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#ifndef lint

static char *RCSid() { return RCSid("$Id: interpol.c,v 1.38 2008/11/12 02:29:43 janert Exp $"); }

#endif

/* GNUPLOT - interpol.c */

/*[

* Permission to use, copy, and distribute this software and its

* documentation for any purpose with or without fee is hereby granted,

* provided that the above copyright notice appear in all copies and

* that both that copyright notice and this permission notice appear

* in supporting documentation.

* Permission to modify the software is granted, but not the right to

* distribute the complete modified source code. Modifications are to

* be distributed as patches to the released version. Permission to

* distribute binaries produced by compiling modified sources is granted,

* provided you

* 1. distribute the corresponding source modifications from the

* released version in the form of a patch file along with the binaries,

* 2. add special version identification to distinguish your version

* in addition to the base release version number,

* 3. provide your name and address as the primary contact for the

* support of your modified version, and

* 4. retain our contact information in regard to use of the base

* software.

* Permission to distribute the released version of the source code along

* with corresponding source modifications in the form of a patch file is

* granted with same provisions 2 through 4 for binary distributions.

* This software is provided "as is" without express or implied warranty

* to the extent permitted by applicable law.

]*/

* C-Source file identification Header

* This file belongs to a project which is:

* done 1993 by MGR-Software, Asgard (Lars Hanke)

* written by Lars Hanke

* Contact me via:

* InterNet: mgr@asgard.bo.open.de

* FIDO: Lars Hanke @ 2:243/4802.22 (as long as they keep addresses)

**************************************************************************

* Project: gnuplot

* Module:

* File: interpol.c

* Revisor: Lars Hanke

* Revised: 26/09/93

* Revision: 1.0

**************************************************************************

* LEGAL

* This module is part of gnuplot and distributed under whatever terms

* gnuplot is or will be published, unless exclusive rights are claimed.

* DESCRIPTION

* Supplies 2-D data interpolation and approximation routines

* IMPORTS

* plot.h

* - cp_extend()

* - structs: curve_points, coordval, coordinate

* setshow.h

* - samples, axis array[] variables

* - plottypes

* proto.h

* - solve_tri_diag()

* - typedef tri_diag

* EXPORTS

* gen_interp()

* sort_points()

* cp_implode()

* BUGS and TODO

* I would really have liked to use Gershon Elbers contouring code for

* all the stuff done here, but I failed. So I used my own code.

* If somebody is able to consolidate Gershon's code for this purpose

* a lot of gnuplot users would be very happy - due to memory problems.

**************************************************************************

* HISTORY

* Changes:

* Nov 24, 1995 Markus Schuh (M.Schuh@meteo.uni-koeln.de):

* changed the algorithm for csplines

* added algorithm for approximation csplines

* copied point storage and range fix from plot2d.c

* Dec 12, 1995 David Denholm

* oops - at the time this is called, stored co-ords are

* internal (ie maybe log of data) but min/max are in

* user co-ordinates.

* Work with min and max of internal co-ords, and

* check at the end whether external min and max need to

* be increased. (since samples_1 is typically 100 ; we

* dont want to take more logs than necessary)

* Also, need to take into account which axes are active

* Jun 30, 1996 Jens Emmerich

* implemented handling of UNDEFINED points

#include "interpol.h"

#include "alloc.h"

#include "axis.h"

#include "contour.h"

#include "graphics.h"

#include "misc.h"

#include "plot2d.h"

/* #include "setshow.h" */

#include "util.h"

/* in order to support multiple axes, and to simplify ranging in

* parametric plots, we use arrays to store some things. For 2d plots,

* elements are z=0,y1=1,x1=2,z2=4,y2=5,x2=6 these are given symbolic

* names in plot.h

* IMHO, code is getting too cluttered with repeated chunks of

* code. Some macros to simplify, I hope.

/* store VALUE or log(VALUE) in STORE, set TYPE as appropriate Do

* OUT_ACTION or UNDEF_ACTION as appropriate. Adjust range provided

* type is INRANGE (ie dont adjust y if x is outrange). VALUE must not

* be same as STORE */

/* FIXME 20010610: UNDEF_ACTION is completely unused ??? Furthermore,

* this is so similar to STORE_WITH_LOG_AND_UPDATE_RANGE() from axis.h

* that the two should probably be merged. */

#define STORE_AND_FIXUP_RANGE(store, value, type, min, max, auto, \

out_action, undef_action) \

do { \

store=value; \

if (type != INRANGE) \

break; /* don't set y range if x is outrange, for example */ \

if ((value) < (min)) { \

if ((auto) & AUTOSCALE_MIN) \

(min) = (value); \

else { \

(type) = OUTRANGE; \

out_action; \

break; \

} \

if ((value) > (max)) { \

if ((auto) & AUTOSCALE_MAX) \

(max) = (value); \

else { \

(type) = OUTRANGE; \

out_action; \

} \

} while(0)

#define UPDATE_RANGE(TEST,OLD,NEW,AXIS) \

do { \

if (TEST) \

(OLD) = AXIS_DE_LOG_VALUE(AXIS,NEW); \

} while(0)

#define spline_coeff_size 4

typedef double spline_coeff[spline_coeff_size];

typedef double five_diag[5];

static int next_curve __PROTO((struct curve_points * plot, int *curve_start));

static int num_curves __PROTO((struct curve_points * plot));

static void eval_kdensity __PROTO((struct curve_points *cp,

int first_point, int num_points, double sr,

coordval *px, coordval *py));

static void do_kdensity __PROTO((struct curve_points *cp, int first_point,

int num_points, struct coordinate *dest));

static double *cp_binomial __PROTO((int points));

static void eval_bezier __PROTO((struct curve_points * cp, int first_point,

int num_points, double sr, coordval * px,

coordval *py, double *c));

static void do_bezier __PROTO((struct curve_points * cp, double *bc, int first_point, int num_points, struct coordinate * dest));

static int solve_five_diag __PROTO((five_diag m[], double r[], double x[], int n));

static spline_coeff *cp_approx_spline __PROTO((struct curve_points * plot, int first_point, int num_points));

static spline_coeff *cp_tridiag __PROTO((struct curve_points * plot, int first_point, int num_points));

static void do_cubic __PROTO((struct curve_points * plot, spline_coeff * sc, int first_point, int num_points, struct coordinate * dest));

static void do_freq __PROTO((struct curve_points *plot, int first_point, int num_points));

int compare_points __PROTO((SORTFUNC_ARGS p1, SORTFUNC_ARGS p2));

* position curve_start to index the next non-UNDEFINDED point,

* start search at initial curve_start,

* return number of non-UNDEFINDED points from there on,

* if no more valid points are found, curve_start is set

* to plot->p_count and 0 is returned

static int

next_curve(struct curve_points *plot, int *curve_start)

{

int curve_length;

/* Skip undefined points */

while (*curve_start < plot->p_count

&& plot->points[*curve_start].type == UNDEFINED) {

(*curve_start)++;

};

curve_length = 0;

/* curve_length is first used as an offset, then the correct # points */

while ((*curve_start) + curve_length < plot->p_count

&& plot->points[(*curve_start) + curve_length].type != UNDEFINED) {

curve_length++;

};

return (curve_length);

}

* determine the number of curves in plot->points, separated by

* UNDEFINED points

static int

num_curves(struct curve_points *plot)

{

int curves;

int first_point;

int num_points;

first_point = 0;

curves = 0;

while ((num_points = next_curve(plot, &first_point)) > 0) {

curves++;

first_point += num_points;

}

return (curves);

}

/* PKJ - May 2008

kdensity (short for Kernel Density) builds histograms using

"Kernel Density Estimation" using Gaussian Kernels.

Check: L. Wassermann: "All of Statistics" for example.

The implementation is based closely on the implementation for Bezier

curves, except for the way the actual interpolation is generated.

/* eval_kdensity is a modification of eval_bezier */

static void

eval_kdensity (

struct curve_points *cp,

int first_point, /* where to start in plot->points (to find x-range) */

int num_points, /* to determine end in plot->points */

double sr, /* position inside curve, range [0:1] */

coordval *px, /* OUTPUT: x and y */

coordval *py ) {

unsigned int i;

unsigned int n = num_points - 1;

struct coordinate GPHUGE *this_points = (cp->points) + first_point;

double x, y, tmp;

double avg, sigma;

double min = DBL_MAX;

double max = -DBL_MAX;

double bandwidth, default_bandwidth;

avg = 0.0;

sigma = 0.0;

for (i = 0; i <= n; i++) {

avg += this_points[i].x;

sigma += this_points[i].x * this_points[i].x;

/* Find min and max of x-range. Necessary since points not sorted! */

min = this_points[i].x < min ? this_points[i].x : min;

max = this_points[i].x > max ? this_points[i].x : max;

}

avg /= (double)n;

sigma = sqrt( sigma/(double)n - avg*avg ); /* Standard Deviation */

/* This is the optimal bandwidth if the point distribution is Gaussian.

(Applied Smoothing Techniques for Data Analysis

by Adrian W, Bowman & Adelchi Azzalini (1997)) */

default_bandwidth = pow( 4.0/(3.0*num_points), 1.0/5.0 )*sigma;

/* If the supplied bandwidth is zero of less, the default bandwidth

is used. If only two columns have been specified in the using

declaration, the value of the third column (z-value) is set to

the value of '-1' in plot2d.c::get_data(). Therefore, a negative

value of z indicates that the default bandwidth should be used.

(I would prefer that a different magic value would be used to

indicate a missing third column, so that we we could fail if

the user supplies a negative bandwidth, but the -1 seems too

deeply ingrained.) */

x = min + sr*(max-min); /* The current x-value */

y = 0;

for (i = 0; i <= n; i++) {

if ( this_points[i].z <= 0 ) {

bandwidth = default_bandwidth;

} else {

bandwidth = this_points[i].z;

}

tmp = ( x - this_points[i].x )/bandwidth;

y += this_points[i].y * exp( - 0.5*tmp*tmp ) / bandwidth;

}

y /= sqrt(2.0*M_PI);

*px = x;

*py = y;

}

/* do_kdensity is based on do_bezier, except for the call to eval_bezier */

static void

do_kdensity(

struct curve_points *cp,

int first_point, /* where to start in plot->points */

int num_points, /* to determine end in plot->points */

struct coordinate *dest) /* where to put the interpolated data */

{

int i;

coordval x, y;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

x_axis = cp->x_axis;

y_axis = cp->y_axis;

ixmin = sxmin = AXIS_LOG_VALUE(x_axis, X_AXIS.min);

ixmax = sxmax = AXIS_LOG_VALUE(x_axis, X_AXIS.max);

iymin = symin = AXIS_LOG_VALUE(y_axis, Y_AXIS.min);

iymax = symax = AXIS_LOG_VALUE(y_axis, Y_AXIS.max);

for (i = 0; i < samples_1; i++) {

eval_kdensity( cp, first_point, num_points,

(double) i / (double) (samples_1 - 1),

&x, &y );

/* now we have to store the points and adjust the ranges */

dest[i].type = INRANGE;

STORE_AND_FIXUP_RANGE( dest[i].x, x, dest[i].type, ixmin, ixmax,

X_AXIS.autoscale, NOOP, continue);

STORE_AND_FIXUP_RANGE( dest[i].y, y, dest[i].type, iymin, iymax,

Y_AXIS.autoscale, NOOP, NOOP);

dest[i].xlow = dest[i].xhigh = dest[i].x;

dest[i].ylow = dest[i].yhigh = dest[i].y;

dest[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, X_AXIS.max, ixmax, x_axis);

UPDATE_RANGE(ixmin < sxmin, X_AXIS.min, ixmin, x_axis);

UPDATE_RANGE(iymax > symax, Y_AXIS.max, iymax, y_axis);

UPDATE_RANGE(iymin < symin, Y_AXIS.min, iymin, y_axis);

}

* build up a cntr_struct list from curve_points

* this funtion is only used for the alternate entry point to

* Gershon's code and thus commented out

***deleted***

/* HBB 990205: rewrote the 'bezier' interpolation routine,

* to prevent numerical overflow and other undesirable things happening

* for large data files (num_data about 1000 or so), where binomial

* coefficients would explode, and powers of 'sr' (0 < sr < 1) become

* extremely small. Method used: compute logarithms of these

* extremely large and small numbers, and only go back to the

* real numbers once they've cancelled out each other, leaving

* a reasonable-sized one. */

* cp_binomial() computes the binomial coefficients needed for BEZIER stuff

* and stores them into an array which is hooked to sdat.

* (MGR 1992)

static double *

cp_binomial(int points)

{

double *coeff;

int n, k;

int e;

e = points; /* well we're going from k=0 to k=p_count-1 */

coeff = gp_alloc(e * sizeof(double), "bezier coefficients");

n = points - 1;

e = n / 2;

/* HBB 990205: calculate these in 'logarithmic space',

* as they become _very_ large, with growing n (4^n) */

coeff[0] = 0.0;

for (k = 0; k < e; k++) {

coeff[k + 1] = coeff[k] + log(((double) (n - k)) / ((double) (k + 1)));

}

for (k = n; k >= e; k--)

coeff[k] = coeff[n - k];

return (coeff);

}

/* This is a subfunction of do_bezier() for BEZIER style computations.

* It is passed the stepration (STEP/MAXSTEPS) and the addresses of

* the double values holding the next x and y coordinates.

* (MGR 1992)

static void

eval_bezier(

struct curve_points *cp,

int first_point, /* where to start in plot->points (to find x-range) */

int num_points, /* to determine end in plot->points */

double sr, /* position inside curve, range [0:1] */

coordval *px, /* OUTPUT: x and y */

coordval *py,

double *c) /* Bezier coefficient array */

{

unsigned int n = num_points - 1;

struct coordinate GPHUGE *this_points;

this_points = (cp->points) + first_point;

if (sr == 0.0) {

*px = this_points[0].x;

*py = this_points[0].y;

} else if (sr == 1.0) {

*px = this_points[n].x;

*py = this_points[n].y;

} else {

/* HBB 990205: do calculation in 'logarithmic space',

* to avoid over/underflow errors, which would exactly cancel

* out each other, anyway, in an exact calculation

unsigned int i;

double lx = 0.0, ly = 0.0;

double log_dsr_to_the_n = n * log(1 - sr);

double log_sr_over_dsr = log(sr) - log(1 - sr);

for (i = 0; i <= n; i++) {

double u = exp(c[i] + log_dsr_to_the_n + i * log_sr_over_dsr);

lx += this_points[i].x * u;

ly += this_points[i].y * u;

}

*px = lx;

*py = ly;

}

* generate a new set of coordinates representing the bezier curve and

* set it to the plot

static void

do_bezier(

struct curve_points *cp,

double *bc, /* Bezier coefficient array */

int first_point, /* where to start in plot->points */

int num_points, /* to determine end in plot->points */

struct coordinate *dest) /* where to put the interpolated data */

{

int i;

coordval x, y;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

x_axis = cp->x_axis;

y_axis = cp->y_axis;

ixmin = sxmin = AXIS_LOG_VALUE(x_axis, X_AXIS.min);

ixmax = sxmax = AXIS_LOG_VALUE(x_axis, X_AXIS.max);

iymin = symin = AXIS_LOG_VALUE(y_axis, Y_AXIS.min);

iymax = symax = AXIS_LOG_VALUE(y_axis, Y_AXIS.max);

for (i = 0; i < samples_1; i++) {

eval_bezier(cp, first_point, num_points,

(double) i / (double) (samples_1 - 1),

&x, &y, bc);

/* now we have to store the points and adjust the ranges */

dest[i].type = INRANGE;

STORE_AND_FIXUP_RANGE(dest[i].x, x, dest[i].type, ixmin, ixmax, X_AXIS.autoscale, NOOP, continue);

STORE_AND_FIXUP_RANGE(dest[i].y, y, dest[i].type, iymin, iymax, Y_AXIS.autoscale, NOOP, NOOP);

dest[i].xlow = dest[i].xhigh = dest[i].x;

dest[i].ylow = dest[i].yhigh = dest[i].y;

dest[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, X_AXIS.max, ixmax, x_axis);

UPDATE_RANGE(ixmin < sxmin, X_AXIS.min, ixmin, x_axis);

UPDATE_RANGE(iymax > symax, Y_AXIS.max, iymax, y_axis);

UPDATE_RANGE(iymin < symin, Y_AXIS.min, iymin, y_axis);

}

* call contouring routines -- main entry

* it should be like this, but it doesn't run. If you find out why,

* contact me: mgr@asgard.bo.open.de or Lars Hanke 2:243/4802.22@fidonet

* Well, all this had originally been inside contour.c, so maybe links

* to functions and of contour.c are broken.

* ***deleted***

* end of unused entry point to Gershon's code

* Solve five diagonal linear system equation. The five diagonal matrix is

* defined via matrix M, right side is r, and solution X i.e. M * X = R.

* Size of system given in n. Return TRUE if solution exist.

* G. Engeln-Muellges/ F.Reutter:

* "Formelsammlung zur Numerischen Mathematik mit Standard-FORTRAN-Programmen"

* ISBN 3-411-01677-9

* / m02 m03 m04 0 0 0 0 . . . \ / x0 \ / r0 \

* I m11 m12 m13 m14 0 0 0 . . . I I x1 I I r1 I

* I m20 m21 m22 m23 m24 0 0 . . . I * I x2 I = I r2 I

* I 0 m30 m31 m32 m33 m34 0 . . . I I x3 I I r3 I

* . . . . . . . . . . . .

* \ m(n-3)0 m(n-2)1 m(n-1)2 / \x(n-1)/ \r(n-1)/

static int

solve_five_diag(five_diag m[], double r[], double x[], int n)

{

int i;

five_diag *hv;

hv = gp_alloc((n + 1) * sizeof(five_diag), "five_diag help vars");

hv[0][0] = m[0][2];

if (hv[0][0] == 0) {

free(hv);

return FALSE;

}

hv[0][1] = m[0][3] / hv[0][0];

hv[0][2] = m[0][4] / hv[0][0];

hv[1][3] = m[1][1];

hv[1][0] = m[1][2] - hv[1][3] * hv[0][1];

if (hv[1][0] == 0) {

free(hv);

return FALSE;

}

hv[1][1] = (m[1][3] - hv[1][3] * hv[0][2]) / hv[1][0];

hv[1][2] = m[1][4] / hv[1][0];

for (i = 2; i < n; i++) {

hv[i][3] = m[i][1] - m[i][0] * hv[i - 2][1];

hv[i][0] = m[i][2] - m[i][0] * hv[i - 2][2] - hv[i][3] * hv[i - 1][1];

if (hv[i][0] == 0) {

free(hv);

return FALSE;

}

hv[i][1] = (m[i][3] - hv[i][3] * hv[i - 1][2]) / hv[i][0];

hv[i][2] = m[i][4] / hv[i][0];

}

hv[0][4] = 0;

hv[1][4] = r[0] / hv[0][0];

for (i = 1; i < n; i++) {

hv[i + 1][4] = (r[i] - m[i][0] * hv[i - 1][4] - hv[i][3] * hv[i][4]) / hv[i][0];

}

x[n - 1] = hv[n][4];

x[n - 2] = hv[n - 1][4] - hv[n - 2][1] * x[n - 1];

for (i = n - 3; i >= 0; i--)

x[i] = hv[i + 1][4] - hv[i][1] * x[i + 1] - hv[i][2] * x[i + 2];

free(hv);

return TRUE;

}

* Calculation of approximation cubic splines

* Input: x[i], y[i], weights z[i]

* Returns matrix of spline coefficients

static spline_coeff *

cp_approx_spline(

struct curve_points *plot,

int first_point, /* where to start in plot->points */

int num_points) /* to determine end in plot->points */

{

spline_coeff *sc;

five_diag *m;

double *r, *x, *h, *xp, *yp;

struct coordinate GPHUGE *this_points;

int i;

x_axis = plot->x_axis;

y_axis = plot->y_axis;

sc = gp_alloc((num_points) * sizeof(spline_coeff),

"spline matrix");

if (num_points < 4)

int_error(plot->token, "Can't calculate approximation splines, need at least 4 points");

this_points = (plot->points) + first_point;

for (i = 0; i < num_points; i++)

if (this_points[i].z <= 0)

int_error(plot->token, "Can't calculate approximation splines, all weights have to be > 0");

m = gp_alloc((num_points - 2) * sizeof(five_diag), "spline help matrix");

r = gp_alloc((num_points - 2) * sizeof(double), "spline right side");

x = gp_alloc((num_points - 2) * sizeof(double), "spline solution vector");

h = gp_alloc((num_points - 1) * sizeof(double), "spline help vector");

xp = gp_alloc((num_points) * sizeof(double), "x pos");

yp = gp_alloc((num_points) * sizeof(double), "y pos");

/* KB 981107: With logarithmic axis first convert back to linear scale */

xp[0] = AXIS_DE_LOG_VALUE(x_axis, this_points[0].x);

yp[0] = AXIS_DE_LOG_VALUE(y_axis, this_points[0].y);

for (i = 1; i < num_points; i++) {

xp[i] = AXIS_DE_LOG_VALUE(x_axis, this_points[i].x);

yp[i] = AXIS_DE_LOG_VALUE(y_axis, this_points[i].y);

h[i - 1] = xp[i] - xp[i - 1];

}

/* set up the matrix and the vector */

for (i = 0; i <= num_points - 3; i++) {

r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1]

- (yp[i + 1] - yp[i]) / h[i]);

if (i < 2)

m[i][0] = 0;

else

m[i][0] = 6 / this_points[i].z / h[i - 1] / h[i];

if (i < 1)

m[i][1] = 0;

else

m[i][1] = h[i] - 6 / this_points[i].z / h[i] * (1 / h[i - 1] + 1 / h[i])

- 6 / this_points[i + 1].z / h[i] * (1 / h[i] + 1 / h[i + 1]);

m[i][2] = 2 * (h[i] + h[i + 1])

+ 6 / this_points[i].z / h[i] / h[i]

+ 6 / this_points[i + 1].z * (1 / h[i] + 1 / h[i + 1]) * (1 / h[i] + 1 / h[i + 1])

+ 6 / this_points[i + 2].z / h[i + 1] / h[i + 1];

if (i > num_points - 4)

m[i][3] = 0;

else

m[i][3] = h[i + 1] - 6 / this_points[i + 1].z / h[i + 1] * (1 / h[i] + 1 / h[i + 1])

- 6 / this_points[i + 2].z / h[i + 1] * (1 / h[i + 1] + 1 / h[i + 2]);

if (i > num_points - 5)

m[i][4] = 0;

else

m[i][4] = 6 / this_points[i + 2].z / h[i + 1] / h[i + 2];

}

/* solve the matrix */

if (!solve_five_diag(m, r, x, num_points - 2)) {

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

int_error(plot->token, "Can't calculate approximation splines");

}

sc[0][2] = 0;

for (i = 1; i <= num_points - 2; i++)

sc[i][2] = x[i - 1];

sc[num_points - 1][2] = 0;

sc[0][0] = yp[0] + 2 / this_points[0].z / h[0] * (sc[0][2] - sc[1][2]);

for (i = 1; i <= num_points - 2; i++)

sc[i][0] = yp[i] - 2 / this_points[i].z *

(sc[i - 1][2] / h[i - 1]

- sc[i][2] * (1 / h[i - 1] + 1 / h[i])

+ sc[i + 1][2] / h[i]);

sc[num_points - 1][0] = yp[num_points - 1]

- 2 / this_points[num_points - 1].z / h[num_points - 2]

* (sc[num_points - 2][2] - sc[num_points - 1][2]);

for (i = 0; i <= num_points - 2; i++) {

sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i]

- h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]);

sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i];

}

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

return (sc);

}

* Calculation of cubic splines

* This can be treated as a special case of approximation cubic splines, with

* all weights -> infinity.

* Returns matrix of spline coefficients

static spline_coeff *

cp_tridiag(struct curve_points *plot, int first_point, int num_points)

{

spline_coeff *sc;

tri_diag *m;

double *r, *x, *h, *xp, *yp;

struct coordinate GPHUGE *this_points;

int i;

x_axis = plot->x_axis;

y_axis = plot->y_axis;

if (num_points < 3)

int_error(plot->token, "Can't calculate splines, need at least 3 points");

this_points = (plot->points) + first_point;

sc = gp_alloc((num_points) * sizeof(spline_coeff), "spline matrix");

m = gp_alloc((num_points - 2) * sizeof(tri_diag), "spline help matrix");

r = gp_alloc((num_points - 2) * sizeof(double), "spline right side");

x = gp_alloc((num_points - 2) * sizeof(double), "spline solution vector");

h = gp_alloc((num_points - 1) * sizeof(double), "spline help vector");

xp = gp_alloc((num_points) * sizeof(double), "x pos");

yp = gp_alloc((num_points) * sizeof(double), "y pos");

/* KB 981107: With logarithmic axis first convert back to linear scale */

xp[0] = AXIS_DE_LOG_VALUE(x_axis,this_points[0].x);

yp[0] = AXIS_DE_LOG_VALUE(y_axis,this_points[0].y);

for (i = 1; i < num_points; i++) {

xp[i] = AXIS_DE_LOG_VALUE(x_axis,this_points[i].x);

yp[i] = AXIS_DE_LOG_VALUE(y_axis,this_points[i].y);

h[i - 1] = xp[i] - xp[i - 1];

}

/* set up the matrix and the vector */

for (i = 0; i <= num_points - 3; i++) {

r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1]

- (yp[i + 1] - yp[i]) / h[i]);

if (i < 1)

m[i][0] = 0;

else

m[i][0] = h[i];

m[i][1] = 2 * (h[i] + h[i + 1]);

if (i > num_points - 4)

m[i][2] = 0;

else

m[i][2] = h[i + 1];

}

/* solve the matrix */

if (!solve_tri_diag(m, r, x, num_points - 2)) {

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

int_error(plot->token, "Can't calculate cubic splines");

}

sc[0][2] = 0;

for (i = 1; i <= num_points - 2; i++)

sc[i][2] = x[i - 1];

sc[num_points - 1][2] = 0;

for (i = 0; i <= num_points - 1; i++)

sc[i][0] = yp[i];

for (i = 0; i <= num_points - 2; i++) {

sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i]

- h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]);

sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i];

}

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

return (sc);

}

static void

do_cubic(

struct curve_points *plot, /* still containes old plot->points */

spline_coeff *sc, /* generated by cp_tridiag */

int first_point, /* where to start in plot->points */

int num_points, /* to determine end in plot->points */

struct coordinate *dest) /* where to put the interpolated data */

{

double xdiff, temp, x, y;

double xstart, xend; /* Endpoints of the sampled x range */

int i, l;

struct coordinate GPHUGE *this_points;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

x_axis = plot->x_axis;

y_axis = plot->y_axis;

ixmin = sxmin = AXIS_LOG_VALUE(x_axis, X_AXIS.min);

ixmax = sxmax = AXIS_LOG_VALUE(x_axis, X_AXIS.max);

iymin = symin = AXIS_LOG_VALUE(y_axis, Y_AXIS.min);

iymax = symax = AXIS_LOG_VALUE(y_axis, Y_AXIS.max);

this_points = (plot->points) + first_point;

l = 0;

/* HBB 20010727: Sample only across the actual x range, not the

* full range of input data */

#if SAMPLE_CSPLINES_TO_FULL_RANGE

xstart = this_points[0].x;

xend = this_points[num_points - 1].x;

#else

xstart = GPMAX(this_points[0].x, sxmin);

xend = GPMIN(this_points[num_points - 1].x, sxmax);

if (xstart >= xend)

int_error(plot->token,

"Cannot smooth: no data within fixed xrange!");

#endif

xdiff = (xend - xstart) / (samples_1 - 1);

for (i = 0; i < samples_1; i++) {

x = xstart + i * xdiff;

/* Move forward to the spline interval this point is in */

while ((x >= this_points[l + 1].x) && (l < num_points - 2))

l++;

/* KB 981107: With logarithmic x axis the values were

* converted back to linear scale before calculating the

* coefficients. Use exponential for log x values. */

temp = AXIS_DE_LOG_VALUE(x_axis, x)

- AXIS_DE_LOG_VALUE(x_axis, this_points[l].x);

/* Evaluate cubic spline polynomial */

y = ((sc[l][3] * temp + sc[l][2]) * temp + sc[l][1]) * temp + sc[l][0];

/* With logarithmic y axis, we need to convert from linear to

* log scale now. */

if (Y_AXIS.log) {

if (y > 0.)

y = AXIS_DO_LOG(y_axis, y);

else

y = symin - (symax - symin);

}

dest[i].type = INRANGE;

STORE_AND_FIXUP_RANGE(dest[i].x, x, dest[i].type, ixmin, ixmax, X_AXIS.autoscale, NOOP, continue);

STORE_AND_FIXUP_RANGE(dest[i].y, y, dest[i].type, iymin, iymax, Y_AXIS.autoscale, NOOP, NOOP);

dest[i].xlow = dest[i].xhigh = dest[i].x;

dest[i].ylow = dest[i].yhigh = dest[i].y;

dest[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, X_AXIS.max, ixmax, x_axis);

UPDATE_RANGE(ixmin < sxmin, X_AXIS.min, ixmin, x_axis);

UPDATE_RANGE(iymax > symax, Y_AXIS.max, iymax, y_axis);

UPDATE_RANGE(iymin < symin, Y_AXIS.min, iymin, y_axis);

}

* do_freq() is like the other smoothers only in that it

* needs to adjust the plot ranges. We don't have to copy

* approximated curves or anything like that.

static void

do_freq(

struct curve_points *plot, /* still contains old plot->points */

int first_point, /* where to start in plot->points */

int num_points) /* to determine end in plot->points */

{

double x, y;

int i;

int x_axis = plot->x_axis;

int y_axis = plot->y_axis;

struct coordinate GPHUGE *this;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

ixmin = sxmin = AXIS_LOG_VALUE(x_axis, X_AXIS.min);

ixmax = sxmax = AXIS_LOG_VALUE(x_axis, X_AXIS.max);

iymin = symin = AXIS_LOG_VALUE(y_axis, Y_AXIS.min);

iymax = symax = AXIS_LOG_VALUE(y_axis, Y_AXIS.max);

this = (plot->points) + first_point;

for (i=0; i<num_points; i++) {

x = this[i].x;

y = this[i].y;

this[i].type = INRANGE;

STORE_AND_FIXUP_RANGE(this[i].x, x, this[i].type, ixmin, ixmax, X_AXIS.autoscale, NOOP, continue);

STORE_AND_FIXUP_RANGE(this[i].y, y, this[i].type, iymin, iymax, Y_AXIS.autoscale, NOOP, NOOP);

this[i].xlow = this[i].xhigh = this[i].x;

this[i].ylow = this[i].yhigh = this[i].y;

this[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, X_AXIS.max, ixmax, x_axis);

UPDATE_RANGE(ixmin < sxmin, X_AXIS.min, ixmin, x_axis);

UPDATE_RANGE(iymax > symax, Y_AXIS.max, iymax, y_axis);

UPDATE_RANGE(iymin < symin, Y_AXIS.min, iymin, y_axis);

}

* Frequency plots have don't need new points allocated; we just need

* to adjust the plot ranges. Wedging this into gen_interp() would

* make that code even harder to read.

void

gen_interp_frequency(struct curve_points *plot)

{

int i, j, curves;

int first_point, num_points;

double y;

View remainder of file in raw view

gnuplot-old/src/interpol.c at gnuplot-4-4-alpha · gnuplot/gnuplot-old · GitHub

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