added pca code

doc/src/DimRed/Programs/PCAsimple.py

@@ -0,0 +1,36 @@
+import numpy as np
+import pandas as pd
+from IPython.display import display
+
+
+n = 100
+mean = (-1, 2)
+cov = [[4, 2], [2, 2]]
+X = np.random.multivariate_normal(mean, cov, n)
+print(X)
+
+df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+