Add an option to pick operator norm or Frobenius to compute relative error.

Calculate the norm directly with singular values instead of computing the approximate of M and then calculate the norm with it.

misc/test/src/Python/test_svd_rc_vs_err.py

@@ -27,25 +27,48 @@ class TruncSvd(Thread):
         self.rcs = rcs
 
     def run(s):
+        global norm_ord
         S = np.zeros([s.U.shape[1], s.V.shape[0]])
+        if(norm_ord == "fro"): nfroM = 0
         for i in range(0, s.S.shape[0]):
             S[i, i] = s.S[i]
+            if(norm_ord == "fro"): nfroM += S[i,i]**2
+        if(norm_ord == "fro"): nfroM = np.sqrt(nfroM)
         # 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] = S[s.r-1,s.r-1] / S[0,0]
-            s.errs[0, s.r-1] = norm(s.M-s.Mr, 'fro')/norm(s.M, 'fro')
+        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, norm_ord)/norm(s.M, norm_ord)
+            if(norm_ord == 2):
+                err = S[s.r, s.r]/S[0,0]
+                #assert(err == s.errs[0, s.r-1])
+                #print(s.errs[0, s.r-1], err)
+                s.errs[0, s.r-1] = err
+            elif(norm_ord == "fro"):
+                err = 0
+                for j in range(s.r, s.S.shape[0]):
+                    err += s.S[j]**2
+                err = np.sqrt(err)/nfroM
+                #print(s.errs[0, s.r-1], err)
+                #assert(err == s.errs[0, s.r-1])
+                s.errs[0, s.r-1] = err
             s.rcs[0, s.r-1] = (s.r*(s.M.shape[0]+s.M.shape[1]))
             s.rcs[0, s.r-1] /= 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>")
+    if(len(argv) < 4):
+        print("USAGE: ", argv[0], "<num_lines> <num_cols> <norm_ord>")
+        print("norm_ord is fro or 2")
         exit(1)
     m = int(argv[1])
     n = int(argv[2])
+    global norm_ord
+    if(argv[3] == "2"):
+        norm_ord=2
+    elif(argv[3] == "fro"):
+        norm_ord="fro"
+    else:
+        raise("Error: norm must be 2 or fro.")
     nthreads = 8
     errs = np.zeros([1, min(m, n)])
     rcs = np.zeros([1, min(m, n)])
@@ -65,9 +88,9 @@ if __name__ == '__main__':
     plt.ylabel('Relative Error')
     plt.title('Relative Error over RC 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(rcs[0,i])+"\n")
-#    f.close()
+    f = open("svd_err_vs_rc_output_"+str(nthreads), "w")
+    for i in range(0,errs.shape[1]):
+        f.write(str(errs[0,i])+" "+str(rcs[0,i])+"\n")
+    f.close()
     #plt.plot(rcs, errs)
     plt.show()