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SwRI can revise these Terms at any time * without notice by updating this posting. * * Trademarks * * The SwRI logo is a trademark of SwRI in the United States and other countries. * */ #ident "@(#) $Id: str_int_pnt_cont.C 18484 2007-07-12 18:55:07Z carrie $ SwRI" #include #include "user_defs.h" #include "libIDFSMath.h" /***************************************************************************** * * * IDFSMATH_STR_INT_POINT_CONT SUBROUTINE * * * * DESCRIPTION * * This routine is called to calculate a trapezoidal integral (point) * * using contiguous band values. Note that in this algorithm rather than * * doing comparisions of the type A > (X[n] + X[n+1])/2.0 in comparing the * * start or stop integration limits with the X values (we are doing * * comparision only with the center value) we will use the form 2*A > * * (X[n] + X[n+1]). Also, note that under normal situations start is less * * than stop. If this is not the case then we assume the special case of * * being asked to integrate over the entire X range - this is useful if you * * are not sure of the X range. The IDFSMath_rmie() function converts the * * values to radians for angular dimensions. * * * * INPUT VARIABLES * * SDDAS_FLOAT *X pointer to the band values * * SDDAS_FLOAT *Y pointer to the data values * * SDDAS_LONG skip number of elements to add to get to next * * data element * * SDDAS_LONG terms number of bands * * SDDAS_FLOAT start starting value to integrate over * * SDDAS_FLOAT stop ending value to integrate over * * 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 * * SDDAS_INT power_sx the power of the extra "x" term or the power * * of the sin term * * SDDAS_INT power_c the power of the cos term * * * * USAGE * * x = IDFSMath_str_int_point_cont (X, Y, skip, terms, start, stop, * * which_dimen, norm, power_sx, power_c) * * * * NECESSARY SUBPROGRAMS * * IDFSMath_rmie () returns the weighted values based on the * * extra values that are in the integral * * * * EXTERNAL VARIABLES * * None * * * * INTERNAL VARIABLES * * std::vector WX weighted values for band values * * reg SDDAS_DOUBLE *wf1, *wf2 pointers to weighted band values * * reg SDDAS_FLOAT *f1, *f2 pointers to band values * * reg SDDAS_FLOAT *f3, *f4 pointers to data values * * reg SDDAS_FLOAT *f_end end of X array * * SDDAS_DOUBLE ret_val resultant value returned to calling module * * SDDAS_DOUBLE wstart weighted starting value for integration * * SDDAS_DOUBLE wstop weighted ending value for integration * * SDDAS_DOUBLE wa, wb weighted band values * * SDDAS_DOUBLE wc, wd weighted variables for trapezoid integration * * SDDAS_DOUBLE *w_end end of weighted X array * * SDDAS_DOUBLE wtop weighted upper band value * * SDDAS_DOUBLE wbot weighted lower band value * * SDDAS_DOUBLE sum summation value of integration * * SDDAS_FLOAT a, b center of first and second band * * SDDAS_FLOAT c, d variables used for trapezoidal integration * * SDDAS_FLOAT top upper band * * SDDAS_FLOAT bot lower band * * SDDAS_FLOAT sumx normalization factor * * SDDAS_LONG loop looping variable * * SDDAS_CHAR valid_data_found flag for data inclusion or missing data * * * * SUBSYSTEM * * Display Level * * * ****************************************************************************/ /*** TRAPAZOIDAL INTEGRAL, CONTIGUOUS X BANDS ***/ SDDAS_FLOAT IDFSMath_str_int_point_cont (SDDAS_FLOAT *X, SDDAS_FLOAT *Y, SDDAS_LONG skip, SDDAS_LONG terms, SDDAS_FLOAT start, SDDAS_FLOAT stop, SDDAS_CHAR which_dimen, SDDAS_CHAR norm, SDDAS_INT power_sx, SDDAS_INT power_c) { std::vector WX; register SDDAS_DOUBLE *wf1, *wf2; register SDDAS_FLOAT *f1, *f2, *f3, *f4, *f_end; SDDAS_DOUBLE ret_val = 0.0, wstart, wstop, wa, wb, wc, wd, *w_end; SDDAS_DOUBLE wtop, wbot, sum = 0.0; SDDAS_FLOAT a, b, c, d, top, bot, sumx = 0.0; SDDAS_LONG loop; SDDAS_CHAR valid_data_found; valid_data_found = 0; f_end = X + terms; /* end of X array */ /***********************************************************************/ /* Allocate space to hold weighted values returned by IDFSMath_rmie().*/ /* Need to account for the one extra bin that is needed. */ /* Get the weighted values based on the extra values that are in the */ /* integral, as indicated by power_sx and power_c arguments. */ /***********************************************************************/ WX.resize (terms + 1); for (loop = 0; loop <= terms; ++loop) WX[loop] = IDFSMath_rmie (*(X + loop), which_dimen, power_sx, power_c); w_end = &WX[terms]; wstart = IDFSMath_rmie (start, which_dimen, power_sx, power_c); wstop = IDFSMath_rmie (stop, which_dimen, power_sx, power_c); wtop = (*w_end + *(w_end - 1)); /* weighted upper band */ wbot = (WX[0] + WX[1]); /* weighted lower band */ top = (*f_end + *(f_end - 1)); /* upper band */ bot = (X[0] + X[1]); /* lower band */ /************************************************************************/ /* Not that we have the weighted matrices and weighted positions, we */ /* can perform a linear trapezoidal integration so multiply BOTH sets */ /* of values by 2 to get rid of having to take the average at every */ /* iteration. */ /************************************************************************/ start *= 2.0; /* twice the start value */ stop *= 2.0; /* twice the end value */ wstart *= 2.0; /* twice the weighted start value */ wstop *= 2.0; /* twice the weighted end value */ /* Increasing array of values? Look at first and last instead of first */ /* 2 values. Indexing by terms is okay since the array of band values */ /* are used and there is always one more element at the end. */ if (X[terms] > X[0]) /* X values increasing */ { if (start > stop) /* check for special request */ { /* to integrate over all X */ start = bot; /* set start to least X */ stop = top; /* set stop to largest X */ wstart = wbot; /* set start to least X */ wstop = wtop; /* set stop to largest X */ } if (start >= top || stop <= bot) /* are integ. limits in X array */ return (OUTSIDE_MIN); /* no? ok return OUTSIDE_MIN */ f1 = X + 1; /* top of first band */ f2 = X + 2; /* top of second band */ wf1 = &WX[1]; /* top of first band */ wf2 = &WX[2]; /* top of second band */ f3 = Y; /* Y value of first band */ f4 = Y + skip; /* Y value of second band */ wa = *wf1 + *(wf1 - 1); /* center of first band */ a = *f1 + *(f1 - 1); /* center of first band */ b = *f2 + *f1; /* center of second band */ wb = *wf2 + *wf1; /* center of second band */ if (start > a) /* if start in X find 1st band */ { while ((start >= b) && (f2 < f_end)) /* begin search */ { wa = wb; /* 1st band now 2nd band */ a = b; /* 1st band now 2nd band */ b = *(++f2) + *(++f1); /* new 2nd band center */ wb = *(++wf2) + *(++wf1); /* new 2nd band center */ f3 += skip; /* increment Y of 1st band */ f4 += skip; /* increment Y of 2nd band */ } if (*f3 >= VALID_MIN && *f4 >= VALID_MIN) /* if data good */ { /* compute 1st trap */ c = (b - a)/2.0; d = (start - a)/2.0; wc = (wb - wa)/2.0; wd = (wstart - wa)/2.0; ret_val = (*f4 - *f3) * (wc * wc - wd * wd) / 2.0 / wc; ret_val += (wb - wstart)/2.0 * *f3; valid_data_found = 1; sumx += (c - d) * 2.0; } /* Added conditional since getting ABR errors from purify from f2. */ if (f2 != f_end) { wa = wb; /* 1st band now 2nd band */ a = b; /* 1st band now 2nd band */ b = *(++f2) + *(++f1); /* new 2nd band center */ wb = *(++wf2) + *(++wf1); /* new 2nd band center */ f3 += skip; /* increment Y of 1st band */ f4 += skip; /* increment Y of 2nd band */ } } while ((stop >= b) && (f2 < f_end)) { if (*f3 >= VALID_MIN && *f4 >= VALID_MIN) { valid_data_found = 1; sum += (wb - wa) * (*f3 + *f4); sumx += b - a; } wa = wb; a = b; b = *(++f2) + *(++f1); wb = *(++wf2) + *(++wf1); f3 += skip; f4 += skip; } ret_val += 0.25 * sum; if ((stop < top) && (*f3 >= VALID_MIN) && (*f4 >= VALID_MIN)) { wc = (wb - wa)/2.0; d = (stop - a)/2.0; wd = (wstop - wa)/2.0; ret_val += (*f4 - *f3) * wd * wd / 2.0 / wc; ret_val += (wstop - wa)/2.0 * *f3; valid_data_found = 1; sumx += d * 2.0; } } else { if (start > stop) /* check for special request */ { /* to integrate over all X */ start = top; /* set start to least X */ stop = bot; /* set stop to largest X */ wstart = wtop; /* set start to least X */ wstop = wbot; /* set stop to largest X */ } if (start >= bot || stop <= top) /* are integ. limits in X array */ return (OUTSIDE_MIN); /* no? ok return OUTSIDE_MIN */ f1 = f_end - 1; f2 = f_end - 2; wf1 = w_end - 1; wf2 = w_end - 2; f3 = Y + (terms - 1) * skip; f4 = Y + (terms - 2) * skip; wa = *wf1 + *(wf1 + 1); a = *f1 + *(f1 + 1); b = *f2 + *f1; wb = *wf2 + *wf1; if (start > a) { while ((start >= b) && (f2 > X)) { wa = wb; a = b; b = *(--f2) + *(--f1); wb = *(--wf2) + *(--wf1); f3 -= skip; f4 -= skip; } if (*f3 >= VALID_MIN && *f4 >= VALID_MIN) { wc = (wb - wa)/2.0; c = (b - a)/2.0; d = (start - a)/2.0; wd = (wstart - wa)/2.0; ret_val = (*f4 - *f3) * (wc * wc - wd * wd ) / 2.0 / wc; ret_val += (wb - wstart)/2.0 * *f3; valid_data_found = 1; sumx += (c - d) * 2.0; } /* Added conditional since getting ABR errors from purify from f2. */ if (f2 > X) { a = b; wa = wb; b = *(--f2) + *(--f1); wb = *(--wf2) + *(--wf1); f3 -= skip; f4 -= skip; } } while ((stop >= b) && (f2 > X)) { if (*f3 >= VALID_MIN && *f4 >= VALID_MIN) { valid_data_found = 1; sum += (wb - wa) * (*f3 + *f4); sumx += b - a; } a = b; wa = wb; b = *(--f2) + *(--f1); wb = *(--wf2) + *(--wf1); f3 -= skip; f4 -= skip; } ret_val += 0.25 * sum; if ((stop < bot) && (*f3 >= VALID_MIN) && (*f4 >= VALID_MIN)) { wc = (wb - wa)/2.0; d = (stop - a)/2.0; wd = (wstop - wa)/2.0; ret_val += (*f4 - *f3) * wd * wd / 2.0 / wc; ret_val += (stop - a)/2.0 * *f3; sumx += d * 2.0; valid_data_found = 1; } } if (norm && sumx > 0.0) { ret_val /= sumx; ret_val *= (stop - start); } /* 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. */ if (!valid_data_found) return (OUTSIDE_MIN); else return ((SDDAS_FLOAT) ret_val); }