruct ``X`` and ``Y`` using mode 1, 3 and 4: + + >>> model.reconstruct_XY([1, 3, 4]) + + Reconstruct ``X`` and ``Y`` using all modes up to mode 10 (including): + + >>> model.reconstruct_XY(slice(10)) + + Reconstruct ``X`` and ``Y`` using every second mode between 4 and 8 (both + including): + + >>> model.reconstruct_XY(slice(4, 8, 2)) + + + ''' + # Select modes to reconstruct X + mode = get_mode_selector(mode) + + Vx = self._Vx[:, mode] + Vy = self._Vy[:, mode] + + Ux = self._Ux[:, mode] * self._norm_X[mode] + Uy = self._Uy[:, mode] * self._norm_Y[mode] + + Xrec = Ux @ Vx.T + Yrec = Uy @ Vy.T + # Unweight and add mean + Xrec = (Xrec / self._weights_X) + self._X_mean + Yrec = (Yrec / self._weights_Y) + self._Y_mean + return Xrec, Yrec + + def project_onto_left_singular_vectors( + self, + X : np.ndarray = None, + scaling : int = 0 + ) -> np.ndarray: + '''Project new data onto the singular vectors. + + Parameters + ---------- + X : np.ndarray + New data to project onto first singular vector. + scaling : [0, 1, 2] + Projections are scaled (i) to be orthonormal (``scaling=0``), (ii) by the + square root of the singular values (``scaling=1``) or (iii) by the + singular values (``scaling=2``) (the default is 0). + + Returns + ------- + np.ndarray + Projections of new data onto left singular vector + + ''' + # Remove mean and apply weights + try: + X -= self._X_mean + except ValueError: + err_msg = ( + 'New data has invalid feature dimensions and cannot be ' + 'projected onto singular vectors. Expected shapes' + ) + raise ValueError(err_msg) + X *= self._weights_X + + # Project new data onto singular values + Ux = X @ self._Vx / np.sqrt(self._singular_values) + + # Apply scaling + if scaling == 0: + pass + elif scaling == 1: + Ux *= np.sqrt(self._singular_values) + elif scaling == 2: + Ux *= self._singular_values + else: + err_msg = ( + 'Scaling option {:} is not valid but must be one ' + 'of [0, 1, 2]' + ) + err_msg = err_msg.foramt(scaling) + raise ValueError(err_msg) + return Ux + + def project_onto_right_singular_vectors( + self, + Y : np.ndarray = None, + scaling : int = 0 + ) -> np.ndarray: + '''Project new data onto the singular vectors. + + Parameters + ---------- + Y : np.ndarray + New data to project onto second singular vector. + scaling : [0, 1, 2] + Projections are scaled (i) to be orthonormal (``scaling=0``), (ii) by the + square root of the singular values (``scaling=1``) or (iii) by the + singular values (``scaling=2``) (the default is 0). + + Returns + ------- + np.ndarray + Projections of new data onto left singular vector + + ''' + # Remove mean and apply weights + try: + Y -= self._Y_mean + except ValueError: + err_msg = ( + 'New data has invalid feature dimensions and cannot be ' + 'projected onto singular vectors. Expected shapes' + ) + raise ValueError(err_msg) + Y *= self._weights_Y + + # Project new data onto singular values + Uy = Y @ self._Vy / np.sqrt(self._singular_values) + + # Apply scaling + if scaling == 0: + pass + elif scaling == 1: + Uy *= np.sqrt(self._singular_values) + elif scaling == 2: + Uy *= self._singular_values + else: + err_msg = ( + 'Scaling option {:} is not valid but must be one ' + 'of [0, 1, 2]' + ) + err_msg = err_msg.foramt(scaling) + raise ValueError(err_msg) + return Uy From 8ded4df531281b3e19359a5d26f3e5bf4c2db320 Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 17:59:39 +0200 Subject: [PATCH 2/8] feat: add MCA support for numpy --- xeofs/models/__init__.py | 1 + xeofs/models/mca.py | 187 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 188 insertions(+) create mode 100644 xeofs/models/mca.py diff --git a/xeofs/models/__init__.py b/xeofs/models/__init__.py index a3a98ba..4f7edff 100644 --- a/xeofs/models/__init__.py +++ b/xeofs/models/__init__.py @@ -1,3 +1,4 @@ from .eof import EOF from .rotator import Rotator from .bootstrapper import Bootstrapper +from .mca import MCA diff --git a/xeofs/models/mca.py b/xeofs/models/mca.py new file mode 100644 index 0000000..cfae98d --- /dev/null +++ b/xeofs/models/mca.py @@ -0,0 +1,187 @@ +from typing import Optional, Union, Iterable, Tuple, List + +import numpy as np + +from xeofs.models._base_mca import _BaseMCA +from xeofs.models._transformer import _MultiArrayTransformer +from ..utils.tools import squeeze + +import warnings + +warnings.filterwarnings("ignore", message="numpy.dtype size changed") +warnings.filterwarnings("ignore", message="numpy.ufunc size changed") + +Array = np.ndarray +ArrayList = Union[Array, List[Array]] + + +class MCA(_BaseMCA): + '''Maximum Covariance Analysis (MCA) of a single or multiple ``np.ndarray``. + + MCA is also known as Singular Value Decomposition (SVD) analysis or + Partial Least Squares (PLS) analysis. + + Parameters + ---------- + X, Y : np.ndarray + Data matrices two compute maximum covariance. ``X`` and ``Y`` can be + any N-dimensional array. Dimensions along which covariance shall be + maximised (denoted as *samples*) have to be defined by the + ``axis`` parameter. All remaining axes will be reshaped into a new + axis called *features*. Sample dimension of ``X`` and ``Y`` must be + the same. + n_modes : Optional[int] + Number of modes to compute. Computing less modes can results in + performance gains. If None, then the maximum number of modes is + equivalent to ``min(n_samples, n_features)`` (the default is None). + norm : bool + Normalize each feature (e.g. grid cell) by its temporal standard + deviation (the default is False). + weights_X : Optional[np.ndarray] = None + Weights applied to features of ``X``. Must have the same dimensions as the + original features which are the remaining axes not specified by + ``axis`` parameter). + weights_Y : Optional[np.ndarray] = None + Weights applied to features of ``Y``. Must have the same dimensions as the + original features which are the remaining axes not specified by + ``axis`` parameter). + axis : Union[int, Iterable[int]] + Axis along which variance should be maximised. Can also be + multi-dimensional. For example, given a data array of dimensions + ``(n x p1 x p2)`` with `n` time series at ``p1`` and ``p2`` different + locations, ``axis=0`` will maximise `temporal` variance along ``n``. + In contrast, ``axis=[1, 2]`` will maximise `spatial` variance along + ``(p1 x p2)`` (the default is 0). + + + Examples + -------- + + Import package and create data: + + >>> import numpy as np + >>> from xeofs.models import MCA + >>> rng = np.random.default_rng(7) + >>> X = rng.standard_normal((45, 4, 3)) + >>> Y = rng.standard_normal((45, 2, 5)) + + Initialize standardized MCA analysis and compute the first 2 modes: + + >>> model = MCA(X, norm=True, n_modes=2, axis=0) + >>> model.solve() + + Get singular vectors: + + >>> model.singular_vectors() + + Get homogeneous patterns: + + >>> model.homogeneous_patterns() + + ''' + def __init__( + self, + X: ArrayList, + Y: ArrayList, + axis : Union[int, Iterable[int]] = 0, + n_modes : Optional[int] = None, + norm : bool = False, + weights_X : Optional[ArrayList] = None, + weights_Y : Optional[ArrayList] = None, + ): + + self._tfx = _MultiArrayTransformer() + self._tfy = _MultiArrayTransformer() + X = self._tfx.fit_transform(X) + Y = self._tfy.fit_transform(Y) + weights_X = self._tfx.transform_weights(weights_X) + weights_Y = self._tfy.transform_weights(weights_Y) + + super().__init__( + X=X, + Y=Y, + n_modes=n_modes, + norm=norm, + weights_X=weights_X, + weights_Y=weights_Y + ) + + def singular_values(self) -> Array: + return super().singular_values() + + def explained_covariance(self) -> Array: + return super().explained_covariance() + + def squared_covariance_fraction(self) -> Array: + return super().squared_covariance_fraction() + + def singular_vectors( + self, scaling : int = 0 + ) -> Tuple[ArrayList, ArrayList]: + Vx, Vy = super().singular_vectors(scaling=scaling) + Vx = self._tfx.back_transform_eofs(Vx) + Vy = self._tfy.back_transform_eofs(Vy) + return squeeze(Vx), squeeze(Vy) + + def pcs(self, scaling : int = 0) -> Tuple[ArrayList, ArrayList]: + Ux, Uy = super().pcs(scaling=scaling) + Ux = self._tfx.back_transform_pcs(Ux) + Uy = self._tfy.back_transform_pcs(Uy) + return Ux, Uy + + def homogeneous_patterns(self) -> Tuple[ArrayList, ArrayList]: + hom_pats, pvals = super().homogeneous_patterns() + hom_patsx = squeeze(self._tfx.back_transform_eofs(hom_pats[0])) + hom_patsy = squeeze(self._tfy.back_transform_eofs(hom_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (hom_patsx, hom_patsy), (pvalsx, pvalsy) + + def heterogeneous_patterns(self) -> Tuple[ArrayList, ArrayList]: + het_pats, pvals = super().heterogeneous_patterns() + het_patsx = squeeze(self._tfx.back_transform_eofs(het_pats[0])) + het_patsy = squeeze(self._tfy.back_transform_eofs(het_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (het_patsx, het_patsy), (pvalsx, pvalsy) + + def reconstruct_XY( + self, + mode : Optional[Union[int, List[int], slice]] = None + ) -> Tuple[ArrayList, ArrayList]: + Xrec, Yrec = super().reconstruct_XY(mode) + Xrec = self._tfx.back_transform(Xrec) + Yrec = self._tfy.back_transform(Yrec) + return squeeze(Xrec), squeeze(Yrec) + + def project_onto_left_singular_vectors( + self, + X : ArrayList = None, + scaling : int = 0 + ) -> Array: + # Transform data to 2D + projx = _MultiArrayTransformer() + X_proj = projx.fit_transform(X, axis=self._tfx.axis_samples) + # Perform projection + pcs_X = super().project_onto_left_singular_vectors( + X=X_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_X = projx.back_transform_pcs(pcs_X) + return pcs_X + + def project_onto_right_singular_vectors( + self, + Y : ArrayList = None, + scaling : int = 0 + ) -> Array: + # Transform data to 2D + projy = _MultiArrayTransformer() + Y_proj = projy.fit_transform(Y, axis=self._tfy.axis_samples) + # Perform projection + pcs_Y = super().project_onto_right_singular_vectors( + Y=Y_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_Y = projy.back_transform_pcs(pcs_Y) + return pcs_Y From 834d7dda131ffaf4336f775519f34228ddf62d69 Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 18:00:05 +0200 Subject: [PATCH 3/8] feat: add MCA support for pandas --- xeofs/pandas/__init__.py | 1 + xeofs/pandas/mca.py | 191 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 192 insertions(+) create mode 100644 xeofs/pandas/mca.py diff --git a/xeofs/pandas/__init__.py b/xeofs/pandas/__init__.py index a3a98ba..4f7edff 100644 --- a/xeofs/pandas/__init__.py +++ b/xeofs/pandas/__init__.py @@ -1,3 +1,4 @@ from .eof import EOF from .rotator import Rotator from .bootstrapper import Bootstrapper +from .mca import MCA diff --git a/xeofs/pandas/mca.py b/xeofs/pandas/mca.py new file mode 100644 index 0000000..0931a3a --- /dev/null +++ b/xeofs/pandas/mca.py @@ -0,0 +1,191 @@ +from typing import Optional, Tuple, Union, List + +import pandas as pd + +from ..models._base_mca import _BaseMCA +from ..utils.tools import squeeze +from ._transformer import _MultiDataFrameTransformer + +DataFrame = pd.DataFrame +DataFrameList = Union[DataFrame, List[DataFrame]] + + +class MCA(_BaseMCA): + '''Maximum Covariance Analysis of two or multiple ``pd.DataFrame``. + + Parameters + ---------- + X, Y : DataFrameList + Data for which to maximise covariance. + axis : int + Axis along which variance should be maximsed (the default is 0). + n_modes : Optional[int] + Number of modes to compute. Computing less modes can results in + performance gains. If None, then the maximum number of modes is + equivalent to ``min(n_samples, n_features)`` (the default is None). + norm : bool + Normalize each feature (e.g. grid cell) by its temporal standard + deviation (the default is False). + weights_X, weights_Y : Optional[DataFrameList] = None + Weights applied to features of ``X`` and ``Y``. Must have the same + dimensions as the original features which are the remaining axes + not specified by ``axis`` parameter). + + + Examples + -------- + + Import package and create data: + + >>> import pandas as pd + >>> from xeofs.pandas import MCA + >>> rng = np.random.default_rng(7) + >>> X = rng.standard_normal((14, 3)) + >>> Y = rng.standard_normal((14, 4)) + >>> dfX = pd.DataFrame(X) + >>> dfY = pd.DataFrame(Y) + + Initialize standardized MCA and compute the first 2 modes: + + >>> model = MCA(dfX, dfY, norm=True, n_modes=2) + >>> model.solve() + + Get squared covariance fraction: + + >>> model.squared_covariance_fraction() + + Get singular vectors: + + >>> left_vectors, right_vectors = model.singular_vectors() + + Get PCs: + + >>> left_pcs, right_pcs = model.pcs() + + ''' + + def __init__( + self, + X: DataFrameList, + Y: DataFrameList, + axis : int = 0, + n_modes : Optional[int] = None, + norm : bool = False, + weights_X : Optional[DataFrameList] = None, + weights_Y : Optional[DataFrameList] = None + ): + + self._tfx = _MultiDataFrameTransformer() + self._tfy = _MultiDataFrameTransformer() + X = self._tfx.fit_transform(X) + Y = self._tfy.fit_transform(Y) + weights_X = self._tfx.transform_weights(weights_X) + weights_Y = self._tfy.transform_weights(weights_Y) + + super().__init__( + X=X, + Y=Y, + n_modes=n_modes, + norm=norm, + weights_X=weights_X, + weights_Y=weights_Y + ) + self._idx_mode = pd.Index(range(1, self.n_modes + 1), name='mode') + + def singular_values(self) -> DataFrame: + svalues = super().singular_values() + svalues = pd.DataFrame( + svalues, + columns=['singular_values'], + index=self._idx_mode + ) + return svalues + + def explained_covariance(self) -> DataFrame: + expvar = super().explained_covariance() + expvar = pd.DataFrame( + expvar, + columns=['explained_covariance'], + index=self._idx_mode + ) + return expvar + + def squared_covariance_fraction(self) -> DataFrame: + scf = super().squared_covariance_fraction() + scf = pd.DataFrame( + scf, + columns=['squared_covariance_fraction'], + index=self._idx_mode + ) + return scf + + def singular_vectors( + self, scaling : int = 0 + ) -> Tuple[DataFrameList, DataFrameList]: + Vx, Vy = super().singular_vectors(scaling=scaling) + Vx = self._tfx.back_transform_eofs(Vx) + Vy = self._tfy.back_transform_eofs(Vy) + return squeeze(Vx), squeeze(Vy) + + def pcs(self, scaling : int = 0) -> Tuple[DataFrame, DataFrame]: + Ux, Uy = super().pcs(scaling=scaling) + Ux = self._tfx.back_transform_pcs(Ux) + Uy = self._tfy.back_transform_pcs(Uy) + return Ux, Uy + + def homogeneous_patterns(self) -> Tuple[DataFrameList, DataFrameList]: + hom_pats, pvals = super().homogeneous_patterns() + hom_patsx = squeeze(self._tfx.back_transform_eofs(hom_pats[0])) + hom_patsy = squeeze(self._tfy.back_transform_eofs(hom_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (hom_patsx, hom_patsy), (pvalsx, pvalsy) + + def heterogenous_patterns(self) -> Tuple[DataFrameList, DataFrameList]: + het_pats, pvals = super().heterogenous_patterns() + het_patsx = squeeze(self._tfx.back_transform_eofs(het_pats[0])) + het_patsy = squeeze(self._tfy.back_transform_eofs(het_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (het_patsx, het_patsy), (pvalsx, pvalsy) + + def reconstruct_XY( + self, + mode : Optional[Union[int, List[int], slice]] = None + ) -> Tuple[DataFrameList, DataFrameList]: + Xrec, Yrec = super().reconstruct_XY(mode) + Xrec = self._tfx.back_transform(Xrec) + Yrec = self._tfy.back_transform(Yrec) + return squeeze(Xrec), squeeze(Yrec) + + def project_onto_left_singular_vectors( + self, + X : DataFrameList = None, + scaling : int = 0 + ) -> DataFrame: + # Transform data to 2D + projx = _MultiDataFrameTransformer() + X_proj = projx.fit_transform(X, axis=self._tfx.axis_samples) + # Perform projection + pcs_X = super().project_onto_left_singular_vectors( + X=X_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_X = projx.back_transform_pcs(pcs_X) + return pcs_X + + def project_onto_right_singular_vectors( + self, + Y : DataFrameList = None, + scaling : int = 0 + ) -> DataFrame: + # Transform data to 2D + projy = _MultiDataFrameTransformer() + Y_proj = projy.fit_transform(Y, axis=self._tfy.axis_samples) + # Perform projection + pcs_Y = super().project_onto_right_singular_vectors( + Y=Y_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_Y = projy.back_transform_pcs(pcs_Y) + return pcs_Y From e816e3699928d19e828fe0bb41b5003bba6a264e Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 18:00:19 +0200 Subject: [PATCH 4/8] feat: add MCA support for xarray --- xeofs/xarray/__init__.py | 1 + xeofs/xarray/mca.py | 200 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 201 insertions(+) create mode 100644 xeofs/xarray/mca.py diff --git a/xeofs/xarray/__init__.py b/xeofs/xarray/__init__.py index a3a98ba..4f7edff 100644 --- a/xeofs/xarray/__init__.py +++ b/xeofs/xarray/__init__.py @@ -1,3 +1,4 @@ from .eof import EOF from .rotator import Rotator from .bootstrapper import Bootstrapper +from .mca import MCA diff --git a/xeofs/xarray/mca.py b/xeofs/xarray/mca.py new file mode 100644 index 0000000..7438864 --- /dev/null +++ b/xeofs/xarray/mca.py @@ -0,0 +1,200 @@ +from typing import Optional, Tuple, Union, List + +import pandas as pd +import xarray as xr + +from ..models._base_mca import _BaseMCA +from ..utils.tools import squeeze +from ._transformer import _MultiDataArrayTransformer + +DataArray = xr.DataArray +DataArrayList = Union[DataArray, List[DataArray]] + + +class MCA(_BaseMCA): + '''Maximum Covariance Analysis of two or multiple ``xr.DataArray``. + + Parameters + ---------- + X, Y : DataArrayList + Data for which to maximise covariance. + axis : int + Axis along which variance should be maximsed (the default is 0). + n_modes : Optional[int] + Number of modes to compute. Computing less modes can results in + performance gains. If None, then the maximum number of modes is + equivalent to ``min(n_samples, n_features)`` (the default is None). + norm : bool + Normalize each feature (e.g. grid cell) by its temporal standard + deviation (the default is False). + weights_X, weights_Y : Optional[DataArrayList] = None + Weights applied to features of ``X`` and ``Y``. Must have the same + dimensions as the original features which are the remaining axes + not specified by ``axis`` parameter). + + + Examples + -------- + + Import package and create data: + + >>> import xarray as xr + >>> from xeofs.xarray import MCA + + Initialize standardized MCA and compute the first 2 modes of two + ``xr.DataArray`` ``da1`` and ``da2``: + + >>> model = MCA(da1, da2, norm=True, n_modes=2) + >>> model.solve() + + Get squared covariance fraction: + + >>> model.squared_covariance_fraction() + + Get singular vectors: + + >>> left_vectors, right_vectors = model.singular_vectors() + + Get PCs: + + >>> left_pcs, right_pcs = model.pcs() + + ''' + + def __init__( + self, + X: DataArrayList, + Y: DataArrayList, + dim : Optional[Union[str, List[str]]] = 'time', + n_modes : Optional[int] = None, + norm : bool = False, + weights_X : Optional[Union[str, DataArrayList]] = None, + weights_Y : Optional[Union[str, DataArrayList]] = None + ): + use_coslat_X = True if weights_X == 'coslat' else False + use_coslat_Y = True if weights_Y == 'coslat' else False + + self._tfx = _MultiDataArrayTransformer() + self._tfy = _MultiDataArrayTransformer() + + X = self._tfx.fit_transform(X, dim=dim, coslat=use_coslat_X) + Y = self._tfy.fit_transform(Y, dim=dim, coslat=use_coslat_Y) + + if use_coslat_X: + weights_X = self._tfx.coslat_weights + if use_coslat_Y: + weights_Y = self._tfy.coslat_weights + + weights_X = self._tfx.transform_weights(weights_X) + weights_Y = self._tfy.transform_weights(weights_Y) + + super().__init__( + X=X, + Y=Y, + n_modes=n_modes, + norm=norm, + weights_X=weights_X, + weights_Y=weights_Y + ) + self._idx_mode = pd.Index(range(1, self.n_modes + 1), name='mode') + + def singular_values(self) -> DataArray: + svalues = super().singular_values() + svalues = xr.DataArray( + svalues, + dims=['mode'], + coords=dict(mode=self._idx_mode), + name='singular_values' + ) + return svalues + + def explained_covariance(self) -> DataArray: + expvar = super().explained_covariance() + expvar = xr.DataArray( + expvar, + dims=['mode'], + coords=dict(mode=self._idx_mode), + name='explained_covariance' + ) + return expvar + + def squared_covariance_fraction(self) -> DataArray: + scf = super().squared_covariance_fraction() + scf = xr.DataArray( + scf, + dims=['mode'], + coords=dict(mode=self._idx_mode), + name='squared_covariance_fraction' + ) + return scf + + def singular_vectors( + self, scaling : int = 0 + ) -> Tuple[DataArrayList, DataArrayList]: + Vx, Vy = super().singular_vectors(scaling=scaling) + Vx = self._tfx.back_transform_eofs(Vx) + Vy = self._tfy.back_transform_eofs(Vy) + return squeeze(Vx), squeeze(Vy) + + def pcs(self, scaling : int = 0) -> Tuple[DataArray, DataArray]: + Ux, Uy = super().pcs(scaling=scaling) + Ux = self._tfx.back_transform_pcs(Ux) + Uy = self._tfy.back_transform_pcs(Uy) + return Ux, Uy + + def homogeneous_patterns(self) -> Tuple[DataArrayList, DataArrayList]: + hom_pats, pvals = super().homogeneous_patterns() + hom_patsx = squeeze(self._tfx.back_transform_eofs(hom_pats[0])) + hom_patsy = squeeze(self._tfy.back_transform_eofs(hom_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (hom_patsx, hom_patsy), (pvalsx, pvalsy) + + def heterogeneous_patterns(self) -> Tuple[DataArrayList, DataArrayList]: + het_pats, pvals = super().heterogeneous_patterns() + het_patsx = squeeze(self._tfx.back_transform_eofs(het_pats[0])) + het_patsy = squeeze(self._tfy.back_transform_eofs(het_pats[1])) + pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) + pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + return (het_patsx, het_patsy), (pvalsx, pvalsy) + + def reconstruct_XY( + self, + mode : Optional[Union[int, List[int], slice]] = None + ) -> Tuple[DataArrayList, DataArrayList]: + Xrec, Yrec = super().reconstruct_XY(mode) + Xrec = self._tfx.back_transform(Xrec) + Yrec = self._tfy.back_transform(Yrec) + return squeeze(Xrec), squeeze(Yrec) + + def project_onto_left_singular_vectors( + self, + X : DataArrayList = None, + scaling : int = 0 + ) -> DataArray: + # Transform data to 2D + projx = _MultiDataArrayTransformer() + X_proj = projx.fit_transform(X, dim=self._tfy.dims_samples) + # Perform projection + pcs_X = super().project_onto_left_singular_vectors( + X=X_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_X = projx.back_transform_pcs(pcs_X) + return pcs_X + + def project_onto_right_singular_vectors( + self, + Y : DataArrayList = None, + scaling : int = 0 + ) -> DataArray: + # Transform data to 2D + projy = _MultiDataArrayTransformer() + Y_proj = projy.fit_transform(Y, dim=self._tfy.dims_samples) + # Perform projection + pcs_Y = super().project_onto_right_singular_vectors( + Y=Y_proj, scaling=scaling + ) + # Backtransform to PC format + pcs_Y = projy.back_transform_pcs(pcs_Y) + return pcs_Y From b5b528678becdf80b511a3883485304341c09692 Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 23:17:17 +0200 Subject: [PATCH 5/8] fix: set informative names of Dataframes and DataArrays --- xeofs/pandas/mca.py | 22 +++++++++---------- xeofs/xarray/mca.py | 52 ++++++++++++++++++++++++++++++++++++++------- 2 files changed, 55 insertions(+), 19 deletions(-) diff --git a/xeofs/pandas/mca.py b/xeofs/pandas/mca.py index 0931a3a..4d8ba52 100644 --- a/xeofs/pandas/mca.py +++ b/xeofs/pandas/mca.py @@ -94,28 +94,28 @@ def __init__( def singular_values(self) -> DataFrame: svalues = super().singular_values() - svalues = pd.DataFrame( + svalues = pd.Series( svalues, - columns=['singular_values'], - index=self._idx_mode + index=self._idx_mode, + name='singular_values', ) return svalues def explained_covariance(self) -> DataFrame: expvar = super().explained_covariance() - expvar = pd.DataFrame( + expvar = pd.Series( expvar, - columns=['explained_covariance'], - index=self._idx_mode + index=self._idx_mode, + name='explained_covariance', ) return expvar def squared_covariance_fraction(self) -> DataFrame: scf = super().squared_covariance_fraction() - scf = pd.DataFrame( + scf = pd.Series( scf, - columns=['squared_covariance_fraction'], - index=self._idx_mode + index=self._idx_mode, + name='squared_covariance_fraction', ) return scf @@ -141,8 +141,8 @@ def homogeneous_patterns(self) -> Tuple[DataFrameList, DataFrameList]: pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) return (hom_patsx, hom_patsy), (pvalsx, pvalsy) - def heterogenous_patterns(self) -> Tuple[DataFrameList, DataFrameList]: - het_pats, pvals = super().heterogenous_patterns() + def heterogeneous_patterns(self) -> Tuple[DataFrameList, DataFrameList]: + het_pats, pvals = super().heterogeneous_patterns() het_patsx = squeeze(self._tfx.back_transform_eofs(het_pats[0])) het_patsy = squeeze(self._tfy.back_transform_eofs(het_pats[1])) pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) diff --git a/xeofs/xarray/mca.py b/xeofs/xarray/mca.py index 7438864..3b956a2 100644 --- a/xeofs/xarray/mca.py +++ b/xeofs/xarray/mca.py @@ -134,28 +134,64 @@ def singular_vectors( Vx, Vy = super().singular_vectors(scaling=scaling) Vx = self._tfx.back_transform_eofs(Vx) Vy = self._tfy.back_transform_eofs(Vy) + # Rename DataArrays + for da in Vx: + da.name = 'left_singular_vectors' + for da in Vy: + da.name = 'right_singular_vectors' return squeeze(Vx), squeeze(Vy) def pcs(self, scaling : int = 0) -> Tuple[DataArray, DataArray]: Ux, Uy = super().pcs(scaling=scaling) Ux = self._tfx.back_transform_pcs(Ux) Uy = self._tfy.back_transform_pcs(Uy) + # Rename DataArrays + Ux.name = 'left_pcs' + Uy.name = 'right_pcs' return Ux, Uy def homogeneous_patterns(self) -> Tuple[DataArrayList, DataArrayList]: hom_pats, pvals = super().homogeneous_patterns() - hom_patsx = squeeze(self._tfx.back_transform_eofs(hom_pats[0])) - hom_patsy = squeeze(self._tfy.back_transform_eofs(hom_pats[1])) - pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) - pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + hom_patsx = self._tfx.back_transform_eofs(hom_pats[0]) + pvalsx = self._tfx.back_transform_eofs(pvals[0]) + hom_patsy = self._tfy.back_transform_eofs(hom_pats[1]) + pvalsy = self._tfy.back_transform_eofs(pvals[1]) + + # Rename DataArrays + for da, p in zip(hom_patsx, pvalsx): + da.name = 'left_homogeneous_patterns' + p.name = 'left_homogeneous_patterns_p_values' + for da, p in zip(hom_patsy, pvalsy): + da.name = 'right_homogeneous_patterns' + p.name = 'right_homogeneous_patterns_p_values' + + # Remove list if single DataArray + hom_patsx = squeeze(hom_patsx) + hom_patsy = squeeze(hom_patsy) + pvalsx = squeeze(pvalsx) + pvalsy = squeeze(pvalsy) return (hom_patsx, hom_patsy), (pvalsx, pvalsy) def heterogeneous_patterns(self) -> Tuple[DataArrayList, DataArrayList]: het_pats, pvals = super().heterogeneous_patterns() - het_patsx = squeeze(self._tfx.back_transform_eofs(het_pats[0])) - het_patsy = squeeze(self._tfy.back_transform_eofs(het_pats[1])) - pvalsx = squeeze(self._tfx.back_transform_eofs(pvals[0])) - pvalsy = squeeze(self._tfy.back_transform_eofs(pvals[1])) + het_patsx = self._tfx.back_transform_eofs(het_pats[0]) + pvalsx = self._tfx.back_transform_eofs(pvals[0]) + het_patsy = self._tfy.back_transform_eofs(het_pats[1]) + pvalsy = self._tfy.back_transform_eofs(pvals[1]) + + # Rename DataArrays + for da, p in zip(het_patsx, pvalsx): + da.name = 'left_heterogeneous_patterns' + p.name = 'left_heterogeneous_patterns_p_values' + for da, p in zip(het_patsy, pvalsy): + da.name = 'right_heterogeneous_patterns' + p.name = 'right_heterogeneous_patterns_p_values' + + # Remove list if single DataArray + het_patsx = squeeze(het_patsx) + het_patsy = squeeze(het_patsy) + pvalsx = squeeze(pvalsx) + pvalsy = squeeze(pvalsy) return (het_patsx, het_patsy), (pvalsx, pvalsy) def reconstruct_XY( From eb2a2808259454adfaba0ce35dff75a445ccab29 Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 23:17:51 +0200 Subject: [PATCH 6/8] test: add MCA test wrapper --- tests/models/test_mca_wrapper.py | 90 ++++++++++++++++++++++++++++++++ 1 file changed, 90 insertions(+) create mode 100644 tests/models/test_mca_wrapper.py diff --git a/tests/models/test_mca_wrapper.py b/tests/models/test_mca_wrapper.py new file mode 100644 index 0000000..62c877d --- /dev/null +++ b/tests/models/test_mca_wrapper.py @@ -0,0 +1,90 @@ +import numpy as np +import pandas as pd +import xarray as xr +import pytest + +from xeofs.models import MCA +from xeofs.pandas import MCA as pdMCA +from xeofs.xarray import MCA as xrMCA + + +def test_wrapper_bootstrapper(sample_array): + # Bootstrapping runs without errors + X = sample_array + df = pd.DataFrame(X) + da = xr.DataArray(X) + # Perform analysis with all three wrappers + numpy_model = MCA(X, X) + numpy_model.solve() + + pandas_model = pdMCA(df, df) + pandas_model.solve() + + xarray_model = xrMCA(da, da, dim='dim_0') + xarray_model.solve() + + # Numpy + desired_svals = numpy_model.singular_values() + desired_expcovar = numpy_model.explained_covariance() + desired_scf = numpy_model.squared_covariance_fraction() + desired_svecs = numpy_model.singular_vectors() + desired_pcs = numpy_model.pcs() + desired_hom_pats, desired_pvals_hom = numpy_model.homogeneous_patterns() + desired_het_pats, desired_pvals_het = numpy_model.heterogeneous_patterns() + desired_xproj = numpy_model.project_onto_left_singular_vectors(X) + desired_yproj = numpy_model.project_onto_right_singular_vectors(X) + desired_Xrec, desired_Yrec = numpy_model.reconstruct_XY() + + # pandas + actual_pd_svals = pandas_model.singular_values() + actual_pd_expcovar = pandas_model.explained_covariance() + actual_pd_scf = pandas_model.squared_covariance_fraction() + actual_pd_svecs = pandas_model.singular_vectors() + actual_pd_pcs = pandas_model.pcs() + actual_pd_hom_pats, actual_pd_pvals_hom = pandas_model.homogeneous_patterns() + actual_pd_het_pats, actual_pd_pvals_het = pandas_model.heterogeneous_patterns() + actual_pd_xproj = pandas_model.project_onto_left_singular_vectors(df) + actual_pd_yproj = pandas_model.project_onto_right_singular_vectors(df) + actual_pd_Xrec, actual_pd_Yrec = pandas_model.reconstruct_XY() + + # xarray + actual_xr_svals = xarray_model.singular_values() + actual_xr_expcovar = xarray_model.explained_covariance() + actual_xr_scf = xarray_model.squared_covariance_fraction() + actual_xr_svecs = xarray_model.singular_vectors() + actual_xr_pcs = xarray_model.pcs() + actual_xr_hom_pats, actual_xr_pvals_hom = xarray_model.homogeneous_patterns() + actual_xr_het_pats, actual_xr_pvals_het = xarray_model.heterogeneous_patterns() + actual_xr_xproj = xarray_model.project_onto_left_singular_vectors(da) + actual_xr_yproj = xarray_model.project_onto_right_singular_vectors(da) + actual_xr_Xrec, actual_xr_Yrec = xarray_model.reconstruct_XY() + + # assert consistent pandas results + np.testing.assert_allclose(desired_svals, actual_pd_svals.values) + np.testing.assert_allclose(desired_expcovar, actual_pd_expcovar.values) + np.testing.assert_allclose(desired_scf, actual_pd_scf.values) + np.testing.assert_allclose(desired_svecs[0], actual_pd_svecs[0].values) + np.testing.assert_allclose(desired_svecs[1], actual_pd_svecs[1].values) + np.testing.assert_allclose(desired_pcs[0], actual_pd_pcs[0].values) + np.testing.assert_allclose(desired_pcs[1], actual_pd_pcs[1].values) + np.testing.assert_allclose(desired_hom_pats[0], actual_pd_hom_pats[0].values) + np.testing.assert_allclose(desired_hom_pats[1], actual_pd_hom_pats[1].values) + np.testing.assert_allclose(desired_het_pats[0], actual_pd_het_pats[0].values) + np.testing.assert_allclose(desired_het_pats[1], actual_pd_het_pats[1].values) + np.testing.assert_allclose(desired_xproj, actual_pd_xproj.values) + np.testing.assert_allclose(desired_yproj, actual_pd_yproj.values) + + # assert consistent pandas results + np.testing.assert_allclose(desired_svals, actual_xr_svals.values) + np.testing.assert_allclose(desired_expcovar, actual_xr_expcovar.values) + np.testing.assert_allclose(desired_scf, actual_xr_scf.values) + np.testing.assert_allclose(desired_svecs[0], actual_xr_svecs[0].values) + np.testing.assert_allclose(desired_svecs[1], actual_xr_svecs[1].values) + np.testing.assert_allclose(desired_pcs[0], actual_xr_pcs[0].values) + np.testing.assert_allclose(desired_pcs[1], actual_xr_pcs[1].values) + np.testing.assert_allclose(desired_hom_pats[0], actual_xr_hom_pats[0].values) + np.testing.assert_allclose(desired_hom_pats[1], actual_xr_hom_pats[1].values) + np.testing.assert_allclose(desired_het_pats[0], actual_xr_het_pats[0].values) + np.testing.assert_allclose(desired_het_pats[1], actual_xr_het_pats[1].values) + np.testing.assert_allclose(desired_xproj, actual_xr_xproj.values) + np.testing.assert_allclose(desired_yproj, actual_xr_yproj.values) From 68d9db004ff23574fafb7b69cc85c7b2b33812c0 Mon Sep 17 00:00:00 2001 From: nicrie Date: Sat, 20 Aug 2022 23:20:28 +0200 Subject: [PATCH 7/8] docs: reorganize examples --- .../images/sphx_glr_plot_bootstrap_001.png | Bin 0 -> 691018 bytes .../thumb/sphx_glr_plot_bootstrap_thumb.png | Bin 0 -> 62990 bytes docs/auto_examples/1eof/plot_bootstrap.ipynb | 137 +++++++++++ .../auto_examples/1eof}/plot_bootstrap.py | 4 +- docs/auto_examples/1eof/plot_bootstrap.py.md5 | 1 + docs/auto_examples/1eof/plot_bootstrap.rst | 221 ++++++++++++++++++ .../1eof/plot_bootstrap_codeobj.pickle | Bin 0 -> 24241 bytes .../auto_examples/1eof/sg_execution_times.rst | 6 +- .../images/sphx_glr_plot_mreof_001.png | Bin 0 -> 75510 bytes .../images/sphx_glr_plot_rotated_eof_001.png | Bin 0 -> 455841 bytes .../thumb/sphx_glr_plot_mreof_thumb.png | Bin 0 -> 46669 bytes .../thumb/sphx_glr_plot_rotated_eof_thumb.png | Bin 0 -> 82934 bytes docs/auto_examples/3rotated/plot_mreof.ipynb | 108 +++++++++ .../auto_examples/3rotated}/plot_mreof.py | 0 docs/auto_examples/3rotated/plot_mreof.py.md5 | 1 + 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+ +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_auto_examples_1eof_plot_bootstrap.py: + + +Significance teting of EOF analysis via bootstrap +================================================= + +Testing the significance of individual modes and obtain confidence intervals +for both EOFs and PCs. + +.. GENERATED FROM PYTHON SOURCE LINES 8-19 + +.. code-block:: default + + + + # Load packages and data: + import numpy as np + import xarray as xr + import matplotlib.pyplot as plt + from matplotlib.gridspec import GridSpec + from cartopy.crs import Orthographic, PlateCarree + + from xeofs.xarray import EOF, Bootstrapper + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 20-23 + +.. code-block:: default + + + t2m = xr.tutorial.load_dataset('air_temperature')['air'] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 24-25 + +Perform EOF analysis + +.. GENERATED FROM PYTHON SOURCE LINES 25-33 + +.. code-block:: default + + + model = EOF(t2m, n_modes=25, norm=False, dim='time') + model.solve() + expvar = model.explained_variance_ratio() + eofs = model.eofs() + pcs = model.pcs() + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 34-38 + +Perform bootstrapping of the model to identy the number of significant modes. +We choose a significance level of alpha=0.05 and perform 25 bootstraps. +Note - if computationallly feasible - you typically want to choose higher +numbers of bootstraps e.g. 100 or 1000. + +.. GENERATED FROM PYTHON SOURCE LINES 38-47 + +.. code-block:: default + + + alpha = .05 + n_boot = 25 + + bs = Bootstrapper(n_boot=n_boot, alpha=alpha) + bs.bootstrap(model) + n_significant_modes = bs.n_significant_modes() + print('{:} modes are significant at alpha={:.2}'.format(n_significant_modes, alpha)) + + + + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + Bootstrap: 0%| | 0/25 [00:00` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: plot_bootstrap.ipynb ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/docs/auto_examples/1eof/plot_bootstrap_codeobj.pickle b/docs/auto_examples/1eof/plot_bootstrap_codeobj.pickle new file mode 100644 index 0000000000000000000000000000000000000000..236f9dff082390e012f6a2fffb8920c0b8909594 GIT binary patch literal 24241 zcmc(n4Tv4p702Ul_VcZ~+0AB6qG{6)+gRll)20LhDeJBVEio}$v{vnN_Pxoz_k3Tz 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b/docs/auto_examples/1eof/sg_execution_times.rst @@ -5,14 +5,16 @@ Computation times ================= -**00:01.629** total execution time for **auto_examples_1eof** files: +**00:12.438** total execution time for **auto_examples_1eof** files: +--------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_examples_1eof_plot_multivariate-eof.py` (``plot_multivariate-eof.py``) | 00:01.629 | 0.0 MB | +| :ref:`sphx_glr_auto_examples_1eof_plot_bootstrap.py` (``plot_bootstrap.py``) | 00:12.438 | 0.0 MB | +--------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_examples_1eof_plot_eof-smode.py` (``plot_eof-smode.py``) | 00:00.000 | 0.0 MB | +--------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_examples_1eof_plot_eof-tmode.py` (``plot_eof-tmode.py``) | 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a/docs/auto_examples/3rotated/plot_mreof.ipynb b/docs/auto_examples/3rotated/plot_mreof.ipynb new file mode 100644 index 0000000..61311be --- /dev/null +++ b/docs/auto_examples/3rotated/plot_mreof.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Varimax-rotated Multivariate EOF analysis\n\nMultivariate EOF analysis with additional Varimax rotation.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Load packages and data:\nimport xarray as xr\nimport matplotlib.pyplot as plt\nfrom matplotlib.gridspec import GridSpec\nfrom cartopy.crs import PlateCarree\n\nfrom xeofs.xarray import EOF, Rotator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create four different dataarrayss\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "t2m = xr.tutorial.load_dataset('air_temperature')['air']\nsubset1 = t2m.isel(lon=slice(0, 4))\nsubset2 = t2m.isel(lon=slice(5, 14))\nsubset3 = t2m.isel(lon=slice(15, 34))\nsubset4 = t2m.isel(lon=slice(35, None))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perform the actual analysis\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mpca = EOF(\n [subset1, subset2, subset3, subset4],\n dim='time',\n norm=False,\n weights='coslat'\n)\nmpca.solve()\nrot = Rotator(mpca, n_rot=50)\nreofs = rot.eofs()\nrpcs = rot.pcs()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot mode 1\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mode = 1\nproj = PlateCarree()\nkwargs = {\n 'cmap' : 'RdBu',\n 'vmin' : -.1,\n 'vmax': .1,\n 'transform': proj,\n 'add_colorbar': False\n}\n\nfig = plt.figure(figsize=(7.3, 6))\nfig.subplots_adjust(wspace=0)\ngs = GridSpec(2, 4, figure=fig, width_ratios=[1, 2, 3, 2])\nax = [fig.add_subplot(gs[0, i], projection=proj) for i in range(4)]\nax_pc = fig.add_subplot(gs[1, :])\n\n# PC\nrpcs.sel(mode=mode).plot(ax=ax_pc)\nax_pc.set_xlabel('')\nax_pc.set_title('')\n\n# EOFs\nfor i, (a, eof) in enumerate(zip(ax, reofs)):\n a.coastlines(color='.5')\n eof.sel(mode=mode).plot(ax=a, **kwargs)\n a.set_xticks([])\n a.set_yticks([])\n a.set_xlabel('')\n a.set_ylabel('')\n a.set_title('Subset {:}'.format(i+1))\nax[0].set_ylabel('EOFs')\nfig.suptitle('Mode {:}'.format(mode))\nplt.savefig('multivariate-eof-analysis.jpg')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/examples/2rotated/plot_mreof.py b/docs/auto_examples/3rotated/plot_mreof.py similarity index 100% rename from examples/2rotated/plot_mreof.py rename to docs/auto_examples/3rotated/plot_mreof.py diff --git a/docs/auto_examples/3rotated/plot_mreof.py.md5 b/docs/auto_examples/3rotated/plot_mreof.py.md5 new file mode 100644 index 0000000..ce90561 --- /dev/null +++ b/docs/auto_examples/3rotated/plot_mreof.py.md5 @@ -0,0 +1 @@ +f6a78a0349bdc68043e00652415b3a8d \ No newline at end of file diff --git a/docs/auto_examples/3rotated/plot_mreof.rst b/docs/auto_examples/3rotated/plot_mreof.rst new file mode 100644 index 0000000..9381237 --- /dev/null +++ b/docs/auto_examples/3rotated/plot_mreof.rst @@ -0,0 +1,180 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "auto_examples/3rotated/plot_mreof.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_auto_examples_3rotated_plot_mreof.py: + + +Varimax-rotated Multivariate EOF analysis +============================================ + +Multivariate EOF analysis with additional Varimax rotation. + +.. GENERATED FROM PYTHON SOURCE LINES 7-17 + +.. code-block:: default + + + + # Load packages and data: + import xarray as xr + import matplotlib.pyplot as plt + from matplotlib.gridspec import GridSpec + from cartopy.crs import PlateCarree + + from xeofs.xarray import EOF, Rotator + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 18-19 + +Create four different dataarrayss + +.. GENERATED FROM PYTHON SOURCE LINES 19-25 + +.. code-block:: default + + t2m = xr.tutorial.load_dataset('air_temperature')['air'] + subset1 = t2m.isel(lon=slice(0, 4)) + subset2 = t2m.isel(lon=slice(5, 14)) + subset3 = t2m.isel(lon=slice(15, 34)) + subset4 = t2m.isel(lon=slice(35, None)) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 26-27 + +Perform the actual analysis + +.. GENERATED FROM PYTHON SOURCE LINES 27-39 + +.. code-block:: default + + + mpca = EOF( + [subset1, subset2, subset3, subset4], + dim='time', + norm=False, + weights='coslat' + ) + mpca.solve() + rot = Rotator(mpca, n_rot=50) + reofs = rot.eofs() + rpcs = rot.pcs() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 40-41 + +Plot mode 1 + +.. GENERATED FROM PYTHON SOURCE LINES 41-75 + +.. code-block:: default + + + mode = 1 + proj = PlateCarree() + kwargs = { + 'cmap' : 'RdBu', + 'vmin' : -.1, + 'vmax': .1, + 'transform': proj, + 'add_colorbar': False + } + + fig = plt.figure(figsize=(7.3, 6)) + fig.subplots_adjust(wspace=0) + gs = GridSpec(2, 4, figure=fig, width_ratios=[1, 2, 3, 2]) + ax = [fig.add_subplot(gs[0, i], projection=proj) for i in range(4)] + ax_pc = fig.add_subplot(gs[1, :]) + + # PC + rpcs.sel(mode=mode).plot(ax=ax_pc) + ax_pc.set_xlabel('') + ax_pc.set_title('') + + # EOFs + for i, (a, eof) in enumerate(zip(ax, reofs)): + a.coastlines(color='.5') + eof.sel(mode=mode).plot(ax=a, **kwargs) + a.set_xticks([]) + a.set_yticks([]) + a.set_xlabel('') + a.set_ylabel('') + a.set_title('Subset {:}'.format(i+1)) + ax[0].set_ylabel('EOFs') + fig.suptitle('Mode {:}'.format(mode)) + plt.savefig('multivariate-eof-analysis.jpg') + + + +.. image-sg:: /auto_examples/3rotated/images/sphx_glr_plot_mreof_001.png + :alt: Mode 1, Subset 1, Subset 2, Subset 3, Subset 4 + :srcset: /auto_examples/3rotated/images/sphx_glr_plot_mreof_001.png + :class: sphx-glr-single-img + + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 0 minutes 3.764 seconds) + + +.. _sphx_glr_download_auto_examples_3rotated_plot_mreof.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: plot_mreof.py ` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: plot_mreof.ipynb ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/docs/auto_examples/3rotated/plot_mreof_codeobj.pickle b/docs/auto_examples/3rotated/plot_mreof_codeobj.pickle new file mode 100644 index 0000000000000000000000000000000000000000..08c6a42105d60393f6004312a228c434c64b89bf GIT binary patch literal 20754 zcmd5^4Tv3A6;867-OavDcC(w^{FqYl2jkz9q@jgE(Cwy)(WYrPmey*0&b~L$%FRxryll5Ecn#>3=hCV{Q%Tb# z?C(|_4br2Lw2-_oWIEpLRIRetZk)6gjZzlCcbVGf@{6(4O70ru7 zXO4pLvS&AxCpXJ+8$1VZrVLteY1$jfIH`;d(Kjl-Nnvf6UZ&)>&M$esYgPSVcEv2G zwXqNLtJ!R~gg-9N!%;$S&I4$q-l}A$h1;&J`zs6Wwp;UZSY4S5q_nQiMQFUr?jw7vVqg%5>l1FWS zrL6|!q~7Q4jtJr_E)z?6c9}Sh=Bk3sMl=_?O$NvJa)6ZJ`#B(u-3OKYOCokxcAK5G zGu|Lp8p)E7aWaZl?pu1B}lBruoNN3Mko6u}~V%I~8D7#-n2$Jk3!w zs`zUiyH<$?=w~>1%JTCZkVf)LLf-C;`TLsXI$9F9NY3Glvs)7l+9>t=6m^5N#`&vC za2l_QK?{IrO7Q%8E|7BiW-dbGb-xmxAq!&;u?O;zl-Wc15RKaRl=KeSuiB)E`Jv&6 z7su~2RZyajFmW2&M-^lnT^?hmDP8;+14M){0_Z8xlzG24uZ{~S*P<@-Djrcr%CA?9R|k_)DhDPA%E#Zo|t{)dH9Je>{e z*R2y6yEo)Qp&+b)Km}oRvF%%a+ZCmQZTh~u3}WGn^qsX1W^c!Jklf`ulak*?Yqip; zDuyLe;Mm!;d{OLZ)R)SlxKXY^Sw}n&8M3o2(i0Y4D0Y%y1!8+9Vq77F@GePnxZ}1R zjpbDh%eNPxN@Ux@m$GQJj}6TcT9&80Fz?=5yG=-Rz!0! zE;A;5C&#);QBu6rOFqj~K^(q_$Zx9%_J*O7Y=Nlo!6@yey^$nRbtZ|IoVWAnkVd={ zp|;Mue%v>l2iZ7Li}edvC!c|nVTC$TUse`J4%L^tZV*)UCWB1ywA3>_m7S%b zNwa;~?6Jdcy>`4~Ym1J0B!Z*n>17c0gecHAKi_<7H;mIr2QhvsFdj=z#011Z4T|{1 zEGG02tG6Jlh@ZJFscjV9H0*Y&+5)2;qkzxS3eJpDG*(11ALle0W>{9sclxq-Ct;+N zty(Qk6V%9>4o4Px3DiyFDQA?WXd>>v8&RJNtp~A5r&o+YhBm_DUc_QLiY*xo;5-SU zj|eVb;XsMGugQ)Wf_jZ|KJK~mHe9}qC}X4AaCuO&L>ZY(lhIS?A-Tqy)4ORDcrWu_55~o0gje^w_Al3GP1CxvnKWdWf%tHpI8;f z)gw5&jC&_l0}>w?JrWudlk=~Laoi>YL5Y#%VqwB1T~NL$Ie$lH>449fC&6kjPF3YZ z!!z`}g@u0ytn-fCo%I{yU2`eiRrz%vZU;!VI}DquPy}K`!K^-0r}SsEr5cY2h8agD zR3F`&5p0(3sALneH&jzhEvCG9hKVJs$sB@h)wffUbV0wHl~IRZz#yP|`lU#Ii`+{| zw#n@VV=HCQV{mfTPRgKxxcaq-`3&AjWzdiIQBIkKH_&$WvXF%CegvA*woH<%p4h3R z=8}9MF?DH#fFmf80>i%Se|9UwSwQTwE@n7~kmw+HGn^v~C{5I_U|_Ti>=+Us=#qxB z$iY&6*Kj}@!RwHGvD+HXJJ?Dn-FLB(8fOcE2D`T5)L3B3bD4$GI64SWvGx#b(2E?-Nj{tsUgJYGzVAb*fo^m-A7ElB(+@Fm8qJR&NP(*z&aDG!pp@?z z2(1zS1OgViY%LqT%bnyvj|hop>!F5nVbC=0krdVywq=uw~k0Zu2T50br zZKtUs_MbxbC*$ll_6TXWN`8Ntiz9}9Eqxx{roZS#A02;0oKr`~UnJAX;6yn%J|P2S zR_w>3-LLi@+?BoaeFjlT*J9e;Jj=uq$DhHlf?M|Im|9H4pJ!qT@fQ%xuRbyx3Y2Lwjg6YjxeL}17)WC5ixI@`ZLn4$287A&a3i?l zL9TS&6Ukb=Ql|m;&#aR+Y_wJ2NWTnrA0jpyBO#pV4S~b!;HzbPyC!}b+y#qnv#x~; zQEJE%H(n!|a~HC(QaX3Og_=l17RKsR=sO69LKX&Phpg{%)tJWV!(1>KJU>7<8L}|% zvkh5T8+H4SITUn%{{#V4PN#-TYRKXxhf0yb)q|=a4u1-f*Mb>#QnCd_^UKV}IKSc1 zA&vMgLdEe7w?GdIsyy|329g;2Qv`uZag>F@$ju#iYnUn->KY7ef95M4m)J zg-W)dXcSaB4UKVL!J|VO@hXJUqoA^8j)JdYAc?WpM-aO=6CRC(Ur1G~ngcf(RYZ)g z4a3<97Jvz;a{(Qk%k~-C2)~O_lXju=l5@c%M3_^zz!F;&Hn_b`ye*r^BtA4|cnR;hR%`~|Ur^}AYesu+XVS#1nZDdOz` zpIG5okkJZaKqd9pvP$W%k_e(%b-wGkvf8U?ge5 z_YzQAiV_T2-$}15J&as45@#kjUx`ad8HJ^h8*j4QWl;qWSq|64F9pJQMISZ(NYdO8 l$co<$gs` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_auto_examples_3rotated_plot_rotated_eof.py: + + +Rotated EOF analysis +======================== + +EOF analysis is often used in climate science to interpret the obtained +eigenvectors (EOFs) as patterns of climatic variability. Given the mathematical +nature of EOF analysis which leads to orthogonal EOFs, this interpretation +is questionable for all but the first EOF. Rotated EOF anaylsis helps to +alleviate the orthogonal constraint of the EOFs by applying an additional +rotation to the (loaded) EOFs by means of a optimization criteria (Varimax, +Promax). Varimax (orthogonal) and Promax (oblique) rotation have the additional +side effect of creating "sparse" solutions, i.e. turning the otherwise dense +EOFs into a more "interpretable" solutions by reducing the number of variables +contributing to an EOF. As such, rotation acts as a kind of regularization of +the EOF solution, with the ``power`` parameter defining its strength (the +higher, the more sparse the EOFs become). In case of small regularization, i.e. +``power=1``, the Promax rotation reduces to a Varimax rotation. + +Here we compare the first three modes of EOF analysis (1) without +regularization, (2) with Varimax rotation and (3) with Promax rotation. + +Load packages and data: + +.. GENERATED FROM PYTHON SOURCE LINES 24-37 + +.. code-block:: default + + import xarray as xr + import matplotlib.pyplot as plt + import seaborn as sns + from matplotlib.gridspec import GridSpec + from cartopy.crs import Orthographic, PlateCarree + + from xeofs.xarray import EOF, Rotator + + + sns.set_context('paper') + + t2m = xr.tutorial.load_dataset('air_temperature')['air'] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 38-39 + +Perform the actual analysis + +.. GENERATED FROM PYTHON SOURCE LINES 39-61 + +.. code-block:: default + + + eofs = [] + pcs = [] + # (1) Standard EOF without regularization + model = EOF(t2m, dim=['time'], weights='coslat') + model.solve() + eofs.append(model.eofs()) + pcs.append(model.pcs()) + # (2) Varimax-rotated EOF analysis + model_var = EOF(t2m, dim=['time'], weights='coslat') + model_var.solve() + rot_var = Rotator(model, n_rot=50, power=1) + eofs.append(rot_var.eofs()) + pcs.append(rot_var.pcs()) + # (3) Promax-rotated EOF analysis + model_pro = EOF(t2m, dim=['time'], weights='coslat') + model_pro.solve() + rot_pro = Rotator(model, n_rot=50, power=2) + eofs.append(rot_pro.eofs()) + pcs.append(rot_pro.pcs()) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 62-67 + +Create figure showing the first 6 modes for all 3 cases. While the first mode +is very similar in all three cases the subsequent modes of the standard +solution exhibit dipole and tripole-like patterns. Under Varimax and Promax +rotation, these structures completely disappear suggesting that these patterns +were mere artifacts due to the orthogonality. + +.. GENERATED FROM PYTHON SOURCE LINES 67-100 + +.. code-block:: default + + + proj = Orthographic(central_latitude=30, central_longitude=-80) + kwargs = { + 'cmap' : 'RdBu', 'transform': PlateCarree(), 'vmin': -.1, 'vmax': +.1, + 'add_colorbar': False + + } + titles = [ + '(1) Covariances', '(2) Covariances + coslat', + '(3) Correlation' + ] + fig = plt.figure(figsize=(15, 5)) + gs = GridSpec(3, 6) + ax_std = [fig.add_subplot(gs[0, i], projection=proj) for i in range(6)] + ax_var = [fig.add_subplot(gs[1, i], projection=proj) for i in range(6)] + ax_pro = [fig.add_subplot(gs[2, i], projection=proj) for i in range(6)] + + for i, (a0, a1, a2) in enumerate(zip(ax_std, ax_var, ax_pro)): + mode = i + 1 + a0.coastlines(color='.5') + a1.coastlines(color='.5') + a2.coastlines(color='.5') + eofs[0].sel(mode=mode).plot(ax=a0, **kwargs) + eofs[1].sel(mode=mode).plot(ax=a1, **kwargs) + eofs[2].sel(mode=mode).plot(ax=a2, **kwargs) + + title_kwargs = dict(rotation=90, va='center', weight='bold') + ax_std[0].text(-.1, .5, 'Standard', transform=ax_std[0].transAxes, **title_kwargs) + ax_var[0].text(-.1, .5, 'Varimax', transform=ax_var[0].transAxes, **title_kwargs) + ax_pro[0].text(-.1, .5, 'Promax', transform=ax_pro[0].transAxes, **title_kwargs) + + plt.tight_layout() + plt.savefig('rotated_eof.jpg', dpi=200) + + + +.. image-sg:: /auto_examples/3rotated/images/sphx_glr_plot_rotated_eof_001.png + :alt: mode = 1, mode = 2, mode = 3, mode = 4, mode = 5, mode = 6, mode = 1, mode = 2, mode = 3, mode = 4, mode = 5, mode = 6, mode = 1, mode = 2, mode = 3, mode = 4, mode = 5, mode = 6 + :srcset: /auto_examples/3rotated/images/sphx_glr_plot_rotated_eof_001.png + :class: sphx-glr-single-img + + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 0 minutes 11.872 seconds) + + +.. _sphx_glr_download_auto_examples_3rotated_plot_rotated_eof.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: 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docs/auto_examples/auto_examples_jupyter.zip | Bin 27838 -> 47016 bytes docs/auto_examples/auto_examples_python.zip | Bin 15348 -> 26356 bytes docs/auto_examples/index.rst | 79 +++--- examples/2cross/mca.jpg | Bin 0 -> 290272 bytes examples/2cross/plot_mca.py | 108 ++++++++ 13 files changed, 663 insertions(+), 29 deletions(-) create mode 100644 docs/auto_examples/2cross/images/sphx_glr_plot_mca_001.png create mode 100644 docs/auto_examples/2cross/images/thumb/sphx_glr_plot_mca_thumb.png create mode 100644 docs/auto_examples/2cross/plot_mca.ipynb create mode 100644 docs/auto_examples/2cross/plot_mca.py create mode 100644 docs/auto_examples/2cross/plot_mca.py.md5 create mode 100644 docs/auto_examples/2cross/plot_mca.rst create mode 100644 docs/auto_examples/2cross/plot_mca_codeobj.pickle create mode 100644 docs/auto_examples/2cross/sg_execution_times.rst create mode 100644 examples/2cross/mca.jpg create mode 100644 examples/2cross/plot_mca.py diff --git 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