Add cross validation module to integrate all modules, including varia…

…ble matrix pretreatment, PLS object, base module for implementing algorithm, plots of cross validation errors, score plots, S-plot and jack-knife interval for variable importance evaluations. Also, testing dataset is included.

base.py

@@ -0,0 +1,57 @@
+import numpy as np
+import numpy.linalg as la
+import typing
+
+
+def nipals(x: np.ndarray, y: np.ndarray,
+           tol: float = 1e-10,
+           max_iter: int = 1000,
+           dot=np.dot) -> typing.Tuple:
+    """
+    Non-linear Iterative Partial Least Squares
+
+    Parameters
+    ----------
+    x: np.ndarray
+        Variable matrix with size n by p, where n number of samples,
+        p number of variables.
+    y: np.ndarray
+        Dependent variable with size n by 1.
+    tol: float
+        Tolerance for the convergence.
+    max_iter: int
+        Maximal number of iterations.
+
+    Returns
+    -------
+    w: np.ndarray
+        Weights with size p by 1.
+    u: np.ndarray
+        Y-scores with size n by 1.
+    c: float
+        Y-weight
+    t: np.ndarray
+        Scores with size n by 1
+
+    References
+    ----------
+    [1] Wold S, et al. PLS-regression: a basic tool of chemometrics.
+        Chemometr Intell Lab Sys 2001, 58, 109–130.
+    [2] Bylesjo M, et al. Model Based Preprocessing and Background
+        Elimination: OSC, OPLS, and O2PLS. in Comprehensive Chemometrics.
+
+    """
+    u = y
+    i = 0
+    d = tol * 10
+    while d > tol and i <= max_iter:
+        w = dot(u, x) / dot(u, u)
+        w /= la.norm(w)
+        t = dot(x, w)
+        c = dot(t, y) / dot(t, t)
+        u_new = y * c / (c * c)
+        d = la.norm(u_new - u) / la.norm(u_new)
+        u = u_new
+        i += 1
+
+    return w, u, c, t