C-LinAlg Library

A practice implementation of linear algebra tools in C

Features

Finished:

• Vector addition, scalar multiplication
• Dot products
• Matrix-vector & Matrix-matrix multiplication
• Gaussian elimination, determinants

Planned:

• Eigenvectors && eigenvalues
• Jordan canonical form
• Stretch goal: linear programming

Usage:

Defining vectors Example: The code

/* Defining vectors, printing */
vector *x = new_vector(3);
x->vals[0]=1.; x->vals[1]=2.5; x->vals[2]=0.;

printf("The vector x = ");
printv(x);
printf("\n");

outputs

The vector x = [1.00,2.50,0.00]

Vector addition, scalar multiples, and dot product Example: the code

vector *y = new_vector(3);
y->vals[0]=0.; y->vals[1]=1.; y->vals[2]=1.;

printf("y= ");printv(y);printf("\n");

vector *z = new_vector(2);
z->vals[0]=2.; z->vals[1]=3.;

struct vector* w = v_add(x,y);
printf("x+y = ");printv(w);
printf("\n");
free_vector(w);

w = scalmul(z, 2.);
printf("2");printv(z);printf(" = ");printv(w);
printf("\n");

double c = v_dot(x,y);
printf("<x,y> = %.2f \n", c);

outputs

y= [0.00,1.00,1.00]
x+y = [1.00,3.50,1.00]
2[2.00,3.00] = [4.00,6.00]
<x,y> = 2.50 

** Matrices, matrix-vector multiplication and matrix multiplication ** Example, defining a matrix: the code

matrix *A = new_matrix(2, 3);
A->cols[0] = x;
A->cols[1] = y;
printf("Matrix A = \n");printM(A);printf("\n");

outputs

Matrix A = 
[1.00,0.00]
[2.50,1.00]
[0.00,1.00]

Example, matrix multiplication: the code

vector *b = matvectmul(A, z);
printf("Multiplying A by [2.,3.] gives ");printv(b);printf("\n\n");

w->vals[0]=3.;
w->vals[1]=-2.;
matrix *B = new_matrix(2,2);
B->cols[0]=w;
B->cols[1]=z;
matrix *C = matmul(A,B);
printM(A);printf("*\n");printM(B);printf("=\n");printM(C);

outputs

Multiplying A by [2.,3.] gives [2.00,8.00,3.00]

[1.00,0.00]
[2.50,1.00]
[0.00,1.00]
*
[3.00,2.00]
[-2.00,3.00]
=
[3.00,2.00]
[5.50,8.00]
[-2.00,3.00]