lin_alg.c File Reference

Detailed Description

Linear algebra with vectors.

Author

Ben Hermans

Common operations, such as vector products, infinity norm, elementwise add/product/division/max etc. are included in this file.

Definition in file lin_alg.c.

#include <qpalm/lin_alg.h>

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Functions
c_float *	vec_copy (const c_float *a, size_t n)
	Copy vector a into output.
void	prea_vec_copy (const c_float *a, c_float *b, size_t n)
	Copy vector a into preallocated vector b.
void	prea_int_vec_copy (const c_int *a, c_int *b, size_t n)
	Copy integer vector a into preallocated vector b.
void	vec_set_scalar (c_float *a, c_float sc, size_t n)
	Fill float vector with a scalar value.
void	vec_set_scalar_int (c_int *a, c_int sc, size_t n)
	Fill int vector with a scalar value.
void	vec_self_mult_scalar (c_float *a, c_float sc, size_t n)
	Mulitply vector with a constant scale factor.
void	vec_mult_scalar (const c_float *a, c_float sc, c_float *b, size_t n)
	Mulitply vector with a constant scale factor and store in a different vector.
c_float	vec_prod (const c_float *a, const c_float *b, size_t n)
	Inner product between two vectors, \(a^T \cdot b\).
c_float	vec_norm_two (const c_float *a, size_t n)
	2-norm of a vector, \(\|a\|_2\).
void	vec_ew_prod (const c_float *a, const c_float *b, c_float *c, size_t n)
	Elementwise product, \(c_i = a_i\cdot b_i\).
void	vec_ew_div (const c_float *a, const c_float *b, c_float *c, size_t n)
	Elementwise division, \(c_i = a_i/b_i\).
void	vec_add_scaled (const c_float *a, const c_float *b, c_float *c, c_float sc, size_t n)
	Scaled addition of one vector to another vector, \(c_i = a_i + sc\cdot b_i\).
void	vec_mult_add_scaled (c_float *a, const c_float *b, c_float sc1, c_float sc2, size_t n)
	Scaled addition of one vector to another vector, both being scaled, \(a_i = sc1\cdot a_i + sc2\cdot b_i\).
c_float	vec_norm_inf (const c_float *a, size_t n)
	Infinity norm of a vector, \(\|a\|_\infty\).
void	vec_ew_recipr (const c_float *a, c_float *b, size_t n)
	Elementwise reciprocal \(b_i = 1/a_i\).
void	vec_ew_max_vec (const c_float *a, const c_float *b, c_float *c, size_t n)
	Elementwise maximum between vectors, \(c_i = \textrm{max}(a_i, b_i)\).
void	vec_ew_min_vec (const c_float *a, const c_float *b, c_float *c, size_t n)
	Elementwise minimum between vectors, \(c_i = \textrm{min}(a_i, b_i)\).
void	vec_ew_mid_vec (const c_float *a, const c_float *bmin, const c_float *bmax, c_float *c, size_t n)
	Elementwise mid between vectors, \(c_i = \textrm{max}(b_{\textrm{min},i}, \textrm{min}(a_i, b_{\textrm{max},i}))\).
void	vec_ew_sqrt (const c_float *a, c_float *b, size_t n)
	Elementwise square root, \(b_i = \sqrt{a_i}\).

Function Documentation

vec_copy()

c_float * vec_copy	(	const c_float *	a,
		size_t	n
	)

Copy vector a into output.

Warning

This function uses malloc.

Parameters

a	Vector
n	Vector length

Returns

Copy of a

Definition at line 11 of file lin_alg.c.

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prea_vec_copy()

void prea_vec_copy	(	const c_float *	a,
		c_float *	b,
		size_t	n
	)

Copy vector a into preallocated vector b.

Parameters

a	Input vector
b	Output vector
n	Vector length

Definition at line 24 of file lin_alg.c.

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prea_int_vec_copy()

void prea_int_vec_copy	(	const c_int *	a,
		c_int *	b,
		size_t	n
	)

Copy integer vector a into preallocated vector b.

Parameters

a	Input vector
b	Output vector
n	Vector length

Definition at line 32 of file lin_alg.c.

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vec_set_scalar()

void vec_set_scalar	(	c_float *	a,
		c_float	sc,
		size_t	n
	)

Fill float vector with a scalar value.

Parameters

a	Vector
sc	Value
n	Vector length

Definition at line 40 of file lin_alg.c.

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vec_set_scalar_int()

void vec_set_scalar_int	(	c_int *	a,
		c_int	sc,
		size_t	n
	)

Fill int vector with a scalar value.

Parameters

a	Vector
sc	Value
n	Vector length

Definition at line 48 of file lin_alg.c.

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vec_self_mult_scalar()

void vec_self_mult_scalar	(	c_float *	a,
		c_float	sc,
		size_t	n
	)

Mulitply vector with a constant scale factor.

Parameters

a	Vector
sc	Value
n	Vector length

Definition at line 56 of file lin_alg.c.

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vec_mult_scalar()

void vec_mult_scalar	(	const c_float *	a,
		c_float	sc,
		c_float *	b,
		size_t	n
	)

Mulitply vector with a constant scale factor and store in a different vector.

Parameters

a	Input vector
sc	Value
b	Output vector
n	Vector length

Definition at line 64 of file lin_alg.c.

vec_prod()

c_float vec_prod	(	const c_float *	a,
		const c_float *	b,
		size_t	n
	)

Inner product between two vectors, \(a^T \cdot b\).

Parameters

a	Vector
b	Vector
n	Vector length

Returns

Result of the inner product

Definition at line 72 of file lin_alg.c.

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vec_norm_two()

c_float vec_norm_two	(	const c_float *	a,
		size_t	n
	)

2-norm of a vector, \(\|a\|_2\).

Parameters

a	Vector
n	Vector length

Returns

2-norm of a

Definition at line 88 of file lin_alg.c.

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vec_ew_prod()

void vec_ew_prod	(	const c_float *	a,
		const c_float *	b,
		c_float *	c,
		size_t	n
	)

Elementwise product, \(c_i = a_i\cdot b_i\).

Parameters

a	Input vector
b	Input vector
c	Output vector
n	Vector length

Definition at line 92 of file lin_alg.c.

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vec_ew_div()

void vec_ew_div	(	const c_float *	a,
		const c_float *	b,
		c_float *	c,
		size_t	n
	)

Elementwise division, \(c_i = a_i/b_i\).

Parameters

a	Input vector
b	Input vector
c	Output vector
n	Vector length

Definition at line 101 of file lin_alg.c.

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vec_add_scaled()

void vec_add_scaled	(	const c_float *	a,
		const c_float *	b,
		c_float *	c,
		c_float	sc,
		size_t	n
	)

Scaled addition of one vector to another vector, \(c_i = a_i + sc\cdot b_i\).

Parameters

a	Input vector
b	Input vector
c	Output vector
sc	Scaling value
n	Vector length

Definition at line 110 of file lin_alg.c.

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vec_mult_add_scaled()

void vec_mult_add_scaled	(	c_float *	a,
		const c_float *	b,
		c_float	sc1,
		c_float	sc2,
		size_t	n
	)

Scaled addition of one vector to another vector, both being scaled, \(a_i = sc1\cdot a_i + sc2\cdot b_i\).

Parameters

a	Input and Output vector
b	Input vector
sc1	Scaling value for a
sc2	Scaling value for b
n	Vector length

Definition at line 118 of file lin_alg.c.

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vec_norm_inf()

c_float vec_norm_inf	(	const c_float *	a,
		size_t	n
	)

Infinity norm of a vector, \(\|a\|_\infty\).

Parameters

a	Vector
n	Vector length

Returns

Infinity norm of a

Definition at line 126 of file lin_alg.c.

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vec_ew_recipr()

void vec_ew_recipr	(	const c_float *	a,
		c_float *	b,
		size_t	n
	)

Elementwise reciprocal \(b_i = 1/a_i\).

This function is used in scaling.

Parameters

a	Input vector
b	Output vector
n	Vector length

Definition at line 176 of file lin_alg.c.

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vec_ew_max_vec()

void vec_ew_max_vec	(	const c_float *	a,
		const c_float *	b,
		c_float *	c,
		size_t	n
	)

Elementwise maximum between vectors, \(c_i = \textrm{max}(a_i, b_i)\).

Parameters

a	Input vector
b	Input vector
c	Output vector
n	Vector length

Definition at line 184 of file lin_alg.c.

vec_ew_min_vec()

void vec_ew_min_vec	(	const c_float *	a,
		const c_float *	b,
		c_float *	c,
		size_t	n
	)

Elementwise minimum between vectors, \(c_i = \textrm{min}(a_i, b_i)\).

Parameters

a	Input vector
b	Input vector
c	Output vector
n	Vector length

Definition at line 192 of file lin_alg.c.

vec_ew_mid_vec()

void vec_ew_mid_vec	(	const c_float *	a,
		const c_float *	bmin,
		const c_float *	bmax,
		c_float *	c,
		size_t	n
	)

Elementwise mid between vectors, \(c_i = \textrm{max}(b_{\textrm{min},i}, \textrm{min}(a_i, b_{\textrm{max},i}))\).

Parameters

a	Input vector
bmin	Lower bounds
bmax	Upper bounds
c	Output vector
n	Vector length

Definition at line 200 of file lin_alg.c.

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vec_ew_sqrt()

void vec_ew_sqrt	(	const c_float *	a,
		c_float *	b,
		size_t	n
	)

Elementwise square root, \(b_i = \sqrt{a_i}\).

Parameters

a	Input vector
b	Output vector
n	Vector length

Definition at line 208 of file lin_alg.c.

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