Add a script for showing truncated SVD accuracy versus the RCG.

It's a way somehow to show out the interest of a particuler FAµST.

misc/test/src/Python/test_svd_rcg_vs_err.py

+
+# this script aims to show how SVD could be useful to get a better RCG than
+# the full matrix while not totally losing the accuracy
+
+# The SVD case here can be seen as a particular situation for a FAµST
+
+from sys import argv
+from matplotlib import pyplot as plt
+import numpy as np
+from numpy.linalg import norm
+from numpy.random import rand
+from threading import Thread
+from scipy.linalg import svd
+
+
+class TruncSvd(Thread):
+
+    def __init__(self, offset, M, U, S, V, r, errs, rcgs):
+        Thread.__init__(self)
+        self.offset = offset
+        self.M = M
+        self.U = U
+        self.V = V
+        self.S = S
+        self.r = r
+        self.errs = errs
+        self.rcgs = rcgs
+
+    def run(s):
+        S = np.zeros([s.U.shape[1], s.V.shape[0]])
+        for i in range(0, s.S.shape[0]):
+            S[i, i] = s.S[i]
+        # assert((abs(M - s.U.dot(S).dot(s.V))/abs(s.M) < .01).all())
+        while(s.r <= min(s.M.shape[0], s.M.shape[1])):
+            s.Mr = (s.U[:, 0:s.r].dot(S[0:s.r, 0:s.r])).dot(s.V[0:s.r, :])
+            s.errs[0, s.r-1] = norm(s.M-s.Mr, 'fro')/norm(s.M, 'fro')
+            s.rcgs[0, s.r-1] = s.M.shape[0] * s.M.shape[1]
+            s.rcgs[0, s.r-1] /= (s.r*(s.M.shape[0]+s.M.shape[1]))
+            s.r += s.offset
+
+
+if __name__ == '__main__':
+    if(len(argv) < 3):
+        print("USAGE: ", argv[0], "<num_lines> <num_cols>")
+        exit(1)
+    m = int(argv[1])
+    n = int(argv[2])
+    nthreads = 8
+    errs = np.zeros([1, min(m, n)])
+    rcgs = np.zeros([1, min(m, n)])
+    M = rand(m, n)
+    U, S, V = svd(M)
+    ths = list()
+    for i in range(1, nthreads+1):
+        th = TruncSvd(nthreads, M, U, S, V, i, errs, rcgs)
+        ths.append(th)
+        th.start()
+    for th in ths:
+        th.join()
+    plt.scatter(rcgs[0, :], errs[0, :], s=1)
+    # plt.gca().set_xscale('log', basex=.5)
+    plt.gca().invert_xaxis()
+    plt.xlabel('Relative Complexity Gain (RCG)')
+    plt.ylabel('Relative Error')
+    plt.title('Relative Error over RCG of Truncated SVDs for a dense matrix M ('
+              + str(m) + 'x' + str(n)+')')
+#    f = open("svd_err_vs_rcg_output_"+str(nthreads), "w")
+#    for i in range(0,errs.shape[1]):
+#        f.write(str(errs[0,i])+" "+str(rcgs[0,i])+"\n")
+#    f.close()
+    # plt.plot(rcgs, errs)
+    plt.show()