B \O4@sddlZddlmZddlmZddlmZmZm Z ddl m Z m Z m Z ddlmZmZddlZddlZdd d gZd dZdd d ZGdd d eee ZdS)N) interpolate) spearmanr) BaseEstimatorTransformerMixinRegressorMixin)as_float_array check_arraycheck_consistent_length)'_inplace_contiguous_isotonic_regression _make_uniquecheck_increasingisotonic_regressionIsotonicRegressionc Cst||\}}|dk}|dkrt|dkrdtd|d|}dtt|d}t|d|}t|d|}t|t|krt d|S) aCDetermine whether y is monotonically correlated with x. y is found increasing or decreasing with respect to x based on a Spearman correlation test. Parameters ---------- x : array-like, shape=(n_samples,) Training data. y : array-like, shape=(n_samples,) Training target. Returns ------- increasing_bool : boolean Whether the relationship is increasing or decreasing. Notes ----- The Spearman correlation coefficient is estimated from the data, and the sign of the resulting estimate is used as the result. In the event that the 95% confidence interval based on Fisher transform spans zero, a warning is raised. References ---------- Fisher transformation. Wikipedia. https://en.wikipedia.org/wiki/Fisher_transformation r)gg?g?g?rg\(\?zwConfidence interval of the Spearman correlation coefficient spans zero. Determination of ``increasing`` may be suspect.) rlenmathlogZsqrtZtanhnpZsignwarningswarn) xyZrho_Zincreasing_boolFZF_seZrho_0Zrho_1r/lib/python3.7/site-packages/sklearn/isotonic.pyr s" TcCs|rtjddntjddd}tj||tjd}|dkrTtjt|tjd}ntj||tjd}t|||dk s|dk r|dkrtj }|dkrtj}t||||||S)aSolve the isotonic regression model:: min sum w[i] (y[i] - y_[i]) ** 2 subject to y_min = y_[1] <= y_[2] ... <= y_[n] = y_max where: - y[i] are inputs (real numbers) - y_[i] are fitted - w[i] are optional strictly positive weights (default to 1.0) Read more in the :ref:`User Guide `. Parameters ---------- y : iterable of floats The data. sample_weight : iterable of floats, optional, default: None Weights on each point of the regression. If None, weight is set to 1 (equal weights). y_min : optional, default: None If not None, set the lowest value of the fit to y_min. y_max : optional, default: None If not None, set the highest value of the fit to y_max. increasing : boolean, optional, default: True Whether to compute ``y_`` is increasing (if set to True) or decreasing (if set to False) Returns ------- y_ : list of floats Isotonic fit of y. References ---------- "Active set algorithms for isotonic regression; A unifying framework" by Michael J. Best and Nilotpal Chakravarti, section 3. N)dtype) rZs_arrayfloat64onesrr infclip)r sample_weighty_miny_max increasingorderrrrrMs," csleZdZdZdddZdddZd d Zdd d Zdd dZddZ ddZ fddZ fddZ Z S)raI Isotonic regression model. The isotonic regression optimization problem is defined by:: min sum w_i (y[i] - y_[i]) ** 2 subject to y_[i] <= y_[j] whenever X[i] <= X[j] and min(y_) = y_min, max(y_) = y_max where: - ``y[i]`` are inputs (real numbers) - ``y_[i]`` are fitted - ``X`` specifies the order. If ``X`` is non-decreasing then ``y_`` is non-decreasing. - ``w[i]`` are optional strictly positive weights (default to 1.0) Read more in the :ref:`User Guide `. Parameters ---------- y_min : optional, default: None If not None, set the lowest value of the fit to y_min. y_max : optional, default: None If not None, set the highest value of the fit to y_max. increasing : boolean or string, optional, default: True If boolean, whether or not to fit the isotonic regression with y increasing or decreasing. The string value "auto" determines whether y should increase or decrease based on the Spearman correlation estimate's sign. out_of_bounds : string, optional, default: "nan" The ``out_of_bounds`` parameter handles how x-values outside of the training domain are handled. When set to "nan", predicted y-values will be NaN. When set to "clip", predicted y-values will be set to the value corresponding to the nearest train interval endpoint. When set to "raise", allow ``interp1d`` to throw ValueError. Attributes ---------- X_min_ : float Minimum value of input array `X_` for left bound. X_max_ : float Maximum value of input array `X_` for right bound. f_ : function The stepwise interpolating function that covers the input domain ``X``. Notes ----- Ties are broken using the secondary method from Leeuw, 1977. References ---------- Isotonic Median Regression: A Linear Programming Approach Nilotpal Chakravarti Mathematics of Operations Research Vol. 14, No. 2 (May, 1989), pp. 303-308 Isotone Optimization in R : Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods Leeuw, Hornik, Mair Journal of Statistical Software 2009 Correctness of Kruskal's algorithms for monotone regression with ties Leeuw, Psychometrica, 1977 NTnancCs||_||_||_||_dS)N)r%r&r' out_of_bounds)selfr%r&r'r*rrr__init__szIsotonicRegression.__init__cCst|jdkrtddS)NrzX should be a 1d array)rshape ValueError)r+Xrr$rrr_check_fit_datasz"IsotonicRegression._check_fit_datacsX|jdkrtd|j|jdk}tdkr@fdd|_ntj|d|d|_d S) zBuild the f_ interp1d function.)raiser)r#zIThe argument ``out_of_bounds`` must be in 'nan', 'clip', 'raise'; got {0}r1rcs |jS)N)repeatr-)r)rrrsz-IsotonicRegression._build_f..Zlinear)Zkind bounds_errorN)r*r.formatrf_rZinterp1d)r+r/rr4r)rr_build_fs     zIsotonicRegression._build_fc st|||dd||gD\}}t|}|||||jdkrPt|||_n|j|_|dk rt|dd}|dk}||||||}}}ntt |}t ||ffdd|||gD\}}}t |||\}}}||_ }t |||j|j|jd |_}t|t||_|_|rtjt |ftd } tt|d d |dd t|d d |dd| d d <|| || fS||fSdS)z Build the y_ IsotonicRegression.cSsg|]}t|ddqS)F) ensure_2d)r ).0rrrr sz/IsotonicRegression._build_y..autoNF)r8rcs g|]}|jtjddqS)F)copy)Zastyperr )r9r)r(rrr:s)r')rrr)r rr0r'r Z increasing_r rr!rZlexsortr Z_X_rr%r&Z_y_minmaxX_min_X_max_boolZ logical_orZ not_equal) r+r/rr$Ztrim_duplicatesmaskZunique_XZunique_yZunique_sample_weightZ keep_datar)r(r_build_ys:     &zIsotonicRegression._build_ycCs0||||\}}|||_|_||||S)axFit the model using X, y as training data. Parameters ---------- X : array-like, shape=(n_samples,) Training data. y : array-like, shape=(n_samples,) Training target. sample_weight : array-like, shape=(n_samples,), optional, default: None Weights. If set to None, all weights will be set to 1 (equal weights). Returns ------- self : object Returns an instance of self. Notes ----- X is stored for future use, as `transform` needs X to interpolate new input data. )rE _necessary_X_ _necessary_y_r7)r+r/rr$rrrfit(s zIsotonicRegression.fitcCs^t|}t|jdkrtd|jdkr8td|j|jdkrTt||j|j }| |S)a Transform new data by linear interpolation Parameters ---------- T : array-like, shape=(n_samples,) Data to transform. Returns ------- T_ : array, shape=(n_samples,) The transformed data rz.Isotonic regression input should be a 1d array)r1r)r#zIThe argument ``out_of_bounds`` must be in 'nan', 'clip', 'raise'; got {0}r#) rrr-r.r*r5rr#rArBr6)r+Trrr transformOs    zIsotonicRegression.transformcCs ||S)a Predict new data by linear interpolation. Parameters ---------- T : array-like, shape=(n_samples,) Data to transform. Returns ------- T_ : array, shape=(n_samples,) Transformed data. )rJ)r+rIrrrpredictjs zIsotonicRegression.predictcstt|}|dd|S)z1Pickle-protocol - return state of the estimator. r6N)superr __getstate__pop)r+state) __class__rrrMys zIsotonicRegression.__getstate__cs8tt||t|dr4t|dr4||j|jdS)znPickle-protocol - set state of the estimator. We need to rebuild the interpolation function. rFrGN)rLr __setstate__hasattrr7rFrG)r+rO)rPrrrQszIsotonicRegression.__setstate__)NNTr))N)T)N)__name__ __module__ __qualname____doc__r,r0r7rErHrJrKrMrQ __classcell__rr)rPrrsH   8 ' )NNNT)ZnumpyrZscipyrZ scipy.statsrbaserrrZutilsrr r Z _isotonicr r rr__all__r rrrrrrs  9 =