Macros
#define	NRANSI

#define	THRESH 0

#define	ITOL 3

#define	TOL 0.00001

#define	ITMAX 1000

#define	SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)

#define	SWAP(a, b) tempr=(a);(a)=(b);(b)=tempr

#define	EPS 1.0e-14

#define	TINY 1.0E-20

Functions
void	convlv (FLOATVECTOR data, unsigned long n, FLOATVECTOR respns, unsigned long m, int isign, double delta_time, FLOATVECTOR *ans)

void	four1 (FLOATVECTOR *data, unsigned long nn, int isign)

void	ludcmp (SHORTVECTOR indx, DOUBLEMATRIX var)

void	lubksb (DOUBLEMATRIX var, SHORTVECTOR indx, DOUBLEVECTOR *gam)

void	realft (FLOATVECTOR *data, unsigned long n, int isign)

void	twofft (FLOATVECTOR data1, FLOATVECTOR data2, FLOATVECTOR fft1, FLOATVECTOR fft2, unsigned long n)

void	sprsin (double *, int, float, long, double , long *)

DOUBLEMATRIX *	vett_mat (double d, double ds, double *di, int n)

double	snrm (long n, double sx[], int itol)

void	atimes (long n, double x[], double r[], int itrnsp, double sa[], long ija[])

void	asolve (long n, double b[], double x[], double sa[])

void	dsprsax (double sa[], long ija[], double x[], double b[], long n)

void	dsprstx (double sa[], long ija[], double x[], double b[], long n)

float	integration (float(*fun)(float), float, float, int)

Macro Definition Documentation

#define EPS 1.0e-14

Definition at line 8 of file linearalgebra.h.

#define ITMAX 1000

Definition at line 5 of file linearalgebra.h.

#define ITOL 3

Definition at line 3 of file linearalgebra.h.

#define NRANSI

Definition at line 1 of file linearalgebra.h.

#define SQR ( a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)

Definition at line 6 of file linearalgebra.h.

Referenced by convlv().

#define SWAP	(	a,
		b
	)	tempr=(a);(a)=(b);(b)=tempr

Definition at line 7 of file linearalgebra.h.

Referenced by four1().

#define THRESH 0

Definition at line 2 of file linearalgebra.h.

#define TINY 1.0E-20

Definition at line 9 of file linearalgebra.h.

Referenced by ludcmp().

#define TOL 0.00001

Definition at line 4 of file linearalgebra.h.

Function Documentation

void asolve	(	long	n,
		double	b[],
		double	x[],
		double	sa[]
	)

Name: asolve

Version:

Synopsis: void asolve(long n, double b[], double x[], int itrnsp,double sa[], long ija[])

Description:

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 89

Definition at line 635 of file linearalgebra.c.

void atimes	(	long	n,
		double	x[],
		double	r[],
		int	itrnsp,
		double	sa[],
		long	ija[]
	)

Name: atimes

Version:

Synopsis: void atimes(long n, double x[], double r[], int itrnsp,double sa[], long ija[]);

Description:

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 88

Notes:

Definition at line 615 of file linearalgebra.c.

References dsprsax(), and dsprstx().

void convlv	(	FLOATVECTOR *	data,
		unsigned long	n,
		FLOATVECTOR *	respns,
		unsigned long	m,
		int	isign,
		double	delta_time,
		FLOATVECTOR *	ans
	)

Name: convlv

Synopsis: void convlv(FLOATVECTOR *data,unsigned long n,FLOATVECTOR *respns,unsigned long m,int isign, double delta_time,FLOATVECTOR *ans);

Description: Convolves or deconvolves a real data set data [1..n] with a responce function respns[1..n] The responce function must be stored in wrap-around order in the first element of respns, where m is an odd integer <=n. Wrap-around order means that the first half of the array respns contains the impulse responce function at positive times, while the second half of the array contains the impulceresponce function at negative times, counting down from the highest element respns[m]. On input isign is +1 for convolution, -1 for deconvolution. The answer is returned in the first n componenets of ans. However, ans must be supplied in the calling program with dimension [1..2*n], for consistency with twofft. n MUST be an integer power of two.

Authors & Date: Angelo Zacchia, Marco Pegoretti, 1998

Inputs: data is a complex array of lenght n

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Notes: It is a modified version of the routine in Numerical Recipes, second edition

Definition at line 6 of file linearalgebra.c.

References FLOATVECTOR::co, free_floatvector(), new_floatvector(), realft(), SQR, t_error(), and twofft().

void dsprsax	(	double	sa[],
		long	ija[],
		double	x[],
		double	b[],
		long	n
	)

Name: dsprsax

Version:

Synopsis: void dsprsax(double sa[], long ija[], double x[], double b[], long n)

Description: Questa funzione moltiplica una matrice, memoririzzata alla maniera di N.R., per un vettore x[]. Il risultato e' un vettore b[].

Inputs:

Return:

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 89

Definition at line 654 of file linearalgebra.c.

References t_error().

Referenced by atimes().

void dsprstx	(	double	sa[],
		long	ija[],
		double	x[],
		double	b[],
		long	n
	)

Name: dsprstx

Synopsis: void dsprsax(double sa[], long ija[], double x[], double b[], long n)

Description: Questa funzione moltiplica la trasposta di una matrice, memoririzzata alla maniera di N.R., per un vettore x[]. Il risultato e' un vettore b[].

Inputs:

Return:

Needs:

Related Routines:

See Also:

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 137

Definition at line 697 of file linearalgebra.c.

void lubksb	(	DOUBLEMATRIX *	var,
		SHORTVECTOR *	indx,
		DOUBLEVECTOR *	gam
	)

Name: lubksb

Synopsis: int lubksb(DOUBLEMATRIX *var, SHORTVECTOR *indx,DOUBLEVECTOR *gam)

Description: Convolves or deconvolves a real data set data [1..n] with a responce function respns[1..n] The responce function must be stored in wrap-around order in the first element of respns, where m is an odd integer <=n. Wrap-around order means that the first half of the array respns contains the impulse responce function at positive times, while the second half of the array contains the impulceresponce function at negative times, counting down from the highest element respns[m]. On input isign is +1 for convolution, -1 for deconvolution. The answer is returned in the first n componenets of ans. However, ans must be supplied in the calling program with dimension [1..2*n], for consistency with twofft. n MUST be an integer power of two.

Authors & Date: Angelo Zacchia, Marco Pegoretti, 1998

Inputs: data is a complex array of lenght n

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Notes: It is a modified version of the routine in Numerical Recipes, second edition

Examples:

References: Pegoretti, Marco, Geomodel, implementazione di un modello scalabile di deflusso e bilancio idrologico di bacino, 1997

Definition at line 169 of file linearalgebra.c.

References SHORTVECTOR::co, DOUBLEVECTOR::co, DOUBLEMATRIX::co, and DOUBLEMATRIX::nrh.

Referenced by ordi_kriging2().

void ludcmp	(	SHORTVECTOR *	indx,
		DOUBLEMATRIX *	var
	)

Name: ludcmp

Synopsis: int ludcmp(SHORTVECTOR *indx, DOUBLEMATRIX *var)

Description: Convolves or deconvolves a real data set data [1..n] with a responce function respns[1..n] The responce function must be stored in wrap-around order in the first element of respns, where m is an odd integer <=n. Wrap-around order means that the first half of the array respns contains the impulse responce function at positive times, while the second half of the array contains the impulceresponce function at negative times, counting down from the highest element respns[m]. On input isign is +1 for convolution, -1 for deconvolution. The answer is returned in the first n componenets of ans. However, ans must be supplied in the calling program with dimension [1..2*n], for consistency with twofft. n MUST be an integer power of two.

Authors & Date: Angelo Zacchia, Marco Pegoretti, 1998

Inputs:

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Notes: It is a modified version of the routine in Numerical Recipes, second edition

Examples:

References: Pegoretti, Marco, Geomodel, implementazione di un modello scalabile di deflusso e bilancio idrologico di bacino, 1997

Definition at line 97 of file linearalgebra.c.

References SHORTVECTOR::co, DOUBLEVECTOR::co, DOUBLEMATRIX::co, free_doublevector(), new_doublevector(), DOUBLEMATRIX::nrh, and TINY.

Referenced by ordi_kriging2().

void realft	(	FLOATVECTOR *	data,
		unsigned long	n,
		int	isign
	)

Name: realft

Synopsis: void realft(FLOATVECTOR *data,unsigned long n,int isign);

Description: Calculates the Fourier transform of a set of n real-value data points. Replaces this data (which is stored in array data[1..n]) by the positive frequency half of its complex Fourier transform. The real-valued first and last components of the complex transform are returned as elements data[1] data[2], respectively, n must be a power of 2. This routine also calculates the inverse transform of a complex data array if it is the transform of real data (result in this case must be multiplied by 2/n).

Authors & Date: modified from NR by Marco Pegoretti and Angelo Zacchia, 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Definition at line 202 of file linearalgebra.c.

References FLOATVECTOR::co, and four1().

Referenced by convlv().

double snrm	(	long	n,
		double	sx[],
		int	itol
	)

Name: snrm

Version:

Synopsis: double snrm(long n, double sx[], int itol);

Description:

Questa funzione calcola la norma di un vettore con la modalita' specificata dal parametro itol

Authors & Date: Angelo Zacchia, June 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 88

Bugs & limitations:

Definition at line 579 of file linearalgebra.c.

void sprsin	(	double **	,
		int	,
		float	,
		long	,
		double *	,
		long *
	)

Name: ris_sistema

Synopsis:

void ris_sistema (double d[], double ds[], double di[], double b[], double x[], int n);

Version:0.9

Description: This solves the specified linear system. Questa funzione innesca la soluzione del sistema lineare. Ha solo lo scopo di ricevere gli argomenti necessari dal programma principale, allocare e deallocare le strutture necessarie e di restituire il risultato.

Definizione dei parametri:

THRESH: gli elementi della matrice che in valore assoluto sono minori di THRESH vengono trascurati;
ITOL: varia da 1 a 4 e determina quale criterio di convergenza adottare per la soluzione del sistema (vedi Numerical Recipes in C pag. 86);
TOL: tolleranza ammessa nella ricerca della soluzione;
ITMAX: numero massimo di iterazioni.

Inputs: In input riceve gli elementi delle diagonali principale d[], superiore ds[], inferiore di[], il vettore dei termini noti b[], una soluzione di primo tentativo x[] e la dimensione del sistema, n.

Return: Vengono restituiti gli elementi del vettore soluzione del sistema x[].

Tutti vettori sopra menzionati devono essere variabili globali, sono quindi dichiarati all'interno del programma principale.

Authors & Date: Angelo Zacchia, June 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Name: sprsin

Synopsis:

void sprsin(double **,int,float,long,double *,long *);

Description: Funzione che ordina una matrice sparsa (in questo caso tridiagonale) alla maniera di Num. Rec. Questa funzione converte una matrice memorizzata nel modo convenzionale in un vettore sa[] che contiene solo i valori non nulli della matrice e in un vettore ija[] che permette di individuare la posizione originale degli elementi di sa[].

Inputs:

**a, un puntatore agli elementi della matrice originale;
n, dimensione della matrice;
thresh, gli elementi della matrice minori di thresh non vengono letti;
nmax, la lunghezza dei vettori sa[] e ija[].

Return:

Authors & Date: Angelo Zacchia, June 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

References: DA NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press).

void twofft	(	FLOATVECTOR *	data1,
		FLOATVECTOR *	data2,
		FLOATVECTOR *	fft1,
		FLOATVECTOR *	fft2,
		unsigned long	n
	)

Name: twofft

Synopsis: voidtwofft(FLOATVECTOR *data1,FLOATVECTOR *data2,FLOATVECTOR *fft1,FLOATVECTOR *fft2,unsigned long n);

Description: Given two real input array data1[1..2n] and data2[1..2n] this routine calls four1 and return two complex output arrays, fft1[1..2n] and fft2[1..2n], each of complex lenght n, which contain the discrete Fourier transforms of the respective data arrays. n MUST be an integer power of 2

Authors & Date: For the Numerical Recipes,1998.

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Definition at line 247 of file linearalgebra.c.

References FLOATVECTOR::co, and four1().

Referenced by convlv().

DOUBLEMATRIX* vett_mat	(	double *	d,
		double *	ds,
		double *	di,
		int	n
	)

Name: linbcg

Description: Questa funzione consente di risolvere di risolvere un sistema lineare del tipo A x = b con il metodo iterativo del gradiente coniugato.

Inputs:

n: dimensione del sistema;
sa[] e ija[]: vettori generati dalla funzione sprssin() che memorizzano la matrice;
b[]: elementi del vettore dei termini noti;
x[]: elementi del vettore soluzione (in ingresso questo vettore deve contenere una soluzione di primo tentativo);
itol, tol, itmax: parametri gli definiti sopra.

Oltre alla soluzione la funzione calcola anche il numero di iterazione effetuate ( iter ) e l'errore commesso ( err ).

Authors & Date: Angelo Zacchia, June 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

References:  NUMERICAL RECIPES IN C. (Second Edition - Cambridge Univ. Press). pag 86-88

 Bugs & limitations:

Name: vett_mat

Version:

Synopsis:

Description:

Questa funzione converte tre vettori in una matrice quadrata tridiagonale.

Inputs: Bisogna passare alla funzione i puntatori agli elementi dei vettori

d elementi delle diagonale principale;
ds elementi della diagonale superiore;
di elementi della diagonale inferiore; inoltre bisogna passare n, che e' la dimensione della matrice che si vuole generare.

Return: La funzione restituisce il puntatore alla matrice.

Authors & Date: Angelo Zacchia, June 1998

FILE: LIBRARIES/LINEARALGEBRA/linearalgebra.c, LIBRARIES/LINEARALGEBRA/linearalgebra.h

Definition at line 369 of file linearalgebra.c.

References DOUBLEMATRIX::co, and new_doublematrix().

Macros

Functions

Macro Definition Documentation

Function Documentation