例題6-8 高斯消去法 Python program to find determinant of Matrix

例題6-8 Python program to find determinant of Matrix


Now consider an example of 4×4 matrix :

Notice the + – + – pattern (+a… -b… +c… -d…). This is important to remember.

The pattern continues for 5×5 matrices and higher.

Now let us see how to write a C program to find determinant of Matrix MxM . The program will accept the order of matrix i.e. M as input from user and then ask user to enter the values of matrix elements. Then it will calculate the determinant of the matrix and returns the output.

#Python program to find determinant of Matrix

def determinant( a , n):

    b=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n], 

    c = [0.0 for i in range(n+1)];   

    if(n==2):

        d=0

        d=(a[1][1]*a[2][2])-(a[1][2]*a[2][1]);

        return(d);

    else:

        for j in range(1 , n+1):

            r=1

            s=1

            for p in range (1, n+1):

                for q in range (1, n+1):

                    if ((p!=1) & (q!=j)):

                        b[r][s]=a[p][q]

                        s=s+1

                        if(s>n-1):

                            r=r+1

                            s=1

            pr=1                

            for t in range (1, j+2):

                pr=(-1)*pr;

                c[j]=pr*determinant(b,n-1);

    d=0

    for j in range (1, n+1):

        d=d+(a[1][j]*c[j]);

    return(d);

#++++++++++++++++++++++++++++++++++++++++++

n=3

a=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n], 

print("------------------------------------------------------------------------")

print("---------Python program to find determinant of Matrix ------------")

print("------------------------------------------------------------------------")

print("\n\nEnter order of matrix : ",n)

print("\nEnter the elements of matrix\n");

print("\n\n---------- Matrix A is --------------\n");   

a=[[ 0.0 ,0.0 ,  0.0 , 0.0 , 0.0],

      [ 0.0 ,2.0 ,  1.0 , -3.0 , 0.0],

      [ 0.0 , -1.0 , 3.0 , 2.0,  0.0],

      [ 0.0 ,3.0 ,  1.0 , -3.0 , 0.0]]

for i in range(1 ,n+1):

    for j in range(1,n+1):

        print( "a[",i,"][",j,"]=",round(a[i][j],4),'\t',end='')

    print("")

print("\n Determinant of Matrix A is %d .",determinant(a,n));

輸出畫面

= RESTART: C:/Users/alex/AppData/Local/Programs/Python/Python37-32/EX6-8.py =

------------------------------------------------------------------------

---------Python program to find determinant of Matrix ------------

------------------------------------------------------------------------

Enter order of matrix :  3

Enter the elements of matrix

---------- Matrix A is --------------

a[ 1 ][ 1 ]= 2.0 a[ 1 ][ 2 ]= 1.0 a[ 1 ][ 3 ]= -3.0

a[ 2 ][ 1 ]= -1.0 a[ 2 ][ 2 ]= 3.0 a[ 2 ][ 3 ]= 2.0

a[ 3 ][ 1 ]= 3.0 a[ 3 ][ 2 ]= 1.0 a[ 3 ][ 3 ]= -3.0

 Determinant of Matrix A is %d . 11.0