U f{jB9@sddlZddlmZddlmZddlmZd ddZd!d d Z d dZ ddZ ddZ ddZ d"ddZd#ddZd$ddZdS)%N)reduce)ascii_uppercase) _check_optionrelativecCsltd|ddgtj|ddd}|dkrJ|dkr>|t|n|}||7}tj|ddt||jdS)aPerform one-sample t-test. This is a modified version of :func:`scipy.stats.ttest_1samp` that avoids a (relatively) time-consuming p-value calculation, and can adjust for implausibly small variance values :footcite:`RidgwayEtAl2012`. Parameters ---------- X : array Array to return t-values for. sigma : float The variance estimate will be given by ``var + sigma * max(var)`` or ``var + sigma``, depending on "method". By default this is 0 (no adjustment). See Notes for details. method : str If 'relative', the minimum variance estimate will be sigma * max(var), if 'absolute' the minimum variance estimate will be sigma. Returns ------- t : array T-values, potentially adjusted using the hat method. Notes ----- To use the "hat" adjustment method :footcite:`RidgwayEtAl2012`, a value of ``sigma=1e-3`` may be a reasonable choice. References ---------- .. footbibliography:: methodabsoluterraxisZddofr )rnpvarmaxmeansqrtshape)XsigmarrlimitrS/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/stats/parametric.pyttest_1samp_no_ps !rTc CsPtj|ddd}tj|ddd}|jd}|jd}|rv||d}|d||d||} | d|d|} nr||} ||} tjddd2| | d| d|d| d|d}W5QRXtt|d|}| | } |dkr| |t| 7} t| } t|dt|d} tjdddt | | }W5QRX|S) aIndependent samples t-test without p calculation. This is a modified version of :func:`scipy.stats.ttest_ind`. It operates along the first axis. The ``sigma`` parameter provides an optional "hat" adjustment (see :func:`ttest_1samp_no_p` and :footcite:`RidgwayEtAl2012`). Parameters ---------- a : array-like The first array. b : array-like The second array. equal_var : bool Assume equal variance. See :func:`scipy.stats.ttest_ind`. sigma : float The regularization. See :func:`ttest_1samp_no_p`. Returns ------- t : array T values. References ---------- .. footbibliography:: rr r g@?ignore)divideinvalidr) r rrZerrstatewhereisnanrrrr)abZ equal_varrZv1Zv2Zn1Zn2dfrZvn1Zvn2denomdtrrrttest_ind_no_p:s*   6  r&cGst|}tdd|D}t|}tdddd|D}dd|D}tdd|d}d d|D}||t|}d } t|D]\} } | || || 7} q| |t|8} || } |d } ||}| t| }| t|}||}|S) aPerform a 1-way ANOVA. The one-way ANOVA tests the null hypothesis that 2 or more groups have the same population mean. The test is applied to samples from two or more groups, possibly with differing sizes :footcite:`Lowry2014`. This is a modified version of :func:`scipy.stats.f_oneway` that avoids computing the associated p-value. Parameters ---------- *args : array_like The sample measurements should be given as arguments. Returns ------- F-value : float The computed F-value of the test. Notes ----- The ANOVA test has important assumptions that must be satisfied in order for the associated p-value to be valid. 1. The samples are independent 2. Each sample is from a normally distributed population 3. The population standard deviations of the groups are all equal. This property is known as homoscedasticity. If these assumptions are not true for a given set of data, it may still be possible to use the Kruskal-Wallis H-test (:func:`scipy.stats.kruskal`) although with some loss of power. The algorithm is from Heiman :footcite:`Heiman2002`, pp.394-7. References ---------- .. footbibliography:: cSsg|] }t|qSr)len.0r rrr szf_oneway..cSs||SNrxyrrrzf_oneway..cSsg|]}tj|dddqS)rrr r sumr(rrrr*scSsg|]}tj|ddqS)rr r1r(rrrr*scSs||Sr+rr,rrrr/r0rcSsg|] }|dqS)rr)r)srrrr*srr )r'r arrayr2rfloat enumerate)argsZ n_classesZn_samples_per_classZ n_samplesZ ss_alldataZ sums_argsZsquare_of_sums_alldataZsquare_of_sums_argsZsstotZssbnk_ZsswnZdfbnZdfwnZmsbZmswfrrrf_onewayps*(    r;c s|ttkrtdttd|t|trd|krHd|krHtdnpd|krbd|krbtdnV|dkrpd}nHt|d ksd|kr|g}n,d|kr|d}nd|krntd |t|trfd d |D}t|d krtd ||tt d|d }t|D]X}t |d |}|d t |d kd}fdd |D}|  d|q|dkst|tr}n|}fdd |D} fdd | Dt|trd|kr|ddd } d| | d| } | fS)zMap effects to indices.z)Maximum number of factors supported is 26N*:z$Not "*" and ":" permitted in effects+z$Not "+" and ":" permitted in effectsallr z("{}" is not a valid option for "effects"csg|]}|kr|qSrrr)e factor_namesrrr*sz _map_effects..zbEffect names: {} are not valid. They should the first `n_factors` ({}) characters from thealphabetrrcsg|] }|qSrrr@rBrrr*scsg|]}|qSr)indexr)selnamesrrr*scsg|] }|qSrrrErGrrr*s)r'r ValueErrorlist isinstancestrsplitformatr Zarange_get_contrast_indicesrsortappendjoinrDreplace) n_factorseffectsZ bad_namesindices this_effect contrast_idxZ this_codeZ this_nameZeffects_Z selectionZsel_indr)rCrHr _map_effectssZ           rYcCs$t||}tjdd|DtdS)z'Henson's factor coding, see num2binvec.cSsg|] }t|qSr)int)r)irrrr*sz)_get_contrast_indices..)Zdtype)r Z binary_reprr4rZ)Z effect_idxrTZbinreprrrrrOs rOccsddlm}g}t|}|D]*}|t|dg|t|ddgq|D]~}t|d|}|d||d} td|D](} ||d| } t | || | } q|tj | } | |d} | | | fVqLdS)zSet up contrasts.r)detrendr Zconstant)typeN) Z scipy.signalr\r'rQr ZoneseyerOrangeZkronZlinalgZ matrix_rank) n_subjects factor_levels effect_picksr\scrTZn_levelsrWrXc_Z i_contrastZ this_contrastdf1df2rrr_iter_contrastss    rgA*B皙?c Cshddlm}tt||\}}g}t|||D] \}}} |||| |q.t|dkr`|S|dS)alCompute F-value thresholds for a two-way ANOVA. Parameters ---------- n_subjects : int The number of subjects to be analyzed. factor_levels : list-like The number of levels per factor. effects : str A string denoting the effect to be returned. The following mapping is currently supported: * ``'A'``: main effect of A * ``'B'``: main effect of B * ``'A:B'``: interaction effect * ``'A+B'``: both main effects * ``'A*B'``: all three effects pvalue : float The p-value to be thresholded. Returns ------- F_threshold : list | float List of F-values for each effect if the number of effects requested > 2, else float. See Also -------- f_oneway f_mway_rm Notes ----- .. versionadded:: 0.10 rr:r ) scipy.statsr:rYr'rgrQZisf) r`rarUZpvaluer:rbr9Z F_thresholdrerfrrrf_threshold_mway_rm s& rlr?Fc s&ddlm}d|jdkr4|ddddtjf}nB|jdkrv|jdd||jd|jdt|jdd}tt ||\}}|jd}|jd} t |d}gg} } t | ||D]N\} } }t || }tj |ddddtjddf}tjtj||dddd}tjtj||dddd||| }||}| ||rtd d |D}td d |Dd| tjtj||dddd}|t|| t||} }|rfd d | |fD\} }|r|| ||}n td}| |qfd d | | fDS)a+Compute M-way repeated measures ANOVA for fully balanced designs. Parameters ---------- data : ndarray 3D array where the first two dimensions are compliant with a subjects X conditions scheme where the first factor repeats slowest:: A1B1 A1B2 A2B1 A2B2 subject 1 1.34 2.53 0.97 1.74 subject ... .... .... .... .... subject k 2.45 7.90 3.09 4.76 The last dimensions is thought to carry the observations for mass univariate analysis. factor_levels : list-like The number of levels per factor. effects : str | list A string denoting the effect to be returned. The following mapping is currently supported (example with 2 factors): * ``'A'``: main effect of A * ``'B'``: main effect of B * ``'A:B'``: interaction effect * ``'A+B'``: both main effects * ``'A*B'``: all three effects * ``'all'``: all effects (equals 'A*B' in a 2 way design) If list, effect names are used: ``['A', 'B', 'A:B']``. correction : bool The correction method to be employed if one factor has more than two levels. If True, sphericity correction using the Greenhouse-Geisser method will be applied. return_pvals : bool If True, return p-values corresponding to F-values. Returns ------- F_vals : ndarray An array of F-statistics with length corresponding to the number of effects estimated. The shape depends on the number of effects estimated. p_vals : ndarray If not requested via return_pvals, defaults to an empty array. See Also -------- f_oneway f_threshold_mway_rm Notes ----- .. versionadded:: 0.10 rrj)rNr r cSsg|]}t|j|qSr)r dotT)r)Zy_rrrr*szf_mway_rm..cSsg|]}t|qSr)r tracer)Zvvrrrr*scs(g|] }t|dddfdqS)Nr)r maximum)r)r$)epsrrr*sc s*g|]"}ttfdd|DqS)csg|]}|qSr)reshape)r)v out_reshaperrr*sz(f_mway_rm...)r ZsqueezeZasarrayrrrwrrr*s)rkr:ndimr ZnewaxisrruprodrYr'Zrollaxisrgrorr2rQr4ZzerosZsfempty)datararUZ correctionZ return_pvalsr:rbr9Zn_obsZn_replicationsZfvaluesZpvaluesrdrerfr.r!ssZmseZfvalsrvZpvalsr)rtrxr f_mway_rm:sR9        "(    r~ffffff?cCs^|d}t|dkr,t|tj}||fSddlm}||d}|jj ||||j ddS)z=Calculate the `ci`% parametric confidence interval for `arr`.rr)stats)locscaler") rr'r Z full_likenanZscipyrZsemr%intervalr)Zarrcirrrrrr_parametric_cis    r)rr)Tr)rhri)r?FT)r)numpyr functoolsrstringrutilsrrr&r;rYrOrgrlr~rrrrrs"    ) 6>; 1 l