calc.h File Reference

A simple calculus library header. More...

#include <math.h>

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Data Structures
struct	calc_function
	Structure representing an function and its derivative. More...

Typedefs
typedef struct calc_function	calc_function
	Structure representing an function and its derivative.
typedef double(*	calc_function_fn) (double)
	A function pointer type for functions.

Functions
double	calc_approx_derivative (double(*f)(double), double x, double h)
	Calculate the numerical derivative of a function at a point.
double	calc_approx_finite_integral (double(*f)(double), double a, double b, int n)
	Calculate the numerical integral of a function over an interval.
double	calc_function_negation (double x)
	Negate the value of a given double.
double	calc_function_negation_derivative (double x)
	Calculate the derivative of the negation function.
double	calc_function_relu (double x)
	Calculate the ReLU (Rectified Linear Unit) function.
double	calc_function_relu_derivative (double x)
	Calculate the derivative of the ReLU function.
double	calc_function_sigmoid (double x)
	Calculate the sigmoid function.
double	calc_function_sigmoid_derivative (double x)
	Calculate the derivative of the sigmoid function.
double	calc_function_square (double x)
	Calculate the square of a given double.
double	calc_function_square_derivative (double x)
	Calculate the derivative of the square function.
double	calc_function_tanh (double x)
	Calculate the Tanh function.
double	calc_function_tanh_derivative (double x)
	Calculate the derivative of the Tanh function.

Variables
const calc_function	CALC_FUNCTION_NEGATION
	Predefined negation function.
const calc_function	CALC_FUNCTION_RELU
	Predefined ReLU function.
const calc_function	CALC_FUNCTION_SIGMOID
	Predefined Sigmoid function.
const calc_function	CALC_FUNCTION_SQUARE
	Predefined square function.
const calc_function	CALC_FUNCTION_TANH
	Predefined Tanh function.

Detailed Description

A simple calculus library header.

This header file contains declarations for mathematical calculation functions, including numerical differentiation and integration. The implementations of these functions are included in the compiled library lib/libcalc.so.

Definition in file calc.h.

Typedef Documentation

calc_function

typedef struct calc_function calc_function

Structure representing an function and its derivative.

This structure holds the name of the function, the function itself, and its derivative function.

calc_function_fn

typedef double(* calc_function_fn) (double)

A function pointer type for functions.

This type represents a function that takes a double and returns a double, typically used for functions in neural networks.

Definition at line 22 of file calc.h.

Function Documentation

calc_approx_derivative()

double calc_approx_derivative	(	double(*)(double)	f,
		double	x,
		double	h )

Calculate the numerical derivative of a function at a point.

This function approximates the derivative of a given function \( f \) at a point \( x \) using the central difference method:

\[ f'(x) \approx \frac{f(x + h) - f(x - h)}{2h} \]

Parameters

f	Pointer to the function to differentiate.
x	The point at which to evaluate the derivative.
h	A small value for the finite difference approximation.

Returns

The numerical derivative of the function at the point \( x \).

calc_approx_finite_integral()

double calc_approx_finite_integral	(	double(*)(double)	f,
		double	a,
		double	b,
		int	n )

Calculate the numerical integral of a function over an interval.

This function approximates the integral of a given function \( f \) over the interval \([a, b]\) using the trapezoidal rule:

\[ \int_a^b f\left(x\right) \, dx \approx \frac{b - a}{2n} \sum_{i=0}^{n-1} \left(f\left(x_i\right) + f\left(x_{i+1}\right)\right) \]

Parameters

f	Pointer to the function to integrate.
a	The lower limit of integration.
b	The upper limit of integration.
n	The number of subintervals.

Returns

The numerical integral of the function over the interval \([a, b]\).

calc_function_negation()

double calc_function_negation

(

double

x

)

Negate the value of a given double.

This function takes a double value and returns its negation.

Example usage:

double value = 5.0;
double neg_value = calc_function_negation(value);
printf("Negation: %f\n", neg_value);

Parameters

x	The value to be negated.

Returns

The negated value.

calc_function_negation_derivative()

double calc_function_negation_derivative

(

double

x

)

Calculate the derivative of the negation function.

This function calculates the derivative of the negation function, which is \( -1 \) for any value of \( x \).

Parameters

x	The value at which to evaluate the derivative.

Returns

The derivative of the negation function, which is \( -1 \).

calc_function_relu()

double calc_function_relu

(

double

x

)

Calculate the ReLU (Rectified Linear Unit) function.

The ReLU function is defined as: \[ \text{ReLU}(x) = \max(0, x) \]

This function is commonly used as an function in neural networks.

Parameters

x	The input value.

Returns

The result of the ReLU function.

Example:

double result = calc_function_relu(0.5); // result = 0.5
result = calc_function_relu(-0.5); // result = 0.0

calc_function_relu_derivative()

double calc_function_relu_derivative

(

double

x

)

Calculate the derivative of the ReLU function.

The derivative of the ReLU function is: \[ \text{ReLU}'(x) = \begin{cases} 1 & \text{if } x > 0 \\ 0 & \text{if } x \leq 0 \end{cases} \]

Parameters

x	The input value.

Returns

The derivative of the ReLU function.

Example:

double result = calc_function_relu_derivative(0.5); // result = 1.0
result = calc_function_relu_derivative(-0.5); // result = 0.0

calc_function_sigmoid()

double calc_function_sigmoid

(

double

x

)

Calculate the sigmoid function.

The sigmoid function, \( \sigma(x) \), is defined as: \[ \sigma(x) = \frac{1}{1 + e^{-x}} \]

The sigmoid function maps any real-valued number \( x \) to a value in the range (0, 1). It is commonly used in logistic regression and as an activation function in neural networks.

Parameters

x	The input value.

Returns

The result of the sigmoid function \( \sigma(x) \).

Example:

double result = calc_function_sigmoid(0.5); // result = 0.622
result = calc_function_sigmoid(-0.5); // result = 0.378

calc_function_sigmoid_derivative()

double calc_function_sigmoid_derivative

(

double

x

)

Calculate the derivative of the sigmoid function.

The derivative of the sigmoid function is defined as: \[ \sigma'(x) = \sigma(x) \cdot (1 - \sigma(x)) \]

This function is used during the backpropagation step in neural networks.

Parameters

x	The input value.

Returns

The derivative of the sigmoid function.

Example:

double result = calc_function_sigmoid_derivative(0.5); // result = 0.235
result = calc_function_sigmoid_derivative(-0.5); // result = 0.235

calc_function_square()

double calc_function_square

(

double

x

)

Calculate the square of a given double.

This function takes a double value and returns its square.

Example usage:

double value = 5.0;
double square_value = calc_function_square(value);
printf("Square: %f\n", square_value);

Parameters

x	The value to be squared.

Returns

The squared value.

calc_function_square_derivative()

double calc_function_square_derivative

(

double

x

)

Calculate the derivative of the square function.

This function calculates the derivative of the square function, which is \( 2x \).

Parameters

x	The value at which to evaluate the derivative.

Returns

The derivative of the square function, which is \( 2x \).

calc_function_tanh()

double calc_function_tanh

(

double

x

)

Calculate the Tanh function.

The Tanh function is defined as: \[ \tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} \]

This function maps any real-valued number \( x \) to a value in the range (-1, 1). It is commonly used as an function in neural networks.

Parameters

x	The input value.

Returns

The result of the Tanh function.

Example:

double result = calc_function_tanh(0.5); // result = 0.462
result = calc_function_tanh(-0.5); // result = -0.462

calc_function_tanh_derivative()

double calc_function_tanh_derivative

(

double

x

)

Calculate the derivative of the Tanh function.

The derivative of the Tanh function is defined as: \[ \tanh'(x) = 1 - \tanh^2(x) \]

This function is used during the backpropagation step in neural networks.

Parameters

x	The input value.

Returns

The derivative of the Tanh function.

Example:

double result = calc_function_tanh_derivative(0.5); // result = 0.786
result = calc_function_tanh_derivative(-0.5); // result = 0.786

Variable Documentation

CALC_FUNCTION_NEGATION

const calc_function CALC_FUNCTION_NEGATION

extern

Predefined negation function.

This constant represents the negation function and its derivative.

CALC_FUNCTION_RELU

const calc_function CALC_FUNCTION_RELU

extern

Predefined ReLU function.

This constant represents the ReLU function and its derivative.

CALC_FUNCTION_SIGMOID

const calc_function CALC_FUNCTION_SIGMOID

extern

Predefined Sigmoid function.

This constant represents the Sigmoid function and its derivative.

CALC_FUNCTION_SQUARE

const calc_function CALC_FUNCTION_SQUARE

extern

Predefined square function.

This constant represents the square function and its derivative.

CALC_FUNCTION_TANH

const calc_function CALC_FUNCTION_TANH

extern

Predefined Tanh function.

This constant represents the Tanh function and its derivative.