appsf.h File Reference

The implementation of the mini-apps with machine numbers. More...

Go to the source code of this file.

Functions
arrayf	appf_join (arrayf z1, arrayf z2)
	Joins the real parts of the sequences z1 and z2 as the real parts and imaginary parts of a new list. More...
arrayf	appf_grid (arrayf z1, arrayf z2)
	Computes the set product of the real parts of two sequences z1 and z2. More...
arrayf	appf_exp (arrayf z)
	Computes the complex exponential of a sequence z. More...
arrayf	appf_rot (arrayf z)
	Computes a*exp(ib) for each term a+ib of a sequence z of complex numbers. More...
arrayf	appf_polar (arrayf z)
	Computes the complex numbers given by a sequence z of their polar coordinates on the sphere. More...
arrayf	appf_unif (ulong n, coeff_t st, coeff_t en)
	Returns the list of n real numbers that split the interval [st,en] in n-1 equal intervals. More...
bool	appf_compare (arrayf z1, arrayf z2, char *output)
	Compares two list of complex values and reports the eventual errors. More...
arrayf	appf_re (arrayf z)
	Returns the real parts of the numbers in the sequence z. More...
arrayf	appf_im (arrayf z)
	Returns the imaginary parts of the numbers in the sequence z. More...
arrayf	appf_conj (arrayf z)
	Returns the conjugates of the numbers in the sequence z. More...
arrayf	appf_tensor (arrayf z1, arrayf z2)
	Computes tensor (or piontwise) product of the sequences z1 and z2. More...
bool	appf_eval_p (polyf P, arrayf z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	appf_eval_d (polyf P, arrayf z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the derivative of the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	appf_eval_n (polyf P, arrayf z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the Newton terms of the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	appf_eval_r (polyf P, arrayf z, ulong maxIter, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the Newton iterates of the polynomial P in all points in the list z, using the FPE algorithm. More...

Detailed Description

The implementation of the mini-apps with machine numbers.

Definition in file appsf.h.

Function Documentation

appf_compare()

bool appf_compare	(	arrayf	z1,
		arrayf	z2,
		char *	output
	)

Compares two list of complex values and reports the eventual errors.

Parameters

z1	the fist list
z2	the second list
output	a file name for the output file, NULL if not used

Returns

true if the comparison is complete, false if some error occurred.

appf_conj()

arrayf appf_conj

(

arrayf

z

)

Returns the conjugates of the numbers in the sequence z.

Parameters

z	the list of points

Returns

the conjugates of z, NULL if some error occurred.

appf_eval_d()

bool appf_eval_d	(	polyf	P,
		arrayf	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the derivative of the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

appf_eval_n()

bool appf_eval_n	(	polyf	P,
		arrayf	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the Newton terms of the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

appf_eval_p()

bool appf_eval_p	(	polyf	P,
		arrayf	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

appf_eval_r()

bool appf_eval_r	(	polyf	P,
		arrayf	z,
		ulong	maxIter,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the Newton iterates of the polynomial P in all points in the list z, using the FPE algorithm.

This is a method to approximate the roots of P, but there are no guarantees for the convergence. If the iterates escape far from the origin, the alogrith stops (for those starting points).

Parameters

P	the polynomial
z	the list of evaluation points
maxIter	the maximum iterates for each starting point
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

appf_exp()

arrayf appf_exp

(

arrayf

z

)

Computes the complex exponential of a sequence z.

Parameters

z	the list of points

Returns

the image by the complex exponential, NULL if some error occurred.

appf_grid()

arrayf appf_grid	(	arrayf	z1,
		arrayf	z2
	)

Computes the set product of the real parts of two sequences z1 and z2.

Parameters

z1	the first list
z2	the second list

Returns

the set product, NULL if some error occurred.

appf_im()

arrayf appf_im

(

arrayf

z

)

Returns the imaginary parts of the numbers in the sequence z.

Parameters

z	the list of points

Returns

the imaginary parts in z, NULL if some error occurred.

appf_join()

arrayf appf_join	(	arrayf	z1,
		arrayf	z2
	)

Joins the real parts of the sequences z1 and z2 as the real parts and imaginary parts of a new list.

Parameters

z1	the first list
z2	the second list

Returns

the joint list, NULL if some error occurred.

appf_polar()

arrayf appf_polar

(

arrayf

z

)

Computes the complex numbers given by a sequence z of their polar coordinates on the sphere.

Parameters

z	the list of polar coordinates

Returns

the complex numbers given by their polar coordinates, NULL if some error occurred.

appf_re()

arrayf appf_re

(

arrayf

z

)

Returns the real parts of the numbers in the sequence z.

Parameters

z	the list of points

Returns

the real parts in z, NULL if some error occurred.

appf_rot()

arrayf appf_rot

(

arrayf

z

)

Computes a*exp(ib) for each term a+ib of a sequence z of complex numbers.

Parameters

z	the list of points

Returns

the image by a+ib->a*exp(ib), NULL if some error occurred.

appf_tensor()

arrayf appf_tensor	(	arrayf	z1,
		arrayf	z2
	)

Computes tensor (or piontwise) product of the sequences z1 and z2.

Parameters

z1	the first list
z2	the second list

Returns

the tensor product, NULL if some error occurred.

appf_unif()

arrayf appf_unif	(	ulong	n,
		coeff_t	st,
		coeff_t	en
	)

Returns the list of n real numbers that split the interval [st,en] in n-1 equal intervals.

Parameters

n	the number of points, at least 2
st	the start point
en	the end point

Returns

the list of real numbers (in complex format), NULL if some error occurred.