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#ident "@(#) $Id: trap_int_ang_c1_sx0.c 21649 2011-12-05 20:50:45Z carrie $ SwRI"
#include
#include "user_defs.h"
#include "libIDFSMath.h"
/*******************************************************************************
* *
* IDFSMATH_TRAPEZOIDAL_INT_ANGLE_C1_SX0 SUBROUTINE *
* *
* DESCRIPTION *
* This routine is called to calculate a trapezoidal integration method on *
* data which exists in a band, which means that X[n] is the starting location*
* of the band, X[n+1] is the ending location of the band, and Y[n] is the *
* ampltude of the band. Assume that the Y[n] values are measured at the *
* centers of the bands. There are terms number of bands, so there are terms *
* values of Y and terms+1 values of X. When converted to trapezoids, there *
* are terms-1 trapezoids. Points are measured as X, Y pairs. This routine *
* is called when the power of the cosine term is 1 and the power of the *
* sine term is 0. *
* *
* INPUT VARIABLES *
* SDDAS_FLOAT *X pointer to the band values (x component) *
* SDDAS_FLOAT *Y pointer to the data values (y component) *
* SDDAS_DOUBLE *X_rad pointer to band values expressed in radians *
* SDDAS_DOUBLE *X_centers pointer to center band values expressed in *
* radians *
* SDDAS_DOUBLE *Sin_Xc pointer to the result of the sin function *
* for the center band values *
* SDDAS_DOUBLE *Cos_Xc pointer to the result of the cos function *
* for the center band values *
* SDDAS_DOUBLE *width pointer to the widths between bin centers *
* SDDAS_DOUBLE *M ptr to the slope of each Y between centers *
* SDDAS_DOUBLE *B ptr to intercept of each Y between centers *
* SDDAS_LONG skip number of elements to add to get to next *
* data element *
* SDDAS_LONG terms number of bands or terms to integrate *
* SDDAS_FLOAT start starting value to integrate over in X *
* SDDAS_FLOAT stop ending value to integrate over in X *
* SDDAS_CHAR which_dimen flag indicating which dimension is being *
* integrated over since multiple dimensions *
* make use of this code *
* SDDAS_CHAR norm flag indicating if the result is to be *
* normalized *
* *
* USAGE *
* x = IDFSMath_trapezoidal_int_angle_c1_sx0 (&X, &Y, &X_rad, &X_centers, *
* &Sin_Xc, &Cos_Xc, &width, &M, &B, skip, *
* terms, start, stop, which_dimen, norm) *
* *
* NECESSARY SUBPROGRAMS *
* cos() returns double-precision cosine function of *
* the argument *
* sin() returns double-precision sine function of *
* the argument *
* *
* EXTERNAL VARIABLES *
* None *
* *
* INTERNAL VARIABLES *
* reg SDDAS_LONG i, next_i looping / indexing variables *
* SDDAS_DOUBLE start_rad start integration value expressed in radians *
* SDDAS_DOUBLE stop_rad end integration value expressed in radians *
* SDDAS_DOUBLE c_factor constant factor computed once used repeatedly*
* SDDAS_DOUBLE width_low width between bin centers used when start *
* of integration is at or less than 1st center *
* SDDAS_DOUBLE M_low slope of Y between centers used when start *
* of integration is at or less than 1st center *
* SDDAS_DOUBLE B_low intercept of Y between centers used if start *
* of integration is at or less than 1st center *
* SDDAS_DOUBLE width_high width between bin centers used when end *
* of integration is greater than last center *
* SDDAS_DOUBLE M_high slope of Y between centers used when end *
* of integration is greater than last center *
* SDDAS_DOUBLE B_high intercept of Y between centers used if end *
* of integration is greater than last center *
* SDDAS_DOUBLE X1, X2 values of X used to get rid of indexing for *
* speed up issues *
* SDDAS_DOUBLE sum summation value of integration *
* SDDAS_DOUBLE sumx normalization factor *
* SDDAS_DOUBLE x1, x2 first and last band for trap. area *
* SDDAS_DOUBLE sine_x1, the result of the sine function for the 1st *
* sine_x2 and last band value used for trap. area *
* SDDAS_DOUBLE cosine_x1, the result of the cosine function for the 1st*
* cosine_x2 and last band value used for trap. area *
* SDDAS_DOUBLE upper1, upper2, used to accumulate trapezoid area *
* lower1, lower2 *
* SDDAS_FLOAT y1, y2 first and last data value *
* SDDAS_LONG terms_minus_one number of terms to integrate reduced by one *
* SDDAS_CHAR wrap flag indicating data is cyclic and wraps *
* around boundary point *
* *
* SUBSYSTEM *
* Display Level *
* *
******************************************************************************/
SDDAS_DOUBLE IDFSMath_trapezoidal_int_angle_c1_sx0 (SDDAS_FLOAT *X, SDDAS_FLOAT *Y,
SDDAS_DOUBLE *X_rad, SDDAS_DOUBLE *X_centers, SDDAS_DOUBLE *Sin_Xc,
SDDAS_DOUBLE *Cos_Xc, SDDAS_DOUBLE *width, SDDAS_DOUBLE *M, SDDAS_DOUBLE *B,
SDDAS_LONG skip, SDDAS_LONG terms, SDDAS_FLOAT start, SDDAS_FLOAT stop,
SDDAS_CHAR which_dimen, SDDAS_CHAR norm)
{
register SDDAS_LONG i, next_i;
SDDAS_DOUBLE width_low, M_low, B_low, width_high, M_high, B_high, X1, X2;
SDDAS_DOUBLE sum, sumx, x1, x2, sine_x1, sine_x2, cosine_x1, cosine_x2;
SDDAS_DOUBLE upper1, upper2, lower1, lower2, start_rad, stop_rad, c_factor;
SDDAS_FLOAT y1, y2;
SDDAS_LONG terms_minus_one;
SDDAS_CHAR wrap;
terms_minus_one = terms - 1;
wrap = (which_dimen == PHI_DIMEN) ? 1 : 0;
if (wrap)
{
X1 = X_centers[0];
X2 = X_centers[terms_minus_one];
y1 = *Y; /* Y value of first band */
y2 = *(Y + terms_minus_one * skip); /* Y value of last band */
c_factor = 2.0 * M_PI;
width_low = X1 - (X2 - c_factor);
width_high = (X1 + c_factor) - X2;
if (y1 >= VALID_MIN && y2 >= VALID_MIN) /* if data good */
{
M_low = (y1 - y2) / width_low;
B_low = (X1 * y2 - (X2 - c_factor) * y1) / width_low;
M_high = (y1 - y2) / width_high;
B_high = ((X1 + c_factor) * y2 - X2 * y1) / width_high;
}
else
{
M_low = OUTSIDE_MIN;
B_low = OUTSIDE_MIN;
M_high = OUTSIDE_MIN;
B_high = OUTSIDE_MIN;
}
}
sumx = 0.0; /* initialize X covered area */
sum = 0.0; /* initialize integration amp*/
start_rad = start * M_PI / 180.0;
stop_rad = stop * M_PI / 180.0;
/*****************************************************************************/
/* Start is at or below the first center. */
/*****************************************************************************/
if (start_rad < X_centers[0])
{
/*************************************************************************/
/* Integrate from the first data or start if bigger. */
/*************************************************************************/
if (start <= X[0])
x1 = X_rad[0];
else
x1 = start_rad;
/*************************************************************************/
/* Integrate to the first data center or the stop if it is less. */
/*************************************************************************/
if (stop_rad >= X_centers[0])
x2 = X_centers[0];
else
x2 = stop_rad;
sine_x1 = sin (x1);
sine_x2 = sin (x2);
cosine_x1 = cos (x1);
cosine_x2 = cos (x2);
/*************************************************************************/
/* Data wrapped accumulate trapezoidal area. */
/*************************************************************************/
if (wrap)
{
if (M_low >= VALID_MIN)
{
upper1 = M_low * cosine_x2;
upper2 = sine_x2 * (M_low * x2 + B_low);
lower1 = M_low * cosine_x1;
lower2 = sine_x1 * (M_low * x1 + B_low);
sum += upper1 - lower1; /* accumulate trapazoid area */
sum += upper2 - lower2; /* accumulate trapazoid area */
sumx += x2 - x1; /* accumulate the width */
}
}
else if (Y[0] >= VALID_MIN)
{
sum += Y[0] * (x2 - x1); /* accumulate the rect area */
sumx += x2 - x1; /* accumulate the width */
}
}
/**************************************************************************/
/* Search through all of the data bands - accumulate them. */
/**************************************************************************/
for (i = 0, next_i = 1; i < terms_minus_one; ++i, ++next_i)
{
if (M[i] < VALID_MIN)
continue;
X1 = X_centers[i];
X2 = X_centers[next_i];
/***********************************************************************/
/* Band is between start and stop, so accumulate this area. */
/***********************************************************************/
if (start_rad < X1 && X2 < stop_rad)
{
x1 = X1;
x2 = X2;
sine_x1 = Sin_Xc[i];
sine_x2 = Sin_Xc[next_i];
cosine_x1 = Cos_Xc[i];
cosine_x2 = Cos_Xc[next_i];
upper1 = M[i] * cosine_x2;
lower1 = M[i] * cosine_x1;
upper2 = sine_x2 * (M[i] * x2 + B[i]);
lower2 = sine_x1 * (M[i] * x1 + B[i]);
sum += upper1 - lower1; /* accumulate trapazoid area */
sum += upper2 - lower2; /* accumulate trapazoid area */
sumx += x2 - x1; /* accumulate the width */
}
/***********************************************************************/
/* The start is within the trapazoid of the data. */
/***********************************************************************/
else if (X1 <= start_rad && start_rad < X2)
{
/********************************************************************/
/* The stop is within the trapazoid of the data. */
/********************************************************************/
if (stop_rad <= X2)
{
x1 = start_rad;
x2 = stop_rad;
}
/********************************************************************/
/* The start is within the trapazoid, but stop is not. */
/********************************************************************/
else
{
x1 = start_rad;
x2 = X2;
}
sine_x1 = sin (x1);
sine_x2 = sin (x2);
cosine_x1 = cos (x1);
cosine_x2 = cos (x2);
sumx += x2 - x1; /* accumulate the width */
upper1 = M[i] * cosine_x2;
upper2 = sine_x2 * (M[i] * x2 + B[i]);
lower1 = M[i] * cosine_x1;
lower2 = sine_x1 * (M[i] * x1 + B[i]);
sum += upper1 - lower1; /* accumulate trapazoid area */
sum += upper2 - lower2; /* accumulate trapazoid area */
}
/***********************************************************************/
/* The stop is within the trapazoid of the data. */
/***********************************************************************/
else if (X1 < stop_rad && stop_rad <= X2)
{
/********************************************************************/
/* The start is within the trapazoid of the data. */
/********************************************************************/
if (start_rad >= X1)
{
x1 = start_rad;
x2 = stop_rad;
}
/********************************************************************/
/* The start is within the trapazoid, but stop is not. */
/********************************************************************/
else
{
x1 = X1;
x2 = stop_rad;
}
sine_x1 = sin (x1);
sine_x2 = sin (x2);
cosine_x1 = cos (x1);
cosine_x2 = cos (x2);
sumx += x2 - x1; /* accumulate the width */
upper1 = M[i] * cosine_x2;
upper2 = sine_x2 * (M[i] * x2 + B[i]);
lower1 = M[i] * cosine_x1;
lower2 = sine_x1 * (M[i] * x1 + B[i]);
sum += upper1 - lower1; /* accumulate trapazoid area */
sum += upper2 - lower2; /* accumulate trapazoid area */
}
}
/**************************************************************************/
/* Stop is above last center. */
/**************************************************************************/
if (stop_rad > X_centers[terms_minus_one])
{
/*************************************************************************/
/* Integrate from the last data or stop if its bigger. */
/*************************************************************************/
if (stop >= X[terms])
x2 = X_rad[terms];
else
x2 = stop_rad;
/*************************************************************************/
/* Integrate to the first data center or the stop if it is less. */
/*************************************************************************/
if (start_rad <= X_centers[terms_minus_one])
x1 = X_centers[terms_minus_one];
else
x1 = start_rad;
y2 = *(Y + terms_minus_one * skip); /* Y value of last band */
sine_x1 = sin (x1);
sine_x2 = sin (x2);
cosine_x1 = cos (x1);
cosine_x2 = cos (x2);
/*************************************************************************/
/* Data wrapped accumulate trapazoidal area. */
/*************************************************************************/
if (wrap)
{
if (M_high >= VALID_MIN)
{
upper1 = M_high * cosine_x2;
upper2 = sine_x2 * (M_high * x2 + B_high);
lower1 = M_high * cosine_x1;
lower2 = sine_x1 * (M_high * x1 + B_high);
sum += upper1 - lower1; /* accumulate trapazoid area */
sum += upper2 - lower2; /* accumulate trapazoid area */
sumx += x2 - x1; /* accumulate the width */
}
}
else if (y2 >= VALID_MIN)
{
sum += y2 * (x2 - x1); /* accumulate the rect area */
sumx += x2 - x1; /* accumulate the width */
}
}
/**************************************************************************/
/* Normalize the data to the start and stop distance. Note that this is */
/* 1.0 when start and stop lie within the data range with no gap. */
/**************************************************************************/
if (norm && sumx > 0.0)
{
sum /= sumx;
sum *= (stop_rad - start_rad);
}
/************************************************************************/
/* If no data was found (all values set to OUTSIDE_MIN), return */
/* OUTSIDE_MIN so that possible later collapsing will also ignore this */
/* missing data. The old way would return a 0.0 which implied that */
/* data was there so the NORM flag had no bearing because the code */
/* for later integrations thought nothing was missing. */
/************************************************************************/
if (sumx > 0.0)
return (sum);
else
return (OUTSIDE_MIN);
}