120 lines
3.7 KiB
C++
120 lines
3.7 KiB
C++
|
/**********************************************************************
|
||
|
|
|
||
|
|
FILENAME: uiuc_1Dinterpolation.cpp
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
DESCRIPTION: reads in the yData and xData arrays and the value of x
|
||
|
|
to be interpolated on; performs 1D interpolation,
|
||
|
|
i.e. y=f(x)
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
STATUS: alpha version
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
REFERENCES: syntax based on interp function in c172_aero.c
|
||
|
|
mathematics based on linear interpolation functions
|
||
|
|
found in
|
||
|
|
Kreyszig, Erwin. Advanced Engineering Mathematics,
|
||
|
|
7th ed. NY: John Wiley & Sons, 1993.
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
HISTORY: 02/03/2000 initial release
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
AUTHOR(S): Jeff Scott <jscott@mail.com>
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
VARIABLES:
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
INPUTS: -array of x data
|
||
|
|
-array of y data
|
||
|
|
-max number of data pairs
|
||
|
|
-x value to be interpolated on
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
OUTPUTS: -y as function of x
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
CALLED BY: uiuc_coefficients.cpp
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
CALLS TO: none
|
||
|
|
|
||
|
|
----------------------------------------------------------------------
|
||
|
|
|
||
|
|
COPYRIGHT: (C) 2000 by Michael Selig
|
||
|
|
|
||
|
|
This program is free software; you can redistribute it and/or
|
||
|
|
modify it under the terms of the GNU General Public License
|
||
|
|
as published by the Free Software Foundation.
|
||
|
|
|
||
|
|
This program is distributed in the hope that it will be useful,
|
||
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||
|
|
GNU General Public License for more details.
|
||
|
|
|
||
|
|
You should have received a copy of the GNU General Public License
|
||
|
|
along with this program; if not, write to the Free Software
|
||
|
|
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
|
||
|
|
USA or view http://www.gnu.org/copyleft/gpl.html.
|
||
|
|
|
||
|
|
**********************************************************************/
|
||
|
|
|
||
|
|
#include "uiuc_1Dinterpolation.h"
|
||
|
|
|
||
|
|
|
||
|
|
double uiuc_1Dinterpolation( double xData[100], double yData[100], int xmax, double x )
|
||
|
|
{
|
||
|
|
double x1=0, x2=0, y1=0, y2=0, L1=0, L2=0;
|
||
|
|
int i=2;
|
||
|
|
float yfx=0;
|
||
|
|
|
||
|
|
//check bounds on x to see if data range encloses it
|
||
|
|
// NOTE: [1] is first element of all arrays, [0] not used
|
||
|
|
if (x <= xData[1]) //if x less than lowest x
|
||
|
|
{
|
||
|
|
yfx = yData[1]; //let y equal lowest y
|
||
|
|
}
|
||
|
|
else if (x >= xData[xmax]) //if x greater than greatest x
|
||
|
|
{
|
||
|
|
yfx = yData[xmax]; //let y equal greatest y
|
||
|
|
}
|
||
|
|
else //x between xmax and x min
|
||
|
|
{
|
||
|
|
/*loop increases i until x is less than a known x,
|
||
|
|
e.g. Alpha from LaRCsim less than Alpha given in
|
||
|
|
tabulated data; once this value is found, i becomes
|
||
|
|
the upper bound and i-1 the lower bound*/
|
||
|
|
while (xData[i] <= x) //bracket upper bound
|
||
|
|
{
|
||
|
|
i++;
|
||
|
|
}
|
||
|
|
x2 = xData[i]; //set upper bounds
|
||
|
|
y2 = yData[i];
|
||
|
|
x1 = xData[i-1]; //set lower bounds
|
||
|
|
y1 = yData[i-1];
|
||
|
|
|
||
|
|
//calculate Langrange polynomial coefficients
|
||
|
|
//(see Kreyszig, pg. 937)
|
||
|
|
L1 = (x - x2) / (x1 - x2);
|
||
|
|
L2 = (x - x1) / (x2 - x1);
|
||
|
|
|
||
|
|
//solve for y=f(x)
|
||
|
|
yfx = L1 * y1 + L2 * y2;
|
||
|
|
}
|
||
|
|
return yfx;
|
||
|
|
}
|
||
|
|
|
||
|
|
// end uiuc_1Dinterpolation.cpp
|