Norms of vectors and matrices

Macros
#define	mirml_mh_v_norm1(x, n)   mirml_mh_v_norm1_s(x,NULL,n)
	Computes uscaled 1-norms of vectors.
#define	mirml_mh_v_norm2(x, n)   mirml_mh_v_norm2_s(x,NULL,n)
	Computes uscaled 2-norm (Euclidean norm) of vectors.
#define	mirml_mh_v_norminf(x, n)   mirml_mh_v_norminf_s(x,NULL,n)
	Computes uscaled infinity-norm (supremum norm) of vectors.

Functions
mirkl_error_t *	mirml_mh_v_norm1_s (const mirml_mh_vector_t *x, const mirml_mh_vector_t *scale, double *norm)
	Computes (scaled) 1-norms of vectors. More...
mirkl_error_t *	mirml_mh_v_norm2_s (const mirml_mh_vector_t *x, const mirml_mh_vector_t *scale, double *norm)
	Computes (scaled) 2-norm (Euclidean norm) of vectors. More...
mirkl_error_t *	mirml_mh_v_norminf_s (const mirml_mh_vector_t *x, const mirml_mh_vector_t *scale, double *norm)
	Computes (scaled) infinity-norm (supremum norm) of vectors. More...
mirkl_error_t *	mirml_mh_m_norm1 (const mirml_mh_matrix_t *A, double *norm)
	Compute matrix unscaled 1-norm. More...
mirkl_error_t *	mirml_mh_m_norm_inf (const mirml_mh_matrix_t *A, double *norm)
	Compute matrix unscaled infinity-norm. More...
mirkl_error_t *	mirml_mh_m_norm_frob (const mirml_mh_matrix_t *A, double *norm)
	Compute matrix unscaled frobenius-norm. More...

Detailed Description

Function Documentation

mirml_mh_m_norm1()

mirkl_error_t * mirml_mh_m_norm1	(	const mirml_mh_matrix_t *	A,
		double *	norm
	)

Compute matrix unscaled 1-norm.

Parameters

[in]	A	Input matrix.
[out]	norm	Norm of input matrix on output.

mirml_mh_m_norm_frob()

mirkl_error_t * mirml_mh_m_norm_frob	(	const mirml_mh_matrix_t *	A,
		double *	norm
	)

Compute matrix unscaled frobenius-norm.

Parameters

[in]	A	Input matrix.
[out]	norm	Norm of input matrix on output.

mirml_mh_m_norm_inf()

mirkl_error_t * mirml_mh_m_norm_inf	(	const mirml_mh_matrix_t *	A,
		double *	norm
	)

Compute matrix unscaled infinity-norm.

Parameters

[in]	A	Input matrix.
[out]	norm	Norm of input matrix on output.

mirml_mh_v_norm1_s()

mirkl_error_t * mirml_mh_v_norm1_s	(	const mirml_mh_vector_t *	x,
		const mirml_mh_vector_t *	scale,
		double *	norm
	)

Computes (scaled) 1-norms of vectors.

Parameters

[in]	x	Input vector.
[in]	scale	Optional scaling vector. If NULL – no scaling required.
[out]	norm	Norm of input vector on output.

Note

scale is used to divide components of input vector: x_i/s_i

mirml_mh_v_norm2_s()

mirkl_error_t * mirml_mh_v_norm2_s	(	const mirml_mh_vector_t *	x,
		const mirml_mh_vector_t *	scale,
		double *	norm
	)

Computes (scaled) 2-norm (Euclidean norm) of vectors.

Parameters

[in]	x	Input vector.
[in]	scale	Optional scaling vector. If NULL – no scaling required.
[out]	norm	Norm of input vector on output.

Note

scale is used to divide components of input vector: x_i/s_i

mirml_mh_v_norminf_s()

mirkl_error_t * mirml_mh_v_norminf_s	(	const mirml_mh_vector_t *	x,
		const mirml_mh_vector_t *	scale,
		double *	norm
	)

Computes (scaled) infinity-norm (supremum norm) of vectors.

Parameters

[in]	x	Input vector.
[in]	scale	Optional scaling vector. If NULL – no scaling required.
[out]	norm	Norm of input vector on output.

Note

scale is used to divide components of input vector: x_i/s_i