linear regression

Collaboration diagram for linear regression:

Data Structures
struct	a_regress_linear
	instance structure for linear regression More...

Typedefs
typedef struct a_regress_linear	a_regress_linear

Functions
void	a_regress_linear_init (a_regress_linear *ctx, double *coef_p, size_t coef_n, double bias)
	initialize for linear regression
double	a_regress_linear_eval (a_regress_linear const *ctx, double const *val)
	calculate predicted value for linear regression
void	a_regress_linear_err1 (a_regress_linear const *ctx, size_t n, double const *x, double const *y, double *err)
	calculate residuals for linear regression
void	a_regress_linear_err2 (a_regress_linear const *ctx, size_t n, double const *const *x, double const *y, double *err)
	calculate residuals for linear regression
void	a_regress_linear_pdm1 (a_regress_linear const *ctx, size_t n, double const *x, double *pdm, double y_mean)
	calculate prediction deviation from mean for linear regression
void	a_regress_linear_pdm2 (a_regress_linear const *ctx, size_t n, double const *const *x, double *pdm, double y_mean)
	calculate prediction deviation from mean for linear regression
void	a_regress_linear_gd (a_regress_linear *ctx, double const *input, double error, double alpha)
	gradient descent for linear regression
void	a_regress_linear_sgd (a_regress_linear *ctx, double const *x, double y, double alpha)
	stochastic gradient descent for linear regression
void	a_regress_linear_sgd1 (a_regress_linear *ctx, size_t n, double const *x, double const *y, double alpha)
	stochastic gradient descent for linear regression
void	a_regress_linear_sgd2 (a_regress_linear *ctx, size_t n, double const *const *x, double const *y, double alpha)
	stochastic gradient descent for linear regression
void	a_regress_linear_bgd1 (a_regress_linear *ctx, size_t n, double const *x, double const *err, double alpha)
	batch gradient descent for linear regression
void	a_regress_linear_bgd2 (a_regress_linear *ctx, size_t n, double const *const *x, double const *err, double alpha)
	batch gradient descent for linear regression
double	a_regress_linear_mgd1 (a_regress_linear *ctx, size_t n, double const *x, double const *y, double *err, double delta, double lrmax, double lrmin, size_t lrtim, size_t epoch, size_t batch)
	mini-batch gradient descent for linear regression
double	a_regress_linear_mgd2 (a_regress_linear *ctx, size_t n, double const *const *x, double const *y, double *err, double delta, double lrmax, double lrmin, size_t lrtim, size_t epoch, size_t batch)
	mini-batch gradient descent for linear regression
void	a_regress_linear_zero (a_regress_linear *ctx)
	zeroing for linear regression

Detailed Description

Function Documentation

a_regress_linear_bgd1()

void a_regress_linear_bgd1	(	a_regress_linear *	ctx,
		size_t	n,
		double const *	x,
		double const *	err,
		double	alpha )

batch gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n*coef_n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	err	residuals, specified as a numeric vector
[in]	alpha	learning rate for gradient descent

a_regress_linear_bgd2()

void a_regress_linear_bgd2	(	a_regress_linear *	ctx,
		size_t	n,
		double const *const *	x,
		double const *	err,
		double	alpha )

batch gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n][coef_n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	err	residuals, specified as a numeric vector
[in]	alpha	learning rate for gradient descent

a_regress_linear_err1()

void a_regress_linear_err1	(	a_regress_linear const *	ctx,
		size_t	n,
		double const *	x,
		double const *	y,
		double *	err )

calculate residuals for linear regression

Parameters

[in]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n*coef_n], y[n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in,out]	err	residuals, specified as a numeric vector

a_regress_linear_err2()

void a_regress_linear_err2	(	a_regress_linear const *	ctx,
		size_t	n,
		double const *const *	x,
		double const *	y,
		double *	err )

calculate residuals for linear regression

Parameters

[in]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n][coef_n], y[n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in,out]	err	residuals, specified as a numeric vector

a_regress_linear_eval()

double a_regress_linear_eval	(	a_regress_linear const *	ctx,
		double const *	val )

calculate predicted value for linear regression

Parameters

[in]	ctx	points to an instance of linear regression
[in]	val	independent variables

Returns

predicted value

a_regress_linear_gd()

void a_regress_linear_gd	(	a_regress_linear *	ctx,
		double const *	input,
		double	error,
		double	alpha )

gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	input	predictor data, specified as a numeric vector
[in]	error	residual, specified as a numeric scalar
[in]	alpha	learning rate for gradient descent

a_regress_linear_init()

void a_regress_linear_init	(	a_regress_linear *	ctx,
		double *	coef_p,
		size_t	coef_n,
		double	bias )

initialize for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	coef_p	points to regression coefficients
[in]	coef_n	number of regression coefficients
[in]	bias	intercept

a_regress_linear_mgd1()

double a_regress_linear_mgd1	(	a_regress_linear *	ctx,
		size_t	n,
		double const *	x,
		double const *	y,
		double *	err,
		double	delta,
		double	lrmax,
		double	lrmin,
		size_t	lrtim,
		size_t	epoch,
		size_t	batch )

mini-batch gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n*coef_n], y[n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in,out]	err	residuals, specified as a numeric vector
[in]	delta	threshold for gradient descent value
[in]	lrmin	minimum learning rate of iterations
[in]	lrmax	maximum learning rate of iterations
[in]	lrtim	total number of learning rate steps
[in]	epoch	maximum number of epochs
[in]	batch	batch size of data

Returns

change in loss function

a_regress_linear_mgd2()

double a_regress_linear_mgd2	(	a_regress_linear *	ctx,
		size_t	n,
		double const *const *	x,
		double const *	y,
		double *	err,
		double	delta,
		double	lrmax,
		double	lrmin,
		size_t	lrtim,
		size_t	epoch,
		size_t	batch )

mini-batch gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n][coef_n], y[n], err[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in,out]	err	residuals, specified as a numeric vector
[in]	delta	threshold for gradient descent value
[in]	lrmin	minimum learning rate of iterations
[in]	lrmax	maximum learning rate of iterations
[in]	lrtim	total number of learning rate steps
[in]	epoch	maximum number of epochs
[in]	batch	batch size of data

Returns

change in loss function

a_regress_linear_pdm1()

void a_regress_linear_pdm1	(	a_regress_linear const *	ctx,
		size_t	n,
		double const *	x,
		double *	pdm,
		double	y_mean )

calculate prediction deviation from mean for linear regression

Parameters

[in]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n*coef_n], pdm[n]
[in]	x	predictor data, specified as a numeric matrix
[in,out]	pdm	deviation, specified as a numeric vector
[in]	y_mean	mean of response data

a_regress_linear_pdm2()

void a_regress_linear_pdm2	(	a_regress_linear const *	ctx,
		size_t	n,
		double const *const *	x,
		double *	pdm,
		double	y_mean )

calculate prediction deviation from mean for linear regression

Parameters

[in]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n][coef_n], pdm[n]
[in]	x	predictor data, specified as a numeric matrix
[in,out]	pdm	deviation, specified as a numeric vector
[in]	y_mean	mean of response data

a_regress_linear_sgd()

void a_regress_linear_sgd	(	a_regress_linear *	ctx,
		double const *	x,
		double	y,
		double	alpha )

stochastic gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	x	predictor data, specified as a numeric vector
[in]	y	response data, specified as a numeric scalar
[in]	alpha	learning rate for gradient descent

a_regress_linear_sgd1()

void a_regress_linear_sgd1	(	a_regress_linear *	ctx,
		size_t	n,
		double const *	x,
		double const *	y,
		double	alpha )

stochastic gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n*coef_n], y[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in]	alpha	learning rate for gradient descent

a_regress_linear_sgd2()

void a_regress_linear_sgd2	(	a_regress_linear *	ctx,
		size_t	n,
		double const *const *	x,
		double const *	y,
		double	alpha )

stochastic gradient descent for linear regression

Parameters

[in,out]	ctx	points to an instance of linear regression
[in]	n	number of samples, x[n][coef_n], y[n]
[in]	x	predictor data, specified as a numeric matrix
[in]	y	response data, specified as a numeric vector
[in]	alpha	learning rate for gradient descent

a_regress_linear_zero()

void a_regress_linear_zero

(

a_regress_linear *

ctx

)

zeroing for linear regression

Parameters

[in,out]

ctx

points to an instance of linear regression