o Eb@s<ddlZddZddZddZdd Zd d Zd d ZdS)NcCs8|d|d|f||dd|ddfS)z>Sum of upper-left and lower right blocks of contingency table.NsumAijr @/usr/lib/python3/dist-packages/scipy/stats/_hypotests_pythran.py_Aij8r cCs8||ddd|f|d||ddfS)z>Sum of lower-left and upper-right blocks of contingency table.rNrrr r r _Dij r r cCJ|j\}}d}t|D]}t|D]}||||ft|||7}qq |S)z5Twice the number of concordant pairs, excluding ties.r)shaperanger rmncountrrr r r _P   rcCr)z5Twice the number of discordant pairs, excluding ties.r)rrr rr r r _Qrrc CsZ|j\}}d}t|D]}t|D]}||||ft|||t|||d7}qq |S)z>A term that appears in the ASE of Kendall's tau and Somers' D.r)rrr r rr r r _a_ij_Aij_Dij2+s   .rcCs||kr ||}}||}||}dttt|||d}}||}td|d|d} tj} tj| | d} d| ||<td|dD]x} ||} }ttt|| ||dd}t||}ttt|| |||d}||krdS|dkrdnd}t||D]}||}| ||| | ||| |}|| |<q||}||krd| ||||||<qH| ||dS)a Count the proportion of paths that do not stay strictly inside two diagonal lines. Parameters ---------- m : integer m > 0 n : integer n > 0 g : integer g is greatest common divisor of m and n h : integer 0 <= h <= lcm(m,n) Returns ------- p : float The proportion of paths that do not stay inside the two lines. The classical algorithm counts the integer lattice paths from (0, 0) to (m, n) which satisfy |x/m - y/n| < h / lcm(m, n). The paths make steps of size +1 in either positive x or positive y directions. We are, however, interested in 1 - proportion to computes p-values, so we change the recursion to compute 1 - p directly while staying within the "inside method" a described by Hodges. We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk. Hodges, J.L. Jr., "The Significance Probability of the Smirnov Two-Sample Test," Arkiv fiur Matematik, 3, No. 43 (1958), 469-86. For the recursion for 1-p see Viehmann, T.: "Numerically more stable computation of the p-values for the two-sample Kolmogorov-Smirnov test," arXiv: 2102.08037 rrr)dtypegg?) minintnpZceilZfloat64ZonesrmaxZfloor)rrghZmgZngZminjZmaxjZcurlenZlenArrrZlastminjZlastlenvalZjjrr r r !_compute_outer_prob_inside_method7s6( "    $ $$ r")Znumpyrr r rrrr"r r r r s