Update

Author: heqin-zhu

README.md

@@ -62,7 +62,7 @@
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+[![License](https://i.creativecommons.org/l/by-nc-sa/4.0/80x15.png)](http://creativecommons.org/licenses/by-nc-sa/4.0/)
 
 >本仓库收录中国科学技术大学众多课程资源，包括电子版教材、参考书、讲义、试卷、学习心得、习题解答等。以计算机学院课程为主，也包含公选课、自由选修等其他课程。
 

utils/config.py

@@ -0,0 +1,57 @@
+#########################################################################
+# File : linear_equation.py
+# Author: mbinary
+# Mail: [email protected]
+# Blog: https://mbinary.xyz
+# Github: https://github.com/mbinary
+# Created Time: 2018-05-20  08:36
+# Description:   书上p186 附录1 程序11
+#########################################################################
+
+import numpy as np
+
+def gauss_prior_elimination(A,b=None):
+    '''using guass elimination,get up_trianglge form of A'''
+    m,n = A.shape
+    res = [0]*m if b is None else b
+    if m!=n:raise Exception("[Error]: matrix is not inversable")
+    B = np.matrix(A,dtype=float) # necessary,otherwise when the dtype of A is int, then it will be wrong
+    for  i in range(m-1):
+        col = abs(B[i:,i]) #  note using abs value,  return a matrix in (m-i)x1 form
+        mx = col.max()
+        if mx==0: raise Exception("[Error]: matrix is not inversable")
+        pos = i+col.argmax()
+        if pos != i :  B[[pos,i],:] = B[[i,pos],:]  #  note how to swap cols/rows
+        #B[i,:] = B[i,:]/mx
+        #res[i]/=mx
+        for j in range(i+1,m):
+            if B[j,i]!=0:
+                B[j,:] -= B[j,i]/B[i,i] * B[i,:]
+                res[j] -= res[i]/B[i,i]*res[j]
+    if b is None:return B
+    return B,res
+
+def det(A):
+    m,n = A.shape
+    ret=1
+    B = gauss_prior_elimination(A)
+    for i in range(m):ret *= B[i,i]
+    return ret
+
+def test(A):
+    print()
+    print('计算行列式')
+    print(A)
+    print('我的结果: det(A) = ',det(A))
+    print('函数调用: det(A) = ',np.linalg.det(A))
+if __name__ == '__main__':
+    A = np.matrix([[10,5,0,0],
+                     [2,2,1,0],
+                     [0,10,0,5],
+                      [0,0,2,1]])
+    test(A)
+
+    A = np.matrix([[-6,3,2],
+                     [3,5,1],
+                     [2,1,6]])
+    test(A)

其他/README.md

@@ -0,0 +1,77 @@
+
+#########################################################################
+# File : numerical integration.py
+# Author: mbinary
+# Mail: [email protected]
+# Blog: https://mbinary.xyz
+# Github: https://github.com/mbinary
+# Created Time: 2018-05-11  08:58
+# Description: 
+#       numerical intergration: using Newton-Cotes integration,  and Simpson
+#       数值积分, 使用 牛顿-科特斯积分, 辛普森
+#########################################################################
+
+from math import sin
+
+import numpy as np
+
+def mypprint(lst):
+    for i in lst:
+        print(('%.4f'%i).ljust(10),end='')
+    print()
+
+def trapezoidal(a,b,h,fs):
+    '''梯形积分公式'''
+    xs = [i for i in np.arange(a,b+h,h)]
+    print('x'.ljust(10),end='')
+    mypprint(xs)
+    print('fx'.ljust(10),end='')
+    mypprint(fs)
+    ret = h*(sum(fs)-fs[0]/2 - fs[-1]/2)
+    print(ret)
+    return ret
+
+
+def simpson(a,b,h,fs):
+    '''辛普森积分公式'''
+    xs = [i for i in np.arange(a,b+h,h)]
+    print('x'.ljust(10),end='')
+    mypprint(xs)
+    print('fx'.ljust(10),end='')
+    mypprint(fs)
+    ret = h/3*(4* sum(fs[1::2])+ 2*sum(fs[2:-1:2]) + fs[0]+fs[-1])
+    print(ret)
+    return ret
+
+
+def romberg(a,b,f,epcilon):
+    '''romberg(龙贝格) 数值积分'''
+    h = b-a
+    lst1=[h*(f(a)+f(b))/2]
+    mypprint(lst1)
+    delta = epcilon
+    k=1
+    while delta >= epcilon:
+        h/=2
+        k+=1
+        lst2=[]
+        lst2.append((lst1[0]+h*2*sum(f(a+(2*i-1)*h) for i in range(1,2**(k-2)+1)))/2)
+        for j in range(0,k-1):
+            lst2.append(lst2[j]+(lst2[j]-lst1[j])/(4**(j+1)-1))
+        delta = abs(lst2[-1]-lst1[-1])
+        lst1=lst2
+        mypprint(lst1)
+
+if __name__=='__main__':
+    print("数值积分")
+    a,b,h = 0.6,1.8,0.2
+    fs=[5.7,4.6,3.5,3.7,4.9,5.2,5.5]
+    print("\n梯形公式")
+    trapezoidal(a,b,h,fs)
+
+    print("\n辛普森公式")
+    simpson(a,b,h,fs)
+
+    print('\n龙贝格公式')
+    print("函数:{},  区间:{}   精度:{}".format('sin(x^4)','[1,2]',1e-4))
+    romberg(1,2,lambda x:sin(x**4),1e-4)