Files
file	fnft__misc.h
	Miscellaneous functions used in the FNFT library.

Functions
void	fnft__misc_print_buf (const FNFT_INT len, FNFT_COMPLEX const const buf, char const const varname)
	Helper function for debugging. Prints an array in MATLAB style. More...

FNFT_REAL	fnft__misc_rel_err (const FNFT_INT len, FNFT_COMPLEX const const vec_numer, FNFT_COMPLEX const const vec_exact)
	Relative l1 error between two vectors. More...

FNFT_REAL	fnft__misc_hausdorff_dist (const FNFT_UINT lenA, FNFT_COMPLEX const const vecA, const FNFT_UINT lenB, FNFT_COMPLEX const const vecB)
	Hausdorff distance between two vectors. More...

FNFT_COMPLEX	fnft__misc_sech (FNFT_COMPLEX Z)
	Hyperbolic secant. More...

FNFT_REAL	fnft__misc_l2norm2 (const FNFT_UINT N, FNFT_COMPLEX const *const Z, const FNFT_REAL a, const FNFT_REAL b)
	Squared l2 norm. More...

FNFT_INT	fnft__misc_filter (FNFT_UINT const N, FNFT_COMPLEX const vals, FNFT_COMPLEX const rearrange_as_well, FNFT_REAL const const bounding_box)
	Filters array by retaining elements inside a bounding box. More...

FNFT_INT	fnft__misc_filter_nonreal (FNFT_UINT N_ptr, FNFT_COMPLEX const vals, const FNFT_REAL tol_im)
	Filter array based on specified tolerance. More...

FNFT_INT	fnft__misc_filter_inv (FNFT_UINT const N_ptr, FNFT_COMPLEX const vals, FNFT_COMPLEX const rearrange_as_well, FNFT_REAL const const bounding_box)
	Filters array by retaining elements outside a bounding box. More...

FNFT_INT	fnft__misc_merge (FNFT_UINT N_ptr, FNFT_COMPLEX const vals, FNFT_REAL tol)
	Merges elements in an array with distance lower than tol. More...

FNFT_INT	fnft__misc_downsample (const FNFT_UINT D, FNFT_COMPLEX const const q, FNFT_UINT const Dsub_ptr, FNFT_COMPLEX *qsub_ptr, FNFT_UINT const first_last_index)
	Downsamples an array. More...

FNFT_COMPLEX	fnft__misc_CSINC (FNFT_COMPLEX x)
	Sinc function for complex arguments. More...

FNFT_UINT	fnft__misc_nextpowerof2 (const FNFT_UINT number)
	Closest larger or equal number that is a power of two. More...

Detailed Description

Function Documentation

◆ fnft__misc_CSINC()

FNFT_COMPLEX fnft__misc_CSINC ( FNFT_COMPLEX x )

Sinc function for complex arguments.

Functions computes the Sinc function sin(x)/x for FNFT_COMPLEX argument.

Parameters

[in] x FNFT_COMPLEX argument.

Returns: Sinc(x).

◆ fnft__misc_downsample()

FNFT_INT fnft__misc_downsample	(	const FNFT_UINT	D,
		FNFT_COMPLEX const *const	q,
		FNFT_UINT *const	Dsub_ptr,
		FNFT_COMPLEX **	qsub_ptr,
		FNFT_UINT *const	first_last_index
	)

Downsamples an array.

Computes a subsampled version of q. The length of q is D>=2. The routine will allocate memory for the subsampled signal qsub and updates the pointer *qsub_ptr such that it points to the newly allocated qsub. The user is responsible to freeing the memory later.

Parameters

[in]	D	Number of samples in array q.
[in]	q	Complex valued array to be subsampled.
[out]	qsub_ptr	Pointer to the starting location of subsampled signal.
[out]	Dsub_ptr	Pointer to new number of samples. Upon entry, Dsub_ptr should contain a desired number of samples. Upon exit, Dsub_ptr has been overwritten with the actual number of samples that the routine has chosen. It is usually close to the desired one.
[out]	first_last_index	Vector of length two. Upon exit, it contains the original index of the first and the last sample in qsub. That is, qsub[0]=q[first_last_index[0]] and qsub[Dsub-1]=q[first_last_index[1]].

Returns: Returns SUCCESS or an error code.

◆ fnft__misc_filter()

FNFT_INT fnft__misc_filter	(	FNFT_UINT *const	N,
		FNFT_COMPLEX *const	vals,
		FNFT_COMPLEX *const	rearrange_as_well,
		FNFT_REAL const *const	bounding_box
	)

Filters array by retaining elements inside a bounding box.

This function filters the array vals. Only values that satisfy

 bounding_box[0] <= real(val) <= bounding_box[1]

and

 bounding_box[2] <= imag(val) <= bounding_box[3]

are kept.

Parameters

[in,out]	N	It is the pointer to the number of values to be filtered. On exit *N is overwritten with the number of values that have survived fitering. Their values will be moved to the beginning of vals.
[in,out]	vals	Complex valued array with elements to be filtered.
[in]	rearrange_as_well	Complex valued array. If the array rearrange_as_well is not NULL, then the values in there are rearranged together with the values in vals.
[in]	bounding_box	A real array of 4 elements. The elements determine the corners of the bounding box being used for filtering.

Returns: Returns SUCCESS or an error code.

◆ fnft__misc_filter_inv()

FNFT_INT fnft__misc_filter_inv	(	FNFT_UINT *const	N_ptr,
		FNFT_COMPLEX *const	vals,
		FNFT_COMPLEX *const	rearrange_as_well,
		FNFT_REAL const *const	bounding_box
	)

Filters array by retaining elements outside a bounding box.

This function filters the array vals. Only values OUTSIDE the bounding box are kept.

Parameters

[in,out]	N_ptr	It is the pointer to the number of values to be filtered. On exit *N_ptr is overwritten with the number of values that have survived fitering. Their values will be moved to the beginning of vals.
[in,out]	vals	Complex valued array with elements to be filtered.
[in]	rearrange_as_well	Complex valued array. If the array rearrange_as_well is not NULL, then the values in there are rearranged together with the values in vals.
[in]	bounding_box	A real array of 4 elements. The elements determine the corners of the bounding box being used for filtering.

Returns: Returns SUCCESS or an error code.

◆ fnft__misc_filter_nonreal()

FNFT_INT fnft__misc_filter_nonreal	(	FNFT_UINT *	N_ptr,
		FNFT_COMPLEX *const	vals,
		const FNFT_REAL	tol_im
	)

Filter array based on specified tolerance.

This function removes all entries from the array vals with |Im(val)|>tol_im.

Parameters

[in,out]	N_ptr	Pointer to number of values to be filtered. On exit *N_ptr is overwritten with the number of values that have survived fitering. Their values will be moved to the beginning of vals.
[in,out]	vals	Complex valued array with elements to be filtered.
[in]	tol_im	Real valued tolerance.

Returns: Returns SUCCESS or an error code.

◆ fnft__misc_hausdorff_dist()

FNFT_REAL fnft__misc_hausdorff_dist	(	const FNFT_UINT	lenA,
		FNFT_COMPLEX const *const	vecA,
		const FNFT_UINT	lenB,
		FNFT_COMPLEX const *const	vecB
	)

Hausdorff distance between two vectors.

This function computes the Hausdorff distance between two vectors vecA and vecB.

Parameters

[in]	lenA	Length of vector vecA.
[in]	vecA	Complex vector of length lenA.
[in]	lenB	length of vector vecB.
[in]	vecB	Complex vector of length lenB.

Returns: Returns the real valued Hausdorff distance between the vectors vecA and vecB.

◆ fnft__misc_l2norm2()

FNFT_REAL fnft__misc_l2norm2	(	const FNFT_UINT	N,
		FNFT_COMPLEX const *const	Z,
		const FNFT_REAL	a,
		const FNFT_REAL	b
	)

Squared l2 norm.

This function computes the quantity
\( val = \frac{b-a}{2N}.(|Z[0]|^2+|Z[N-1]|^2)+\sum_{i=1}^{i=N-2}\frac{b-a}{N}.|Z[i]|^2\).

Parameters

[in]	N	Number of elements in the array.
[in]	Z	Complex valued array of length N.
[in]	a	Real number corresponding to first element of Z.
[in]	b	Real number corresponding to last element of Z.

Returns: Returns the quantity val. Returns NAN if N<2 or a>=b.

◆ fnft__misc_merge()

FNFT_INT fnft__misc_merge	(	FNFT_UINT *	N_ptr,
		FNFT_COMPLEX *const	vals,
		FNFT_REAL	tol
	)

Merges elements in an array with distance lower than tol.

This function filters an array by merging elements if distance between the elements is less than tol.

Parameters

[in,out]	N_ptr	It is the pointer to the number of elements to be filtered. On exit *N_ptr is overwritten with the number of values that have survived fitering. Their values will be moved to the beginning of vals.
[in,out]	vals	Complex valued array with elements to be filtered.
[in]	tol	Real valued tolerance.

Returns: Returns SUCCESS or an error code.

◆ fnft__misc_nextpowerof2()

FNFT_UINT fnft__misc_nextpowerof2 ( const FNFT_UINT number )

Closest larger or equal number that is a power of two.

Parameters

[in] number

Returns: min{r >= number : exists d such that r = 2^d}

◆ fnft__misc_print_buf()

void fnft__misc_print_buf	(	const FNFT_INT	len,
		FNFT_COMPLEX const *const	buf,
		char const *const	varname
	)

Helper function for debugging. Prints an array in MATLAB style.

This function prints an array in MATLAB style.

Parameters

[in]	len	Length of the array to be printed.
[in]	buf	Array to be printed.
[in]	varname	Name of the array being printed.

◆ fnft__misc_rel_err()

FNFT_REAL fnft__misc_rel_err	(	const FNFT_INT	len,
		FNFT_COMPLEX const *const	vec_numer,
		FNFT_COMPLEX const *const	vec_exact
	)

Relative l1 error between two vectors.

This function computes the relative l1 error between two vectors.
\(err = \frac{\sum_{i=0}^{i=len-1} |vec\_numer[i]-vec\_exact[i]|}{\sum_{i=0}^{i=len-1} |vec\_exact[i]|}\).

Parameters

[in]	len	Length of the vectors
[in]	vec_numer	Complex array of numerically computed result of length len.
[in]	vec_exact	Complex array of exact result of length len.

Returns: Returns the real valued relative error err.

◆ fnft__misc_sech()

FNFT_COMPLEX fnft__misc_sech ( FNFT_COMPLEX Z )

Hyperbolic secant.

This function returns the hyperbolic secant of a FNFT_COMPLEX.

Parameters

[in] Z FNFT_COMPLEX argument.

Returns: hyperbolic secant of Z.

Files

Functions

Detailed Description

Function Documentation

◆ fnft__misc_CSINC()

◆ fnft__misc_downsample()

◆ fnft__misc_filter()

◆ fnft__misc_filter_inv()

◆ fnft__misc_filter_nonreal()

◆ fnft__misc_hausdorff_dist()

◆ fnft__misc_l2norm2()

◆ fnft__misc_merge()

◆ fnft__misc_nextpowerof2()

◆ fnft__misc_print_buf()

◆ fnft__misc_rel_err()

◆ fnft__misc_sech()