Example: API documentation

Numerical Method example

Numerical Programming API

#include "myNM.h"

Non-Linear Solver

newtonRaphson()

Solves the non-linear problem using Newton-Raphson method

double newtonRaphson(double x0, double tol);

Parameters

• x0: initial value.

• tol: tolerance error

Example code

double tol = 0.00001;
double x0 = 3;
double NR_result;
​
NR_result = newtonRaphson(x0, tol);

Linear Solver

gaussElim()

solves for vector x from Ax=b, a linear system problem Using Gauss Elimination

void gaussElim(Matrix _A, Matrix _B, Matrix* _U, Matrix* _B_out);

Parameters

• A: Matrix A in structure Matrix form. Should be (nxn) square.

• B: vector b in structure Matrix form. Should be (nx1)

• U: Matrix U in structure Matrix form. Should be (nxn) square.

• B_out: vector B_out in structure Matrix form. Should be (nx1)

Example code

Matrix matA = txt2Mat(path, "prob1_matA");
Matrix vecb = txt2Mat(path, "prob1_vecb");
Matrix matU = zeros(matA.rows, matA.cols);
Matrix vecd = zeros(vecb.rows, vecb.cols);
​
gaussElim(matA, vecb, matU, vecd);

inv()

Find the inverse Matrix.

void inv(Matrix _A, Matrix _Ainv);

Parameters

• A: Matrix A in structure Matrix form. Should be (nxn) square.

• Ainv: Matrix Ainv in structure Matrix form. Should be (nxn) square.

Example code

Matrix matA = txt2Mat(path, "prob1_matA");
Matrix matAinv = zeros(matA.rows, matA.cols);
​
inv(matA, matAinv);

Numerical Differentiation

gradient1D()

Solve for numerical gradient (dy/dt) from a 1D-array form.

void gradient1D(double x[], double y[], double dydx[], int m);

Parameters

• x[]: input data vector x in 1D-array .

• y[]: input data vector y in 1D-array.

• dydx[]: output vector dydx in 1D-array.

• m: length x and y.

Example code

double x[21];
    for (int i = 0; i < 21; i++) {
        x[i] = 0.2 * i;
    }
double y[] = { -5.87, -4.23, -2.55, -0.89, 0.67, 2.09, 3.31, 4.31, 5.06, 5.55, 5.78, 5.77, 5.52, 5.08, 4.46, 3.72, 2.88, 2.00, 1.10, 0.23, -0.59 };
double dydx[21];
​
gradient1D(x, y, dydx, 21);

Integration

integral()

Integral using Simpson 1/3 Method.

double integral(double func(const double _x), double a, double b, int n);

Parameters

• func: Function func is defined.

• a is starting point of x.

• b is ending point of x.

• n is the length between a and b

Example code

double I_simpson13 = integral(myFunc, -1, 1, 12);

double myFunc(const double _x) {
	return sqrt(1 - (_x * _x));
}

ODE-IVP

odeEU()

Solve the 1st-order ODE using Euler's Explicit Method.

void odeEU(double func(const double x, const double y), double y[], double t0, double tf, double h, double y0);

Parameters

• func: Function func is defined.

• y[]: Solution of ODE in structure 1D-array form.

• t0 is starting point.

• tf is ending point.

• h is length of step.

• y0 is initial value of y[].

Example code

double a = 0;
double b = 0.1;
double h = 0.001;
double y_EU[200] = { 0 };
double v0 = 0;

odeEU(odeFunc_rc, y_EU, a, b, h, v0);

double odeFunc_rc(const double t, const double v) {
	double tau = 1;
	double T = 1 / tau;
	double f = 10;
	double Vm = 1;
	double omega = 2 * PI * f;
	return  -T * v + T * Vm * cos(omega * t);
}

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Class or Header name

Function Name

Parameters

• p1

• p2

Example code