Merge pull request #52 from Nunigan/master

Multiplikation #1

1 files changed, 311 insertions, 0 deletions

diff --git a/buch/papers/multiplikation/code/MM.py b/buch/papers/multiplikation/code/MM.py
new file mode 100644
index 0000000..626b82d
--- /dev/null
+++ b/buch/papers/multiplikation/code/MM.py
@@ -0,0 +1,311 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Mar 19 07:31:29 2021
+
+@author: nunigan
+"""
+import numpy as np
+import time
+import matplotlib.pyplot as plt
+from scipy.optimize import curve_fit
+import tikzplotlib
+def MM(A, B):
+    n = np.shape(A)[0]
+    C = np.zeros((n, n))
+    for i in range(n):
+        for j in range(n):
+            C[i, j] = 0
+            for k in range(n):
+                C[i, j] += A[i, k]*B[k, j]
+    return C
+
+
+def MM_dc(A, B):
+    n = np.shape(A)[0]
+    if(n <= 2):
+        C = np.zeros((n, n))
+        C[0, 0] = A[0, 0]*B[0, 0]+A[0, 1]*B[1, 0]
+        C[0, 1] = A[0, 0]*B[0, 1]+A[0, 1]*B[1, 1]
+        C[1, 0] = A[1, 0]*B[0, 0]+A[1, 1]*B[1, 0]
+        C[1, 1] = A[1, 0]*B[0, 1]+A[1, 1]*B[1, 1]
+        return C
+    else:
+        A11, A12, A21, A22 = A[:n//2, :n//2], A[:n//2, n//2:], A[n//2:, :n//2], A[n//2:, n//2:]
+        B11, B12, B21, B22 = B[:n//2, :n//2], B[:n//2, n//2:], B[n//2:, :n//2], B[n//2:, n//2:]
+        C11 = MM_dc(A11, B11) + MM_dc(A12, B21)
+        C12 = MM_dc(A11, B12) + MM_dc(A12, B22)
+        C21 = MM_dc(A21, B11) + MM_dc(A22, B21)
+        C22 = MM_dc(A21, B12) + MM_dc(A22, B22)
+        C = np.vstack((np.hstack((C11, C12)), np.hstack((C21, C22))))
+    return C
+
+
+def strassen(A, B):
+    n = np.shape(A)[0]
+    if(n <= 2):
+        C = np.zeros((n, n))
+        P = (A[0, 0]+A[1, 1])*(B[0, 0]+B[1, 1])
+        Q = (A[1, 0]+A[1, 1])*B[0, 0]
+        R = A[0, 0]*(B[0, 1]-B[1, 1])
+        S = A[1, 1]*(B[1, 0]-B[0, 0])
+        T = (A[0, 0]+A[0, 1])*B[1, 1]
+        U = (A[1, 0]-A[0, 0])*(B[0, 0]+B[0, 1])
+        V = (A[0, 1]-A[1, 1])*(B[1, 0]+B[1, 1])
+        C[0, 0] = P+S-T+V
+        C[0, 1] = R+T
+        C[1, 0] = Q+S
+        C[1, 1] = P+R-Q+U
+        return C
+    else:
+        m = n//2
+        A11, A12, A21, A22 = A[:m, :m], A[:m, m:], A[m:, :m], A[m:, m:]
+        B11, B12, B21, B22 = B[:m, :m], B[:m, m:], B[m:, :m], B[m:, m:]
+        P = strassen((A11+A22),(B11+B22))
+        Q = strassen((A21+A22),B11)
+        R = strassen(A11,(B12-B22))
+        S = strassen(A22,(B21-B11))
+        T = strassen((A11+A12),B22)
+        U = strassen((A21-A11),(B11+B12))
+        V = strassen((A12-A22),(B21+B22))
+        
+        C11 = P+S-T+V
+        C12 = R+T
+        C21 = Q+S
+        C22 = P+R-Q+U
+
+        C = np.vstack((np.hstack((C11, C12)), np.hstack((C21, C22))))
+    return C
+
+def winograd_inner(a, b):
+    n = np.shape(a)[0]
+    if n%2 == 0:
+        xi = np.sum(a[::2]*a[1::2])
+        etha = np.sum(b[::2]*b[1::2])
+        # print("xi = {}, etha = {}".format(xi, etha))
+        ab = np.sum((a[::2]+b[1::2])*(a[1::2]+b[::2]))-xi-etha
+    else:
+        xi = np.sum(a[0:-1:2]*a[1::2])
+        etha = np.sum(b[0:-1:2]*b[1::2])
+        ab = np.sum((a[0:-1:2]+b[1::2])*(a[1::2]+b[0:-1:2]))-xi-etha+a[-1]*b[-1]
+    return ab
+
+def winograd(A, B):
+    m,n = np.shape(A)
+    n2,p = np.shape(B)
+    C = np.zeros((m,p))
+    for i in range(np.shape(A)[0]):
+        for j in range(np.shape(B)[1]):
+            C[i,j] = winograd_inner(A[i,:], B[:,j])
+    return C
+
+def winograd2(A, B):
+    m,n = np.shape(A)
+    n2,p = np.shape(B)
+    C = np.zeros((m,p))
+    xi = np.zeros((m))
+    eta = np.zeros((p))
+    ab = 0
+    for i in range(m):
+        for j in range(n//2):
+            xi[i] += A[i,2*j]*A[i,2*j+1]
+
+    for i in range(p):
+        for j in range(n//2):
+           eta[i] += B[2*j,i]*B[2*j+1,i]
+
+    if n%2==0:
+        for i in range(m):
+            for j in range(p):
+                ab = 0
+                for k in range(n//2):
+                    ab += (A[i,2*k]+B[2*k+1,j])*(A[i,2*k+1]+B[2*k,j])
+                C[i,j] = ab-eta[j]-xi[i]
+    else:
+        for i in range(m):
+            for j in range(p):
+                ab = 0
+                for k in range(n//2):
+                    ab += (A[i,2*k]+B[2*k+1,j])*(A[i,2*k+1]+B[2*k,j])
+                C[i,j] = ab-eta[j]-xi[i]+A[i,-1]*B[-1,j]
+        
+    return C
+        
+def test_perfomance(n):
+    t_mm = []
+    t_mm_dc = []
+    t_mm_strassen = []
+    t_wino = []
+    t_np = []
+
+    for i in n:
+        A = np.random.randn(i, i)
+        B = np.random.randn(i, i)
+        # A = np.random.randint(-100, 100,(i, i))
+        # B = np.random.randint(-100, 100,(i, i))
+
+        start = time.time()
+        C3 = strassen(A, B)
+        t_mm_strassen.append(time.time() - start)
+
+        start = time.time()
+        C1 = MM(A, B)
+        t_mm.append(time.time() - start)
+
+        start = time.time()
+        C2 = MM_dc(A, B)
+        t_mm_dc.append(time.time() - start)
+
+        start = time.time()
+        C4 = winograd2(A, B)
+        t_wino.append(time.time() - start)
+
+        start = time.time()
+        C = A@B
+        t_np.append(time.time() - start)
+
+    plt.figure(figsize=(13,8))
+    plt.rcParams['font.family'] = 'STIXGeneral'
+    plt.rc('axes', labelsize=23)
+    plt.rc('xtick', labelsize=23)
+    plt.rc('ytick', labelsize=23)
+    plt.plot(n, t_mm, label='Standard', lw=5)
+    plt.plot(n, t_mm_dc, label='Divide and conquer', lw=5)
+    plt.plot(n, t_mm_strassen, label='Strassen', lw=5)
+    plt.plot(n, t_wino, label='Winograd', lw=5)
+    plt.plot(n, t_np, label='NumPy A@B', lw=5)
+    plt.legend()
+    plt.xlabel("n")
+    plt.ylabel("time (s)")
+    plt.grid(True)
+    plt.tight_layout()
+    # plt.yscale('log')
+    plt.legend(fontsize=19)
+    plt.savefig('meas_' + str(max(n))+ '.pdf')
+    arr = np.array([n, t_mm, t_mm_dc, t_mm_strassen, t_wino, t_np])
+    np.savetxt('meas_' + str(max(n))+ '.txt',arr)    
+    return arr
+
+
+def plot(num):
+    arr = np.loadtxt('meas_{}.txt'.format(num))
+    n, t_mm, t_mm_dc, t_mm_strassen, t_wino, t_np = arr
+    plt.figure(figsize=(13,8))
+    plt.rcParams['font.family'] = 'STIXGeneral'
+    plt.rc('axes', labelsize=23)
+    plt.rc('xtick', labelsize=23)
+    plt.rc('ytick', labelsize=23)
+    plt.plot(n, t_mm, label='3 For Loops', lw=5)
+    plt.plot(n, t_mm_dc, label='Divide and Conquer', lw=5)
+    plt.plot(n, t_mm_strassen, label='Strassen', lw=5)
+    # plt.plot(n, t_wino, label='Winograd', lw=5)
+    plt.plot(n, t_np, label='NumPy A@B', lw=5)
+    plt.legend()
+    plt.xlabel("n")
+    plt.ylabel("time (s)")
+    plt.grid(True)
+    plt.tight_layout()
+    # plt.yscale('log')
+    plt.legend(fontsize=19)
+    plt.savefig('meas_' + str(num)+ '.pdf')    
+    return arr
+
+def plot_c_res(ave, num):
+    MM = np.loadtxt("meas/MM.txt", delimiter=',')
+    # winograd = np.loadtxt("meas/winograd.txt", delimiter=',')
+    blas = np.loadtxt("meas/blas.txt", delimiter=',')
+    MM_dc = np.loadtxt("meas/MM_dc.txt", delimiter=',')
+    strassen = np.loadtxt("meas/strassen.txt", delimiter=',')
+
+    MM_t = MM[:,0] 
+    MM_n = MM[:,1] 
+    MM_t = np.mean(MM_t.reshape(-1,ave),axis=1)
+    MM_n = np.mean(MM_n.reshape(-1,ave),axis=1)
+
+    MM_dc_t = MM_dc[:,0] 
+    MM_dc_n = MM_dc[:,1] 
+    MM_dc_t = np.mean(MM_dc_t.reshape(-1,ave),axis=1)
+    MM_dc_n = np.mean(MM_dc_n.reshape(-1,ave),axis=1)
+
+    strassen_t = strassen[:,0] 
+    strassen_n = strassen[:,1] 
+    strassen_t = np.mean(strassen_t.reshape(-1,ave),axis=1)
+    strassen_n = np.mean(strassen_n.reshape(-1,ave),axis=1)
+    
+    # winograd_t = winograd[:,0] 
+    # winograd_n = winograd[:,1] 
+    # winograd_t = np.mean(winograd_t.reshape(-1,ave),axis=1)
+    # winograd_n = np.mean(winograd_n.reshape(-1,ave),axis=1)
+    
+    blas_t = blas[:,0] 
+    blas_n = blas[:,1] 
+    blas_t = np.mean(blas_t.reshape(-1,ave),axis=1)
+    blas_n = np.mean(blas_n.reshape(-1,ave),axis=1)
+
+    def func(x, a,b):
+        return b*x**a
+
+    # popt, pcov = curve_fit(func, blas_n, blas_t)
+    # popt1, pcov2 = curve_fit(func, blas_n, winograd_t)
+    # popt2, pcov2 = curve_fit(func, blas_n, MM_t)
+
+    plt.figure(figsize=(13,8))
+    plt.rcParams['font.family'] = 'STIXGeneral'
+    plt.rc('axes', labelsize=23)
+    plt.rc('xtick', labelsize=23)
+    plt.rc('ytick', labelsize=23)
+    plt.plot(MM_n, MM_t, label='3 For Loops', lw=5)
+    # plt.plot(winograd_n, winograd_t, label='Winograd MM', lw=5)
+    plt.plot(blas_n, blas_t, label='Blas', lw=5)
+    plt.plot(strassen_n, strassen_t, label='Strassen', lw=5)
+    plt.plot(MM_dc_n, MM_dc_t, label='Divide and Conquer', lw=5)
+    plt.xlabel("n")
+    plt.ylabel("time (s)")
+    plt.grid(True)
+    plt.tight_layout()
+    plt.legend(fontsize=19)
+    plt.savefig('c_meas_' + str(num)+ '.pdf')    
+
+    # plt.plot(blas_n, func(blas_n, *popt), 'r-', label='fit blas: a=%5.5f, b=%5.10f' % tuple(popt))
+    # plt.plot(blas_n, func(blas_n, *popt1), 'r-', label='fit winograd: a=%5.5f, b=%5.10f' % tuple(popt1))
+    # plt.plot(blas_n, func(blas_n, *popt2), 'r-', label='fit MM: a=%5.5f, b=%5.10f' % tuple(popt2))
+  
+    plt.legend()
+    
+
+# test%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+if __name__ == '__main__':
+    plot_c_res(1, 4096)
+
+ 
+    # plot(8)    
+    # n = np.logspace(1,10,10,base=2,dtype=(np.int))
+    # n = np.arange(1,50,2)  
+    A = np.random.randint(-10, 10, (5,3))
+    B = np.random.randint(-10, 10, (3,5))
+
+    C = winograd2(A, B)
+    C_test = A@B
+    print(C)
+    print(C_test)
+    # print(np.equal(C, C_test))
+
+    # t_np = test_perfomance(n)
+    # C = strassen(A, B)
+    # C_test = A@B
+    
+    
+    # plot_c_res()
+    # def func(x, a):
+    #     return x**a
+
+    # popt, pcov = curve_fit(func, n, t_np, bounds=(2, 3))
+
+
+    # plt.figure()
+    # plt.plot(n, t_np, 'b-', label='data')
+    # plt.plot(n, func(n, *popt), 'r-', label='fit: a=%5.3f' % tuple(popt))
+    # plt.xlabel('x')
+    # plt.ylabel('y')
+    # plt.legend()
+    
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