B {‹d/ã@sLdZddlmZmZmZddlmZe ¡ddlZ d dd„Z d d d „Z dS) z\ Part of awkde package --------------------- Helper tools for standardizing a data sample. é)Úprint_functionÚdivisionÚabsolute_import)Ústandard_libraryNTFc Cs>t|jƒdkrtdƒ‚|dkrJ|dkrJtj|dd}t tj|dd¡}nZ|dk r¤|dk r¤t |¡}t |¡}t|ƒ|jdkrˆtd ƒ‚|jd|jdkr¤td ƒ‚|rÂt |¡t  |jd¡}|rÞtj   tj   |¡¡j }n4tj  tj   |¡¡\}}t |¡} t | ||j ¡}t |||j ¡j } |r6| ||fS| SdS) aæ Standardizes a n-dimensional sample using the Mahalanobis distance. .. math:: x' = \Sigma^{-1/2} (x - y) The resulting sample :math:`x'` has a zero mean vector and an identity covariance. Parameters ---------- sam : array-like, shape (n_samples, n_features) Data points in the sample, each column is a feature, each row a point. mean : array-like, shape (n_features), optional If explicitely given, use this mean vector for the transformation. If None, the estimated mean from data is used. (default: None) cov : array-like, shape (n_features, n_features), optional If explicitely given, use this covariance matrix for the transformation. If None, the estimated cov from data is used. (default: None) cholesky : bool, optional If true, use fast Cholesky decomposition to calculate the sqrt of the inverse covariance matrix. Else use eigenvalue decomposition (Can be numerically unstable, not recommended). (default: True) ret_stats : bool, optional If True, the mean vector and covariance matrix of the input sample are returned, too. (default: False) diag : bool If True, only scale by variance, diagonal cov matrix. (default: False) Returns ------- stand_sam : array-like, shape (n_samples, n_features) Standardized sample, with mean = [0., ..., 0.] and cov = identity. Optional Returns ---------------- mean : array-like, shape(n_features) Mean vector of the input data, only if ret_stats is True. cov : array-like, shape(n_features, n_features) Covariance matrix of the input data, only if ret_stats is True. Example ------- >>> mean = [10, -0.01, 1] >>> cov = [[14, -.2, 0], [-.2, .1, -0.1], [0, -0.1, 1]] >>> sam = np.random.multivariate_normal(mean, cov, size=1000) >>> std_sam = standardize_nd_sample(sam) >>> print(np.mean(std_sam, axis=0)) >>> print(np.cov(std_sam, rowvar=False)) éz/Shape of `sam` must be (n_samples, n_features).Nr)ZaxisF)Zrowvaréz*Dimensions of mean and sample don't match.z)Dimensions of cov and sample don't match.)ÚlenÚshapeÚ ValueErrorÚ_npÚmeanÚ atleast_2dÚcovÚ atleast_1dÚdiagÚeyeÚlinalgÚcholeskyÚinvÚTZeigÚsqrtÚdot) Úsamr rrZ ret_statsrÚ sqrtinvcovZlamÚQZsqrtlamZ stand_sam©rúX/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/awkde/tools.pyÚstandardize_nd_samples.3    rcCs–t|jƒdkrtdƒ‚t |¡}t |¡}t|ƒ|jdkrDtdƒ‚|jd|jdkr`tdƒ‚tj tj |¡¡j }tj |¡}t  ||j ¡j |S)a‹ Shift and scale a nD sample by given mean and covariance matrix. This is the inverse operation of `standardize_nd_sample`. If a standardized sample :math:`x'` with zero mean vector and identity covariance matrix is given, it is rescaled and shifted using .. math:: x = (\Sigma^{1/2} x) + y then having a mean vector `mean` and a covariance matrix `cov`. Parameters ---------- sam : array-like, shape (n_samples, n_features) Data points in the sample, each column is a feature, each row a point. mean : array-like, shape (n_features) Mean vector used for the transformation. cov : array-like, shape (n_features, n_features) Covariance matrix used for the transformation. Returns ------- scaled_sam : array-like, shape (n_samples, n_features) Scaled sample using the transformation with the given mean and cov. rz/Shape of `sam` must be (n_samples, n_features).rz*Dimensions of mean and sample don't match.rz)Dimensions of cov and sample don't match.) rr r r rr rrrrr)rr rrrZsqrtcovrrrÚshift_and_scale_nd_samplejs   r)NNTFF)T) Ú__doc__Ú __future__rrrÚfuturerZinstall_aliasesÚnumpyr rrrrrrÚs  X