added more comments

Author: luk036

.markdownlint.json

@@ -0,0 +1,9 @@
+{
+    "default": true,
+    "MD003": { "style": "setext_with_atx" },
+    "MD007": { "indent": 4 },
+    "MD013": { "line_length": 500 },
+    "MD026": { "punctuation" : ",;:!" },
+    "MD030": { "ul_single": 3, "ol_single": 2, "ul_multi": 3, "ol_multi": 2 },
+    "no-hard-tabs": false
+}

README.md

@@ -1,4 +1,5 @@
-# ellpy
+ellpy
+=====
 
 [![Build Status](https://travis-ci.org/luk036/ellpy.svg?branch=master)](https://travis-ci.org/luk036/ellpy)
 [![Build status](https://ci.appveyor.com/api/projects/status/0v1cf05tcueny7d9?svg=true)](https://ci.appveyor.com/project/luk036/ellpy)
@@ -9,3 +10,22 @@
 [![BCH compliance](https://bettercodehub.com/edge/badge/luk036/ellpy?branch=master)](https://bettercodehub.com/)
 
 ellipsoid method python code
+
+Features
+--------
+
+-   At most one square-root per iteration.
+-   Include oracles for Matrix Inequalities and Network problems.
+-   Suport Parallel-Cuts.
+
+See also
+--------
+
+-   [ellcpp](https://github.com/luk036/ellcpp)
+-   [Presentation Slides](https://luk036.github.io/cvx)
+
+Note
+----
+
+This project has been set up using PyScaffold 3.2.1. For details and usage
+information on PyScaffold see <https://pyscaffold.org/>.

experiments/corr_fn_cvx.py

@@ -3,7 +3,11 @@
 import numpy as np
 from scipy.interpolate import BSpline
 
-from ellpy.oracles.corr_oracle import construct_distance_matrix
+from ellpy.oracles.corr_oracle import (
+    construct_distance_matrix,
+    create_2d_isotropic,
+    create_2d_sites
+)
 
 # function [sp, tau2, Sig]
 
@@ -92,3 +96,29 @@ def lsq_corr_bspline(Y, s, n):
     if prob.status != cvx.OPTIMAL:
         raise Exception('CVXPY Error')
     return BSpline(t, np.array(c.value).flatten(), k)
+
+
+if __name__ == "__main__":
+    import matplotlib.pyplot as plt
+    # import matplotlib.pylab as lab
+    s = create_2d_sites(10, 8)
+    Y = create_2d_isotropic(s, 1000)
+    # print('start ell...')
+    # spl, num_iters, _ = lsq_corr_bspline(Y, s, 5)
+    # pol, num_iters, _ = lsq_corr_poly(Y, s, 5)
+    # # pol, num_iters, _ = mle_corr_poly(Y, s, 4)
+    # print(pol)
+    # print(num_iters)
+    print('start cvx...')
+    splcvx = lsq_corr_bspline(Y, s, 5)
+    polcvx = lsq_corr_poly(Y, s, 5)
+
+    # h = s[-1] - s[0]
+    d = np.sqrt(10**2 + 8**2)
+    xs = np.linspace(0, d, 100)
+    # plt.plot(xs, spl(xs), 'g', label='BSpline')
+    plt.plot(xs, splcvx(xs), 'b', label='BSpline CVX')
+    # plt.plot(xs, np.polyval(pol, xs), 'r', label='Polynomial')
+    plt.plot(xs, np.polyval(polcvx, xs), 'r', label='Polynomial CVX')
+    plt.legend(loc='best')
+    plt.show()

experiments/exp2d.py

@@ -31,7 +31,7 @@
 for i in range(n):
     for j in range(i, n):
         d = np.array(s[j]) - np.array(s[i])
-        Sig[i, j] = np.exp(-sdkern * np.sqrt(np.dot(d, d)))
+        Sig[i, j] = np.exp(-sdkern * np.dot(d, d))
         Sig[j, i] = Sig[i, j]
 
 A = linalg.sqrtm(Sig)

src/ellpy/oracles/lsq_corr_oracle.py

@@ -25,7 +25,7 @@ class lsq_oracle:
     where
         F(x) = F[1] x[1] + ··· + F[n] x[n]
 
-        {Fk}i,j = Ψk(‖sj − si‖^2)
+        {Fk}i,j = Ψk(‖sj − si‖)
 
     Returns:
         [type] -- [description]

src/ellpy/oracles/mle_corr_oracle.py

@@ -13,12 +13,15 @@
 
 
 class mle_oracle:
-    def __init__(self, Sig, Y):
-        """[summary]
+    def __init__(self, Sig: Arr, Y: Arr):
+        """Maximum likelyhood estimation:
+
+            min  ​log det Ω(p) + Tr( Ω(p)^{−1} Y )
+            ​s.t.​ 2Y ⪰ Ω(p) ⪰ 0,​
 
         Arguments:
-            Sig {[type]} -- [description]
-            Y {[type]} -- [description]
+            Sig {Arr} -- Covariance matrix
+            Y {Arr} -- Biased covariance matrix
         """
         self.Y = Y
         self.Sig = Sig
@@ -30,7 +33,7 @@ def __call__(self, x: Arr, t: float) -> Tuple[Cut, float]:
         """[summary]
 
         Arguments:
-            x {Arr} -- [description]
+            x {Arr} -- coefficients of basis functions
             t {float} -- the best-so-far optimal value
 
         Returns:
@@ -52,7 +55,7 @@ def __call__(self, x: Arr, t: float) -> Tuple[Cut, float]:
         f1 = 2 * np.sum(np.log(diag)) + np.trace(SY)
 
         f = f1 - t
-        if f < 0:
+        if f < 0.:
             t = f1
             f = 0.