JSOC/proj/sharp/apps/sw_functions.c - diff

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Diff for /JSOC/proj/sharp/apps/sw_functions.c between version 1.9 and 1.31

version 1.9, 2013/05/20 23:55:32

version 1.31, 2014/06/05 21:27:04

Line 17

MEANPOT Mean photospheric excess magnetic energy density in ergs per cubic centimeter

TOTPOT Total photospheric magnetic energy density in ergs per cubic centimeter

MEANSHR Mean shear angle (measured using Btotal) in degrees

R_VALUE Karel Schrijver's R parameter

The indices are calculated on the pixels in which the conf_disambig segment is greater than 70 and

pixels in which the bitmap segment is greater than 30. These ranges are selected because the CCD

coordinate bitmaps are interpolated.

coordinate bitmaps are interpolated for certain data (at the time of this CVS submit, all data

prior to 2013.08.21_17:24:00_TAI contain interpolated bitmaps; data post-2013.08.21_17:24:00_TAI

contain nearest-neighbor bitmaps).

In the CCD coordinates, this means that we are selecting the pixels that equal 90 in conf_disambig

and the pixels that equal 33 or 44 in bitmap. Here are the definitions of the pixel values:

and the pixels that equal 33 or 34 in bitmap. Here are the definitions of the pixel values:

For conf_disambig:

50 : not all solutions agree (weak field method applied)

Line 39

Line 42

Written by Monica Bobra 15 August 2012

Potential Field code (appended) written by Keiji Hayashi

Error analysis modification 21 October 2013

===========================================*/

#include <math.h>

Line 60

Line 64

// To convert G to G*cm^2, simply multiply by the number of square centimeters per pixel.

// As an order of magnitude estimate, we can assign 0.5 to CDELT1 and 722500m/arcsec to (RSUN_REF/RSUN_OBS).

// (Gauss/pix^2)(CDELT1)^2(RSUN_REF/RSUN_OBS)^2(100.cm/m)^2

// =(Gauss/pix^2)(0.5 arcsec/pix)^2(722500m/arcsec)^2(100cm/m)^2

// =Gauss*cm^2

// =(1.30501e15)Gauss*cm^2

// The disambig mask value selects only the pixels with values of 5 or 7 -- that is,

// 5: pixels for which the radial acute disambiguation solution was chosen

// 7: pixels for which the radial acute and NRWA disambiguation agree

int computeAbsFlux(float *bz_err, float *bz, int *dims, float *absFlux,

float *mean_vf_ptr, float *mean_vf_err_ptr, float *count_mask_ptr, int *mask,

Line 73 int computeAbsFlux(float *bz_err, float

Line 72 int computeAbsFlux(float *bz_err, float

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

double sum,err=0.0;

int i = 0;

int j = 0;

if (nx <= 0 || ny <= 0) return 1;

int count_mask = 0;

double sum = 0.0;

double err = 0.0;

*absFlux = 0.0;

*mean_vf_ptr =0.0;

if (nx <= 0 || ny <= 0) return 1;

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

{

for (j = 0; j < ny; j++)

Line 97 int computeAbsFlux(float *bz_err, float

Line 100 int computeAbsFlux(float *bz_err, float

*mean_vf_ptr = sum*cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0;

*mean_vf_err_ptr = (sqrt(err))*fabs(cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0); // error in the unsigned flux

*count_mask_ptr = count_mask;

printf("CMASK=%g\n",*count_mask_ptr);

printf("USFLUX=%g\n",*mean_vf_ptr);

printf("sum=%f\n",sum);

printf("USFLUX_err=%g\n",*mean_vf_err_ptr);

return 0;

}

Line 113 int computeBh(float *bx_err, float *by_e

Line 112 int computeBh(float *bx_err, float *by_e

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

float sum=0.0;

int i = 0;

int j = 0;

int count_mask = 0;

double sum = 0.0;

*mean_hf_ptr = 0.0;

if (nx <= 0 || ny <= 0) return 1;

Line 124 int computeBh(float *bx_err, float *by_e

Line 126 int computeBh(float *bx_err, float *by_e

{

for (j = 0; j < ny; j++)

{

if isnan(bx[j * nx + i]) continue;

if isnan(bx[j * nx + i])

if isnan(by[j * nx + i]) continue;

{

bh[j * nx + i] = NAN;

bh_err[j * nx + i] = NAN;

continue;

}

if isnan(by[j * nx + i])

{

bh[j * nx + i] = NAN;

bh_err[j * nx + i] = NAN;

continue;

}

bh[j * nx + i] = sqrt( bx[j * nx + i]*bx[j * nx + i] + by[j * nx + i]*by[j * nx + i] );

sum += bh[j * nx + i];

bh_err[j * nx + i]=sqrt( bx[j * nx + i]*bx[j * nx + i]*bx_err[j * nx + i]*bx_err[j * nx + i] + by[j * nx + i]*by[j * nx + i]*by_err[j * nx + i]*by_err[j * nx + i])/ bh[j * nx + i];

Line 141 int computeBh(float *bx_err, float *by_e

Line 153 int computeBh(float *bx_err, float *by_e

/*===========================================*/

/* Example function 3: Calculate Gamma in units of degrees */

// Native units of atan(x) are in radians; to convert from radians to degrees, multiply by (180./PI)

// Redo calculation in radians for error analysis (since derivatives are only true in units of radians).

// Error analysis calculations are done in radians (since derivatives are only true in units of radians),

// and multiplied by (180./PI) at the end for consistency in units.

int computeGamma(float *bz_err, float *bh_err, float *bx, float *by, float *bz, float *bh, int *dims,

float *mean_gamma_ptr, float *mean_gamma_err_ptr, int *mask, int *bitmask)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

if (nx <= 0 || ny <= 0) return 1;

int j = 0;

int count_mask = 0;

double sum = 0.0;

double err = 0.0;

*mean_gamma_ptr=0.0;

float sum,err,err_value=0.0;

if (nx <= 0 || ny <= 0) return 1;

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

{

Line 165 int computeGamma(float *bz_err, float *b

Line 181 int computeGamma(float *bz_err, float *b

if isnan(bz[j * nx + i]) continue;

if isnan(bz_err[j * nx + i]) continue;

if isnan(bh_err[j * nx + i]) continue;

if isnan(bh[j * nx + i]) continue;

if (bz[j * nx + i] == 0) continue;

sum += (atan(fabs(bz[j * nx + i]/bh[j * nx + i] )))*(180./PI);

sum += fabs(atan(bh[j * nx + i]/fabs(bz[j * nx + i])))*(180./PI);

err += (( sqrt ( ((bz_err[j * nx + i]*bz_err[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i])) + ((bh_err[j * nx + i]*bh_err[j * nx + i])/(bh[j * nx + i]*bh[j * nx + i]))) * fabs(bz[j * nx + i]/bh[j * nx + i]) ) / (1 + (bz[j * nx + i]/bh[j * nx + i])*(bz[j * nx + i]/bh[j * nx + i]))) *(180./PI);

err += (1/(1+((bh[j * nx + i]*bh[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i]))))*(1/(1+((bh[j * nx + i]*bh[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i])))) *

( ((bh_err[j * nx + i]*bh_err[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i])) +

((bh[j * nx + i]*bh[j * nx + i]*bz_err[j * nx + i]*bz_err[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i]*bz[j * nx + i]*bz[j * nx + i])) );

count_mask++;

}

*mean_gamma_ptr = sum/count_mask;

*mean_gamma_err_ptr = (sqrt(err*err))/(count_mask*100.); // error in the quantity (sum)/(count_mask)

*mean_gamma_err_ptr = (sqrt(err)/(count_mask))*(180./PI);

printf("MEANGAM=%f\n",*mean_gamma_ptr);

//printf("MEANGAM=%f\n",*mean_gamma_ptr);

printf("MEANGAM_err=%f\n",*mean_gamma_err_ptr);

//printf("MEANGAM_err=%f\n",*mean_gamma_err_ptr);

return 0;

}

Line 187 int computeGamma(float *bz_err, float *b

Line 206 int computeGamma(float *bz_err, float *b

int computeB_total(float *bx_err, float *by_err, float *bz_err, float *bt_err, float *bx, float *by, float *bz, float *bt, int *dims, int *mask, int *bitmask)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

int j = 0;

int count_mask = 0;

if (nx <= 0 || ny <= 0) return 1;

Line 196 int computeB_total(float *bx_err, float

Line 218 int computeB_total(float *bx_err, float

{

for (j = 0; j < ny; j++)

{

if isnan(bx[j * nx + i]) continue;

if isnan(bx[j * nx + i])

if isnan(by[j * nx + i]) continue;

{

if isnan(bz[j * nx + i]) continue;

bt[j * nx + i] = NAN;

bt_err[j * nx + i] = NAN;

continue;

}

if isnan(by[j * nx + i])

{

bt[j * nx + i] = NAN;

bt_err[j * nx + i] = NAN;

continue;

}

if isnan(bz[j * nx + i])

{

bt[j * nx + i] = NAN;

bt_err[j * nx + i] = NAN;

continue;

}

bt[j * nx + i] = sqrt( bx[j * nx + i]*bx[j * nx + i] + by[j * nx + i]*by[j * nx + i] + bz[j * nx + i]*bz[j * nx + i]);

bt_err[j * nx + i]=sqrt(bx[j * nx + i]*bx[j * nx + i]*bx_err[j * nx + i]*bx_err[j * nx + i] + by[j * nx + i]*by[j * nx + i]*by_err[j * nx + i]*by_err[j * nx + i] + bz[j * nx + i]*bz[j * nx + i]*bz_err[j * nx + i]*bz_err[j * nx + i] )/bt[j * nx + i];

}

Line 212 int computeB_total(float *bx_err, float

Line 249 int computeB_total(float *bx_err, float

int computeBtotalderivative(float *bt, int *dims, float *mean_derivative_btotal_ptr, int *mask, int *bitmask, float *derx_bt, float *dery_bt, float *bt_err, float *mean_derivative_btotal_err_ptr)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

if (nx <= 0 || ny <= 0) return 1;

int j = 0;

int count_mask = 0;

double sum = 0.0;

double err = 0.0;

*mean_derivative_btotal_ptr = 0.0;

float sum, err = 0.0;

if (nx <= 0 || ny <= 0) return 1;

/* brute force method of calculating the derivative (no consideration for edges) */

for (i = 3; i <= nx-4; i++)

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

{

for (j = 0; j <= ny-1; j++)

{

derx_bt[j * nx + i] = (-bt[j * nx + (i-3)] + 9.0*bt[j * nx + (i-2)] - 45.0*bt[j * nx + (i-1)] + 45*bt[j * nx + (i+1)] - 9.0*bt[j * nx + (i+2)] + bt[j * nx + (i+3)])*(1.0/60.0);

derx_bt[j * nx + i] = (bt[j * nx + i+1] - bt[j * nx + i-1])*0.5;

}

/* brute force method of calculating the derivative (no consideration for edges) */

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

{

for (j = 3; j <= ny-4; j++)

for (j = 1; j <= ny-2; j++)

{

dery_bt[j * nx + i] = (-bt[(j-3) * nx + i] + 9.0*bt[(j-2) * nx + i] - 45.0*bt[(j-1) * nx + i] + 45*bt[(j+1) * nx + i] - 9.0*bt[(j+2) * nx + i] + bt[(j+3) * nx + i])*(1.0/60.0);

dery_bt[j * nx + i] = (bt[(j+1) * nx + i] - bt[(j-1) * nx + i])*0.5;

}

/* consider the edges: 3 pixels on each edge, for a total of 12 edge formulae below */

/* consider the edges */

i=0;

for (j = 0; j <= ny-1; j++)

{

derx_bt[j * nx + i] = (-147.0*bt[j * nx + i] + 360.0*bt[j * nx + (i+1)] - 450.0*bt[j * nx + (i+2)] + 400.0*bt[j * nx + (i+3)] - 225.0*bt[j * nx + (i+4)] + 72.0*bt[j * nx + (i+5)] - 10.0*bt[j * nx + (i+6)])*(1.0/60.0);

derx_bt[j * nx + i] = ( (-3*bt[j * nx + i]) + (4*bt[j * nx + (i+1)]) - (bt[j * nx + (i+2)]) )*0.5;

}

i=nx-1;

for (j = 0; j <= ny-1; j++)

{

derx_bt[j * nx + i] = ( 147.0*bt[j * nx + i] - 360.0*bt[j * nx + (i-1)] + 450.0*bt[j * nx + (i-2)] - 400.0*bt[j * nx + (i-3)] + 225.0*bt[j * nx + (i-4)] - 72.0*bt[j * nx + (i-5)] + 10.0*bt[j * nx + (i-6)])*(1.0/60.0);

derx_bt[j * nx + i] = ( (3*bt[j * nx + i]) + (-4*bt[j * nx + (i-1)]) - (-bt[j * nx + (i-2)]) )*0.5;

}

i=1;

for (j = 0; j <= ny-2; j++)

{

derx_bt[j * nx + i] = (-10.0*bt[j * nx + i] - 77.0*bt[j * nx + (i+1)] + 150.0*bt[j * nx + (i+2)] - 100.0*bt[j * nx + (i+3)] + 50.0*bt[j * nx + (i+4)] - 15.0*bt[j * nx + (i+5)] + 2.0*bt[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-2;

for (j = 0; j <= ny-2; j++)

{

derx_bt[j * nx + i] = ( 10.0*bt[j * nx + i] + 77.0*bt[j * nx + (i-1)] - 150.0*bt[j * nx + (i-2)] + 100.0*bt[j * nx + (i-3)] - 50.0*bt[j * nx + (i-4)] + 15.0*bt[j * nx + (i-5)] - 2.0*bt[j * nx + (i-6)])*(1.0/60.0);

}

i=2;

for (j = 0; j <= ny-2; j++)

{

derx_bt[j * nx + i] = ( 2.0*bt[j * nx + i] - 24.0*bt[j * nx + (i+1)] - 35.0*bt[j * nx + (i+2)] + 80.0*bt[j * nx + (i+3)] - 30.0*bt[j * nx + (i+4)] + 8.0*bt[j * nx + (i+5)] - bt[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-3;

for (j = 0; j <= ny-2; j++)

{

derx_bt[j * nx + i] = (-2.0*bt[j * nx + i] + 24.0*bt[j * nx + (i-1)] + 35.0*bt[j * nx + (i-2)] - 80.0*bt[j * nx + (i-3)] + 30.0*bt[j * nx + (i-4)] - 8.0*bt[j * nx + (i-5)] + bt[j * nx + (i-6)])*(1.0/60.0);

}

j=0;

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

{

dery_bt[j * nx + i] = (-147.0*bt[j * nx + i] + 360.0*bt[(j+1) * nx + i] - 450.0*bt[(j+2) * nx + i] + 400.0*bt[(j+3) * nx + i] - 225.0*bt[(j+4) * nx + i] + 72.0*bt[(j+5) * nx + i] - 10.0*bt[(j+6) * nx + i])*(1.0/60.0);

dery_bt[j * nx + i] = ( (-3*bt[j*nx + i]) + (4*bt[(j+1) * nx + i]) - (bt[(j+2) * nx + i]) )*0.5;

}

j=ny-1;

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

{

dery_bt[j * nx + i] = ( 147.0*bt[j * nx + i] - 360.0*bt[(j-1) * nx + i] + 450.0*bt[(j-2) * nx + i] - 400.0*bt[(j-3) * nx + i] + 225.0*bt[(j-4) * nx + i] - 72.0*bt[(j-5) * nx + i] + 10.0*bt[(j-6) * nx + i])*(1.0/60.0);

dery_bt[j * nx + i] = ( (3*bt[j * nx + i]) + (-4*bt[(j-1) * nx + i]) - (-bt[(j-2) * nx + i]) )*0.5;

}

j=1;

for (i = 0; i <= nx-2; i++)

{

dery_bt[j * nx + i] = (-10.0*bt[j * nx + i] - 77.0*bt[(j+1) * nx + i] + 150.0*bt[(j+2) * nx + i] - 100.0*bt[(j+3) * nx + i] + 50.0*bt[(j+4) * nx + i] - 15.0*bt[(j+5) * nx + i] + 2.0*bt[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-2;

for (i = 0; i <= nx-2; i++)

{

dery_bt[j * nx + i] = ( 10.0*bt[j * nx + i] + 77.0*bt[(j-1) * nx + i] - 150.0*bt[(j-2) * nx + i] + 100.0*bt[(j-3) * nx + i] - 50.0*bt[(j-4) * nx + i] + 15.0*bt[(j-5) * nx + i] - 2.0*bt[(j-6) * nx + i])*(1.0/60.0);

}

j=2;

for (i = 0; i <= nx-3; i++)

{

dery_bt[j * nx + i] = ( 2.0*bt[j * nx + i] - 24.0*bt[(j+1) * nx + i] - 35.0*bt[(j+2) * nx + i] + 80.0*bt[(j+3) * nx + i] - 30.0*bt[(j+4) * nx + i] + 8.0*bt[(j+5) * nx + i] - bt[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-3;

for (i = 0; i <= nx-3; i++)

{

dery_bt[j * nx + i] = (-2.0*bt[j * nx + i] + 24.0*bt[(j-1) * nx + i] + 35.0*bt[(j-2) * nx + i] - 80.0*bt[(j-3) * nx + i] + 30.0*bt[(j-4) * nx + i] - 8.0*bt[(j-5) * nx + i] + bt[(j-6) * nx + i])*(1.0/60.0);

}

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

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

{

for (j = 0; j <= ny-1; j++)

for (j = 1; j <= ny-2; j++)

{

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if ( (derx_bt[j * nx + i] + dery_bt[j * nx + i]) == 0) continue;

if isnan(bt[j * nx + i]) continue;

if isnan(bt[(j+1) * nx + i]) continue;

if isnan(bt[(j-1) * nx + i]) continue;

if isnan(bt[j * nx + i-1]) continue;

if isnan(bt[j * nx + i+1]) continue;

if isnan(bt_err[j * nx + i]) continue;

if isnan(derx_bt[j * nx + i]) continue;

if isnan(dery_bt[j * nx + i]) continue;

sum += sqrt( derx_bt[j * nx + i]*derx_bt[j * nx + i] + dery_bt[j * nx + i]*dery_bt[j * nx + i] ); /* Units of Gauss */

err += (2.0)*bt_err[j * nx + i]*bt_err[j * nx + i];

err += (((bt[(j+1) * nx + i]-bt[(j-1) * nx + i])*(bt[(j+1) * nx + i]-bt[(j-1) * nx + i])) * (bt_err[(j+1) * nx + i]*bt_err[(j+1) * nx + i] + bt_err[(j-1) * nx + i]*bt_err[(j-1) * nx + i])) / (16.0*( derx_bt[j * nx + i]*derx_bt[j * nx + i] + dery_bt[j * nx + i]*dery_bt[j * nx + i] ))+

(((bt[j * nx + (i+1)]-bt[j * nx + (i-1)])*(bt[j * nx + (i+1)]-bt[j * nx + (i-1)])) * (bt_err[j * nx + (i+1)]*bt_err[j * nx + (i+1)] + bt_err[j * nx + (i-1)]*bt_err[j * nx + (i-1)])) / (16.0*( derx_bt[j * nx + i]*derx_bt[j * nx + i] + dery_bt[j * nx + i]*dery_bt[j * nx + i] )) ;

count_mask++;

}

*mean_derivative_btotal_ptr = (sum)/(count_mask); // would be divided by ((nx-2)*(ny-2)) if shape of count_mask = shape of magnetogram

*mean_derivative_btotal_ptr = (sum)/(count_mask);

*mean_derivative_btotal_err_ptr = (sqrt(err))/(count_mask); // error in the quantity (sum)/(count_mask)

*mean_derivative_btotal_err_ptr = (sqrt(err))/(count_mask);

printf("MEANGBT=%f\n",*mean_derivative_btotal_ptr);

//printf("MEANGBT=%f\n",*mean_derivative_btotal_ptr);

printf("MEANGBT_err=%f\n",*mean_derivative_btotal_err_ptr);

//printf("MEANGBT_err=%f\n",*mean_derivative_btotal_err_ptr);

return 0;

}

Line 344 int computeBtotalderivative(float *bt, i

Line 341 int computeBtotalderivative(float *bt, i

int computeBhderivative(float *bh, float *bh_err, int *dims, float *mean_derivative_bh_ptr, float *mean_derivative_bh_err_ptr, int *mask, int *bitmask, float *derx_bh, float *dery_bh)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

int j = 0;

int count_mask = 0;

double sum= 0.0;

double err =0.0;

*mean_derivative_bh_ptr = 0.0;

if (nx <= 0 || ny <= 0) return 1;

*mean_derivative_bh_ptr = 0.0;

float sum,err = 0.0;

/* brute force method of calculating the derivative (no consideration for edges) */

for (i = 3; i <= nx-4; i++)

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

{

for (j = 0; j <= ny-1; j++)

{

derx_bh[j * nx + i] = (-bh[j * nx + (i-3)] + 9.0*bh[j * nx + (i-2)] - 45.0*bh[j * nx + (i-1)] + 45*bh[j * nx + (i+1)] - 9.0*bh[j * nx + (i+2)] + bh[j * nx + (i+3)])*(1.0/60.0);

derx_bh[j * nx + i] = (bh[j * nx + i+1] - bh[j * nx + i-1])*0.5;

}

/* brute force method of calculating the derivative (no consideration for edges) */

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

{

for (j = 3; j <= ny-4; j++)

for (j = 1; j <= ny-2; j++)

{

dery_bh[j * nx + i] = (-bh[(j-3) * nx + i] + 9.0*bh[(j-2) * nx + i] - 45.0*bh[(j-1) * nx + i] + 45*bh[(j+1) * nx + i] - 9.0*bh[(j+2) * nx + i] + bh[(j+3) * nx + i])*(1.0/60.0);

dery_bh[j * nx + i] = (bh[(j+1) * nx + i] - bh[(j-1) * nx + i])*0.5;

}

/* consider the edges: 3 pixels on each edge, for a total of 12 edge formulae below */

/* consider the edges */

i=0;

for (j = 0; j <= ny-1; j++)

{

derx_bh[j * nx + i] = (-147.0*bh[j * nx + i] + 360.0*bh[j * nx + (i+1)] - 450.0*bh[j * nx + (i+2)] + 400.0*bh[j * nx + (i+3)] - 225.0*bh[j * nx + (i+4)] + 72.0*bh[j * nx + (i+5)] - 10.0*bh[j * nx + (i+6)])*(1.0/60.0);

derx_bh[j * nx + i] = ( (-3*bh[j * nx + i]) + (4*bh[j * nx + (i+1)]) - (bh[j * nx + (i+2)]) )*0.5;

}

i=nx-1;

for (j = 0; j <= ny-1; j++)

{

derx_bh[j * nx + i] = ( 147.0*bh[j * nx + i] - 360.0*bh[j * nx + (i-1)] + 450.0*bh[j * nx + (i-2)] - 400.0*bh[j * nx + (i-3)] + 225.0*bh[j * nx + (i-4)] - 72.0*bh[j * nx + (i-5)] + 10.0*bh[j * nx + (i-6)])*(1.0/60.0);

derx_bh[j * nx + i] = ( (3*bh[j * nx + i]) + (-4*bh[j * nx + (i-1)]) - (-bh[j * nx + (i-2)]) )*0.5;

}

i=1;

for (j = 0; j <= ny-2; j++)

{

derx_bh[j * nx + i] = (-10.0*bh[j * nx + i] - 77.0*bh[j * nx + (i+1)] + 150.0*bh[j * nx + (i+2)] - 100.0*bh[j * nx + (i+3)] + 50.0*bh[j * nx + (i+4)] - 15.0*bh[j * nx + (i+5)] + 2.0*bh[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-2;

for (j = 0; j <= ny-2; j++)

{

derx_bh[j * nx + i] = ( 10.0*bh[j * nx + i] + 77.0*bh[j * nx + (i-1)] - 150.0*bh[j * nx + (i-2)] + 100.0*bh[j * nx + (i-3)] - 50.0*bh[j * nx + (i-4)] + 15.0*bh[j * nx + (i-5)] - 2.0*bh[j * nx + (i-6)])*(1.0/60.0);

}

i=2;

for (j = 0; j <= ny-2; j++)

{

derx_bh[j * nx + i] = ( 2.0*bh[j * nx + i] - 24.0*bh[j * nx + (i+1)] - 35.0*bh[j * nx + (i+2)] + 80.0*bh[j * nx + (i+3)] - 30.0*bh[j * nx + (i+4)] + 8.0*bh[j * nx + (i+5)] - bh[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-3;

for (j = 0; j <= ny-2; j++)

{

derx_bh[j * nx + i] = (-2.0*bh[j * nx + i] + 24.0*bh[j * nx + (i-1)] + 35.0*bh[j * nx + (i-2)] - 80.0*bh[j * nx + (i-3)] + 30.0*bh[j * nx + (i-4)] - 8.0*bh[j * nx + (i-5)] + bh[j * nx + (i-6)])*(1.0/60.0);

}

j=0;

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

{

dery_bh[j * nx + i] = (-147.0*bh[j * nx + i] + 360.0*bh[(j+1) * nx + i] - 450.0*bh[(j+2) * nx + i] + 400.0*bh[(j+3) * nx + i] - 225.0*bh[(j+4) * nx + i] + 72.0*bh[(j+5) * nx + i] - 10.0*bh[(j+6) * nx + i])*(1.0/60.0);

dery_bh[j * nx + i] = ( (-3*bh[j*nx + i]) + (4*bh[(j+1) * nx + i]) - (bh[(j+2) * nx + i]) )*0.5;

}

j=ny-1;

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

{

dery_bh[j * nx + i] = ( 147.0*bh[j * nx + i] - 360.0*bh[(j-1) * nx + i] + 450.0*bh[(j-2) * nx + i] - 400.0*bh[(j-3) * nx + i] + 225.0*bh[(j-4) * nx + i] - 72.0*bh[(j-5) * nx + i] + 10.0*bh[(j-6) * nx + i])*(1.0/60.0);

dery_bh[j * nx + i] = ( (3*bh[j * nx + i]) + (-4*bh[(j-1) * nx + i]) - (-bh[(j-2) * nx + i]) )*0.5;

}

j=1;

for (i = 0; i <= nx-2; i++)

{

dery_bh[j * nx + i] = (-10.0*bh[j * nx + i] - 77.0*bh[(j+1) * nx + i] + 150.0*bh[(j+2) * nx + i] - 100.0*bh[(j+3) * nx + i] + 50.0*bh[(j+4) * nx + i] - 15.0*bh[(j+5) * nx + i] + 2.0*bh[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-2;

for (i = 0; i <= nx-2; i++)

{

dery_bh[j * nx + i] = ( 10.0*bh[j * nx + i] + 77.0*bh[(j-1) * nx + i] - 150.0*bh[(j-2) * nx + i] + 100.0*bh[(j-3) * nx + i] - 50.0*bh[(j-4) * nx + i] + 15.0*bh[(j-5) * nx + i] - 2.0*bh[(j-6) * nx + i])*(1.0/60.0);

}

j=2;

for (i = 0; i <= nx-3; i++)

{

dery_bh[j * nx + i] = ( 2.0*bh[j * nx + i] - 24.0*bh[(j+1) * nx + i] - 35.0*bh[(j+2) * nx + i] + 80.0*bh[(j+3) * nx + i] - 30.0*bh[(j+4) * nx + i] + 8.0*bh[(j+5) * nx + i] - bh[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-3;

for (i = 0; i <= nx-3; i++)

{

dery_bh[j * nx + i] = (-2.0*bh[j * nx + i] + 24.0*bh[(j-1) * nx + i] + 35.0*bh[(j-2) * nx + i] - 80.0*bh[(j-3) * nx + i] + 30.0*bh[(j-4) * nx + i] - 8.0*bh[(j-5) * nx + i] + bh[(j-6) * nx + i])*(1.0/60.0);

}

Line 453 int computeBhderivative(float *bh, float

Line 402 int computeBhderivative(float *bh, float

for (j = 0; j <= ny-1; j++)

{

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if ( (derx_bh[j * nx + i] + dery_bh[j * nx + i]) == 0) continue;

if isnan(bh[j * nx + i]) continue;

if isnan(bh[(j+1) * nx + i]) continue;

if isnan(bh[(j-1) * nx + i]) continue;

if isnan(bh[j * nx + i-1]) continue;

if isnan(bh[j * nx + i+1]) continue;

if isnan(bh_err[j * nx + i]) continue;

if isnan(derx_bh[j * nx + i]) continue;

if isnan(dery_bh[j * nx + i]) continue;

sum += sqrt( derx_bh[j * nx + i]*derx_bh[j * nx + i] + dery_bh[j * nx + i]*dery_bh[j * nx + i] ); /* Units of Gauss */

err += (2.0)*bh_err[j * nx + i]*bh_err[j * nx + i];

err += (((bh[(j+1) * nx + i]-bh[(j-1) * nx + i])*(bh[(j+1) * nx + i]-bh[(j-1) * nx + i])) * (bh_err[(j+1) * nx + i]*bh_err[(j+1) * nx + i] + bh_err[(j-1) * nx + i]*bh_err[(j-1) * nx + i])) / (16.0*( derx_bh[j * nx + i]*derx_bh[j * nx + i] + dery_bh[j * nx + i]*dery_bh[j * nx + i] ))+

(((bh[j * nx + (i+1)]-bh[j * nx + (i-1)])*(bh[j * nx + (i+1)]-bh[j * nx + (i-1)])) * (bh_err[j * nx + (i+1)]*bh_err[j * nx + (i+1)] + bh_err[j * nx + (i-1)]*bh_err[j * nx + (i-1)])) / (16.0*( derx_bh[j * nx + i]*derx_bh[j * nx + i] + dery_bh[j * nx + i]*dery_bh[j * nx + i] )) ;

count_mask++;

}

*mean_derivative_bh_ptr = (sum)/(count_mask); // would be divided by ((nx-2)*(ny-2)) if shape of count_mask = shape of magnetogram

*mean_derivative_bh_err_ptr = (sqrt(err))/(count_mask); // error in the quantity (sum)/(count_mask)

printf("MEANGBH=%f\n",*mean_derivative_bh_ptr);

//printf("MEANGBH=%f\n",*mean_derivative_bh_ptr);

printf("MEANGBH_err=%f\n",*mean_derivative_bh_err_ptr);

//printf("MEANGBH_err=%f\n",*mean_derivative_bh_err_ptr);

return 0;

}

Line 475 int computeBhderivative(float *bh, float

Line 432 int computeBhderivative(float *bh, float

int computeBzderivative(float *bz, float *bz_err, int *dims, float *mean_derivative_bz_ptr, float *mean_derivative_bz_err_ptr, int *mask, int *bitmask, float *derx_bz, float *dery_bz)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

if (nx <= 0 || ny <= 0) return 1;

int j = 0;

int count_mask = 0;

double sum = 0.0;

double err = 0.0;

*mean_derivative_bz_ptr = 0.0;

float sum,err = 0.0;

if (nx <= 0 || ny <= 0) return 1;

/* brute force method of calculating the derivative (no consideration for edges) */

for (i = 3; i <= nx-4; i++)

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

{

for (j = 0; j <= ny-1; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = (-bz[j * nx + (i-3)] + 9.0*bz[j * nx + (i-2)] - 45.0*bz[j * nx + (i-1)] + 45*bz[j * nx + (i+1)] - 9.0*bz[j * nx + (i+2)] + bz[j * nx + (i+3)])*(1.0/60.0);

derx_bz[j * nx + i] = (bz[j * nx + i+1] - bz[j * nx + i-1])*0.5;

}

/* brute force method of calculating the derivative (no consideration for edges) */

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

{

for (j = 3; j <= ny-4; j++)

for (j = 1; j <= ny-2; j++)

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = (-bz[(j-3) * nx + i] + 9.0*bz[(j-2) * nx + i] - 45.0*bz[(j-1) * nx + i] + 45*bz[(j+1) * nx + i] - 9.0*bz[(j+2) * nx + i] + bz[(j+3) * nx + i])*(1.0/60.0);

dery_bz[j * nx + i] = (bz[(j+1) * nx + i] - bz[(j-1) * nx + i])*0.5;

}

/* consider the edges: 3 pixels on each edge, for a total of 12 edge formulae below */

/* consider the edges */

i=0;

for (j = 0; j <= ny-1; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = (-147.0*bz[j * nx + i] + 360.0*bz[j * nx + (i+1)] - 450.0*bz[j * nx + (i+2)] + 400.0*bz[j * nx + (i+3)] - 225.0*bz[j * nx + (i+4)] + 72.0*bz[j * nx + (i+5)] - 10.0*bz[j * nx + (i+6)])*(1.0/60.0);

derx_bz[j * nx + i] = ( (-3*bz[j * nx + i]) + (4*bz[j * nx + (i+1)]) - (bz[j * nx + (i+2)]) )*0.5;

}

i=nx-1;

for (j = 0; j <= ny-1; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = ( 147.0*bz[j * nx + i] - 360.0*bz[j * nx + (i-1)] + 450.0*bz[j * nx + (i-2)] - 400.0*bz[j * nx + (i-3)] + 225.0*bz[j * nx + (i-4)] - 72.0*bz[j * nx + (i-5)] + 10.0*bz[j * nx + (i-6)])*(1.0/60.0);

derx_bz[j * nx + i] = ( (3*bz[j * nx + i]) + (-4*bz[j * nx + (i-1)]) - (-bz[j * nx + (i-2)]) )*0.5;

}

i=1;

for (j = 0; j <= ny-2; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = (-10.0*bz[j * nx + i] - 77.0*bz[j * nx + (i+1)] + 150.0*bz[j * nx + (i+2)] - 100.0*bz[j * nx + (i+3)] + 50.0*bz[j * nx + (i+4)] - 15.0*bz[j * nx + (i+5)] + 2.0*bz[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-2;

for (j = 0; j <= ny-2; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = ( 10.0*bz[j * nx + i] + 77.0*bz[j * nx + (i-1)] - 150.0*bz[j * nx + (i-2)] + 100.0*bz[j * nx + (i-3)] - 50.0*bz[j * nx + (i-4)] + 15.0*bz[j * nx + (i-5)] - 2.0*bz[j * nx + (i-6)])*(1.0/60.0);

}

i=2;

for (j = 0; j <= ny-2; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = ( 2.0*bz[j * nx + i] - 24.0*bz[j * nx + (i+1)] - 35.0*bz[j * nx + (i+2)] + 80.0*bz[j * nx + (i+3)] - 30.0*bz[j * nx + (i+4)] + 8.0*bz[j * nx + (i+5)] - bz[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-3;

for (j = 0; j <= ny-2; j++)

{

if isnan(bz[j * nx + i]) continue;

derx_bz[j * nx + i] = (-2.0*bz[j * nx + i] + 24.0*bz[j * nx + (i-1)] + 35.0*bz[j * nx + (i-2)] - 80.0*bz[j * nx + (i-3)] + 30.0*bz[j * nx + (i-4)] - 8.0*bz[j * nx + (i-5)] + bz[j * nx + (i-6)])*(1.0/60.0);

}

j=0;

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

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = (-147.0*bz[j * nx + i] + 360.0*bz[(j+1) * nx + i] - 450.0*bz[(j+2) * nx + i] + 400.0*bz[(j+3) * nx + i] - 225.0*bz[(j+4) * nx + i] + 72.0*bz[(j+5) * nx + i] - 10.0*bz[(j+6) * nx + i])*(1.0/60.0);

dery_bz[j * nx + i] = ( (-3*bz[j*nx + i]) + (4*bz[(j+1) * nx + i]) - (bz[(j+2) * nx + i]) )*0.5;

}

j=ny-1;

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

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = ( 147.0*bz[j * nx + i] - 360.0*bz[(j-1) * nx + i] + 450.0*bz[(j-2) * nx + i] - 400.0*bz[(j-3) * nx + i] + 225.0*bz[(j-4) * nx + i] - 72.0*bz[(j-5) * nx + i] + 10.0*bz[(j-6) * nx + i])*(1.0/60.0);

dery_bz[j * nx + i] = ( (3*bz[j * nx + i]) + (-4*bz[(j-1) * nx + i]) - (-bz[(j-2) * nx + i]) )*0.5;

}

j=1;

for (i = 0; i <= nx-2; i++)

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = (-10.0*bz[j * nx + i] - 77.0*bz[(j+1) * nx + i] + 150.0*bz[(j+2) * nx + i] - 100.0*bz[(j+3) * nx + i] + 50.0*bz[(j+4) * nx + i] - 15.0*bz[(j+5) * nx + i] + 2.0*bz[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-2;

for (i = 0; i <= nx-2; i++)

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = ( 10.0*bz[j * nx + i] + 77.0*bz[(j-1) * nx + i] - 150.0*bz[(j-2) * nx + i] + 100.0*bz[(j-3) * nx + i] - 50.0*bz[(j-4) * nx + i] + 15.0*bz[(j-5) * nx + i] - 2.0*bz[(j-6) * nx + i])*(1.0/60.0);

}

j=2;

for (i = 0; i <= nx-3; i++)

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = ( 2.0*bz[j * nx + i] - 24.0*bz[(j+1) * nx + i] - 35.0*bz[(j+2) * nx + i] + 80.0*bz[(j+3) * nx + i] - 30.0*bz[(j+4) * nx + i] + 8.0*bz[(j+5) * nx + i] - bz[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-3;

for (i = 0; i <= nx-3; i++)

{

if isnan(bz[j * nx + i]) continue;

dery_bz[j * nx + i] = (-2.0*bz[j * nx + i] + 24.0*bz[(j-1) * nx + i] + 35.0*bz[(j-2) * nx + i] - 80.0*bz[(j-3) * nx + i] + 30.0*bz[(j-4) * nx + i] - 8.0*bz[(j-5) * nx + i] + bz[(j-6) * nx + i])*(1.0/60.0);

}

Line 598 int computeBzderivative(float *bz, float

Line 498 int computeBzderivative(float *bz, float

{

for (j = 0; j <= ny-1; j++)

{

// if ( (derx_bz[j * nx + i]-dery_bz[j * nx + i]) == 0) continue;

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if ( (derx_bz[j * nx + i] + dery_bz[j * nx + i]) == 0) continue;

if isnan(bz[j * nx + i]) continue;

//if isnan(bz_err[j * nx + i]) continue;

if isnan(bz[(j+1) * nx + i]) continue;

if isnan(bz[(j-1) * nx + i]) continue;

if isnan(bz[j * nx + i-1]) continue;

if isnan(bz[j * nx + i+1]) continue;

if isnan(bz_err[j * nx + i]) continue;

if isnan(derx_bz[j * nx + i]) continue;

if isnan(dery_bz[j * nx + i]) continue;

sum += sqrt( derx_bz[j * nx + i]*derx_bz[j * nx + i] + dery_bz[j * nx + i]*dery_bz[j * nx + i] ); /* Units of Gauss */

err += 2.0*bz_err[j * nx + i]*bz_err[j * nx + i];

err += (((bz[(j+1) * nx + i]-bz[(j-1) * nx + i])*(bz[(j+1) * nx + i]-bz[(j-1) * nx + i])) * (bz_err[(j+1) * nx + i]*bz_err[(j+1) * nx + i] + bz_err[(j-1) * nx + i]*bz_err[(j-1) * nx + i])) /

(16.0*( derx_bz[j * nx + i]*derx_bz[j * nx + i] + dery_bz[j * nx + i]*dery_bz[j * nx + i] )) +

(((bz[j * nx + (i+1)]-bz[j * nx + (i-1)])*(bz[j * nx + (i+1)]-bz[j * nx + (i-1)])) * (bz_err[j * nx + (i+1)]*bz_err[j * nx + (i+1)] + bz_err[j * nx + (i-1)]*bz_err[j * nx + (i-1)])) /

(16.0*( derx_bz[j * nx + i]*derx_bz[j * nx + i] + dery_bz[j * nx + i]*dery_bz[j * nx + i] )) ;

count_mask++;

}

*mean_derivative_bz_ptr = (sum)/(count_mask); // would be divided by ((nx-2)*(ny-2)) if shape of count_mask = shape of magnetogram

*mean_derivative_bz_err_ptr = (sqrt(err))/(count_mask); // error in the quantity (sum)/(count_mask)

printf("MEANGBZ=%f\n",*mean_derivative_bz_ptr);

//printf("MEANGBZ=%f\n",*mean_derivative_bz_ptr);

printf("MEANGBZ_err=%f\n",*mean_derivative_bz_err_ptr);

//printf("MEANGBZ_err=%f\n",*mean_derivative_bz_err_ptr);

return 0;

}

/*===========================================*/

/* Example function 8: Current Jz = (dBy/dx) - (dBx/dy) */

// In discretized space like data pixels,

Line 627 int computeBzderivative(float *bz, float

Line 533 int computeBzderivative(float *bz, float

// the integration of the field Bx and By along

// the circumference of the data pixel divided by the area of the pixel.

// One form of differencing (a word for the differential operator

// in the discretized space) of the curl is expressed as the following,

// in the discretized space) of the curl is expressed as

// which utilizes a second-order finite difference method:

// (dx * (Bx(i,j-1)+Bx(i,j)) / 2

// +dy * (By(i+1,j)+By(i,j)) / 2

// -dx * (Bx(i,j+1)+Bx(i,j)) / 2

// -dy * (By(i-1,j)+By(i,j)) / 2) / (dx * dy)

// However, for the purposes of this calculation, we will use a sixth-order finite difference

// method taken from the pencil code:

// dBy/dx = ( -By*(i-3,j) + 9By(i-2,j) - 45By(i-1,j) + 45By(i+1,j) - 9By(i+2,j) + By(i+3,j) )/ 60

// and similarly for dBx/dy.

// To change units from Gauss/pixel to mA/m^2 (the units for Jz in Leka and Barnes, 2003),

// one must perform the following unit conversions:

// (Gauss)(1/arcsec)(arcsec/meter)(Newton/Gauss*Ampere*meter)(Ampere^2/Newton)(milliAmpere/Ampere), or

Line 664 int computeBzderivative(float *bz, float

Line 562 int computeBzderivative(float *bz, float

// int *mask, int *bitmask, float cdelt1, double rsun_ref, double rsun_obs,float *derx, float *dery, float *noisebx,

// float *noiseby, float *noisebz)

int computeJz(float *bx_err, float *by_err, float *bx, float *by, int *dims, float *jz, float *jz_err, float *jz_err_squared,

int *mask, int *bitmask, float cdelt1, double rsun_ref, double rsun_obs,float *derx, float *dery)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

printf("nx=%d\n",nx);

int i = 0;

printf("ny=%d\n",ny);

int j = 0;

int count_mask = 0;

if (nx <= 0 || ny <= 0) return 1;

float curl=0.0, us_i=0.0,test_perimeter=0.0,mean_curl=0.0;

/* Calculate the derivative*/

/* brute force method of calculating the derivative (no consideration for edges) */

for (i = 3; i <= nx-4; i++)

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

{

for (j = 0; j <= ny-1; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = (-by[j * nx + (i-3)] + 9.0*by[j * nx + (i-2)] - 45.0*by[j * nx + (i-1)] + 45*by[j * nx + (i+1)] - 9.0*by[j * nx + (i+2)] + by[j * nx + (i+3)])*(1.0/60.0);

derx[j * nx + i] = (by[j * nx + i+1] - by[j * nx + i-1])*0.5;

}

/* brute force method of calculating the derivative (no consideration for edges) */

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

{

for (j = 3; j <= ny-4; j++)

for (j = 1; j <= ny-2; j++)

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = (-bx[(j-3) * nx + i] + 9.0*bx[(j-2) * nx + i] - 45.0*bx[(j-1) * nx + i] + 45*bx[(j+1) * nx + i] - 9.0*bx[(j+2) * nx + i] + bx[(j+3) * nx + i])*(1.0/60.0);

dery[j * nx + i] = (bx[(j+1) * nx + i] - bx[(j-1) * nx + i])*0.5;

}

/* consider the edges: 3 pixels on each edge, for a total of 12 edge formulae below */

// consider the edges

i=0;

for (j = 0; j <= ny-1; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = (-147.0*by[j * nx + i] + 360.0*by[j * nx + (i+1)] - 450.0*by[j * nx + (i+2)] + 400.0*by[j * nx + (i+3)] - 225.0*by[j * nx + (i+4)] + 72.0*by[j * nx + (i+5)] - 10.0*by[j * nx + (i+6)])*(1.0/60.0);

derx[j * nx + i] = ( (-3*by[j * nx + i]) + (4*by[j * nx + (i+1)]) - (by[j * nx + (i+2)]) )*0.5;

}

i=nx-1;

for (j = 0; j <= ny-1; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = ( 147.0*by[j * nx + i] - 360.0*by[j * nx + (i-1)] + 450.0*by[j * nx + (i-2)] - 400.0*by[j * nx + (i-3)] + 225.0*by[j * nx + (i-4)] - 72.0*by[j * nx + (i-5)] + 10.0*by[j * nx + (i-6)])*(1.0/60.0);

derx[j * nx + i] = ( (3*by[j * nx + i]) + (-4*by[j * nx + (i-1)]) - (-by[j * nx + (i-2)]) )*0.5;

}

i=1;

for (j = 0; j <= ny-2; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = (-10.0*by[j * nx + i] - 77.0*by[j * nx + (i+1)] + 150.0*by[j * nx + (i+2)] - 100.0*by[j * nx + (i+3)] + 50.0*by[j * nx + (i+4)] - 15.0*by[j * nx + (i+5)] + 2.0*by[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-2;

for (j = 0; j <= ny-2; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = ( 10.0*by[j * nx + i] + 77.0*by[j * nx + (i-1)] - 150.0*by[j * nx + (i-2)] + 100.0*by[j * nx + (i-3)] - 50.0*by[j * nx + (i-4)] + 15.0*by[j * nx + (i-5)] - 2.0*by[j * nx + (i-6)])*(1.0/60.0);

}

i=2;

for (j = 0; j <= ny-2; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = ( 2.0*by[j * nx + i] - 24.0*by[j * nx + (i+1)] - 35.0*by[j * nx + (i+2)] + 80.0*by[j * nx + (i+3)] - 30.0*by[j * nx + (i+4)] + 8.0*by[j * nx + (i+5)] - by[j * nx + (i+6)])*(1.0/60.0);

}

i=nx-3;

for (j = 0; j <= ny-2; j++)

{

if isnan(by[j * nx + i]) continue;

derx[j * nx + i] = (-2.0*by[j * nx + i] + 24.0*by[j * nx + (i-1)] + 35.0*by[j * nx + (i-2)] - 80.0*by[j * nx + (i-3)] + 30.0*by[j * nx + (i-4)] - 8.0*by[j * nx + (i-5)] + by[j * nx + (i-6)])*(1.0/60.0);

}

j=0;

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

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = (-147.0*bx[j * nx + i] + 360.0*bx[(j+1) * nx + i] - 450.0*bx[(j+2) * nx + i] + 400.0*bx[(j+3) * nx + i] - 225.0*bx[(j+4) * nx + i] + 72.0*bx[(j+5) * nx + i] - 10.0*bx[(j+6) * nx + i])*(1.0/60.0);

dery[j * nx + i] = ( (-3*bx[j*nx + i]) + (4*bx[(j+1) * nx + i]) - (bx[(j+2) * nx + i]) )*0.5;

}

j=ny-1;

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

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = ( 147.0*bx[j * nx + i] - 360.0*bx[(j-1) * nx + i] + 450.0*bx[(j-2) * nx + i] - 400.0*bx[(j-3) * nx + i] + 225.0*bx[(j-4) * nx + i] - 72.0*bx[(j-5) * nx + i] + 10.0*bx[(j-6) * nx + i])*(1.0/60.0);

dery[j * nx + i] = ( (3*bx[j * nx + i]) + (-4*bx[(j-1) * nx + i]) - (-bx[(j-2) * nx + i]) )*0.5;

}

j=1;

for (i = 0; i <= nx-2; i++)

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = (-10.0*bx[j * nx + i] - 77.0*bx[(j+1) * nx + i] + 150.0*bx[(j+2) * nx + i] - 100.0*bx[(j+3) * nx + i] + 50.0*bx[(j+4) * nx + i] - 15.0*bx[(j+5) * nx + i] + 2.0*bx[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-2;

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

for (i = 0; i <= nx-2; i++)

{

if isnan(bx[j * nx + i]) continue;

for (j = 1; j <= ny-2; j++)

dery[j * nx + i] = ( 10.0*bx[j * nx + i] + 77.0*bx[(j-1) * nx + i] - 150.0*bx[(j-2) * nx + i] + 100.0*bx[(j-3) * nx + i] - 50.0*bx[(j-4) * nx + i] + 15.0*bx[(j-5) * nx + i] - 2.0*bx[(j-6) * nx + i])*(1.0/60.0);

}

j=2;

for (i = 0; i <= nx-3; i++)

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = ( 2.0*bx[j * nx + i] - 24.0*bx[(j+1) * nx + i] - 35.0*bx[(j+2) * nx + i] + 80.0*bx[(j+3) * nx + i] - 30.0*bx[(j+4) * nx + i] + 8.0*bx[(j+5) * nx + i] - bx[(j+6) * nx + i])*(1.0/60.0);

}

j=ny-3;

for (i = 0; i <= nx-3; i++)

{

if isnan(bx[j * nx + i]) continue;

dery[j * nx + i] = (-2.0*bx[j * nx + i] + 24.0*bx[(j-1) * nx + i] + 35.0*bx[(j-2) * nx + i] - 80.0*bx[(j-3) * nx + i] + 30.0*bx[(j-4) * nx + i] - 8.0*bx[(j-5) * nx + i] + bx[(j-6) * nx + i])*(1.0/60.0);

}

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

{

for (j = 0; j <= ny-1; j++)

{

/* calculate jz at all points */

// calculate jz at all points

jz[j * nx + i] = (derx[j * nx + i]-dery[j * nx + i]); /* jz is in units of Gauss/pix */

/* calculate the error in jz at all points */

jz_err[j * nx + i]=sqrt( (1.0/60.0)*bx_err[(j-3) * nx + i]*(1.0/60.0)*bx_err[(j-3) * nx + i] + (9.0/60.0)*bx_err[(j-2) * nx + i]*(9.0/60.0)*bx_err[(j-2) * nx + i] + (45.0/60.0)*bx_err[(j-1) * nx + i]*(45.0/60.0)*bx_err[(j-1) * nx + i] +

(1.0/60.0)*bx_err[(j+3) * nx + i]*(1.0/60.0)*bx_err[(j+3) * nx + i] + (9.0/60.0)*bx_err[(j+2) * nx + i]*(9.0/60.0)*bx_err[(j+2) * nx + i] + (45.0/60.0)*bx_err[(j+1) * nx + i]*(45.0/60.0)*bx_err[(j+1) * nx + i] +

(1.0/60.0)*by_err[j * nx + (i-3)]*(1.0/60.0)*by_err[j * nx + (i-3)] + (9.0/60.0)*by_err[j * nx + (i-2)]*(9.0/60.0)*by_err[j * nx + (i-2)] + (45.0/60.0)*by_err[j * nx + (i-1)]*(45.0/60.0)*by_err[j * nx + (i-1)] +

(1.0/60.0)*by_err[j * nx + (i+3)]*(1.0/60.0)*by_err[j * nx + (i+3)] + (9.0/60.0)*by_err[j * nx + (i+2)]*(9.0/60.0)*by_err[j * nx + (i+2)] + (45.0/60.0)*by_err[j * nx + (i+1)]*(45.0/60.0)*by_err[j * nx + (i+1)] );

jz[j * nx + i] = (derx[j * nx + i]-dery[j * nx + i]); // jz is in units of Gauss/pix

jz_err[j * nx + i] = 0.5*sqrt( (bx_err[(j+1) * nx + i]*bx_err[(j+1) * nx + i]) + (bx_err[(j-1) * nx + i]*bx_err[(j-1) * nx + i]) +

(by_err[j * nx + (i+1)]*by_err[j * nx + (i+1)]) + (by_err[j * nx + (i-1)]*by_err[j * nx + (i-1)]) ) ;

jz_err_squared[j * nx + i]=(jz_err[j * nx + i]*jz_err[j * nx + i]);

count_mask++;

}

//printf("\n");

}

return 0;

}

/*===========================================*/

/* Example function 9: Compute quantities on Jz array */

/* Example function 9: Compute quantities on smoothed Jz array */

// Compute mean and total current on Jz array.

// All of the subsequent functions, including this one, use a smoothed Jz array. The smoothing is performed by Jesper's

// fresize routines. These routines are located at /cvs/JSOC/proj/libs/interpolate. A Gaussian with a FWHM of 4 pixels

// and truncation width of 12 pixels is used to smooth the array; however, a quick analysis shows that the mean values

// of qualities like Jz and helicity do not change much as a result of smoothing. The smoothed array will, of course,

// give a lower total Jz as the stron field pixels have been smoothed out to neighboring weaker field pixels.

int computeJzsmooth(float *bx, float *by, int *dims, float *jz, float *jz_smooth, float *jz_err, float *jz_rms_err, float *jz_err_squared_smooth,

float *mean_jz_ptr, float *mean_jz_err_ptr, float *us_i_ptr, float *us_i_err_ptr, int *mask, int *bitmask,

Line 826 int computeJzsmooth(float *bx, float *by

Line 653 int computeJzsmooth(float *bx, float *by

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

int j = 0;

int count_mask = 0;

double curl = 0.0;

double us_i = 0.0;

double err = 0.0;

if (nx <= 0 || ny <= 0) return 1;

float curl,us_i,test_perimeter,mean_curl,err=0.0;

/* At this point, use the smoothed Jz array with a Gaussian (FWHM of 4 pix and truncation width of 12 pixels) but keep the original array dimensions*/

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

{

for (j = 0; j <= ny-1; j++)

{

//printf("%f ",jz_smooth[j * nx + i]);

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if isnan(derx[j * nx + i]) continue;

if isnan(dery[j * nx + i]) continue;

//if isnan(jz_smooth[j * nx + i]) continue;

//curl += (jz_smooth[j * nx + i])*(1/cdelt1)*(rsun_obs/rsun_ref)*(0.00010)*(1/MUNAUGHT)*(1000.); /* curl is in units of mA / m^2 */

//us_i += fabs(jz_smooth[j * nx + i])*(cdelt1/1)*(rsun_ref/rsun_obs)*(0.00010)*(1/MUNAUGHT); /* us_i is in units of A */

//jz_rms_err[j * nx + i] = sqrt(jz_err_squared_smooth[j * nx + i]);

//err += (jz_rms_err[j * nx + i]*jz_rms_err[j * nx + i]);

if isnan(jz[j * nx + i]) continue;

curl += (jz[j * nx + i])*(1/cdelt1)*(rsun_obs/rsun_ref)*(0.00010)*(1/MUNAUGHT)*(1000.); /* curl is in units of mA / m^2 */

us_i += fabs(jz[j * nx + i])*(cdelt1/1)*(rsun_ref/rsun_obs)*(0.00010)*(1/MUNAUGHT); /* us_i is in units of A */

err += (jz_err[j * nx + i]*jz_err[j * nx + i]);

count_mask++;

}

//printf("\n");

}

/* Calculate mean vertical current density (mean_curl) and total unsigned vertical current (us_i) using smoothed Jz array and continue conditions above */

/* Calculate mean vertical current density (mean_jz) and total unsigned vertical current (us_i) using smoothed Jz array and continue conditions above */

*mean_jz_ptr = curl/(count_mask); /* mean_jz gets populated as MEANJZD */

*mean_jz_err_ptr = (sqrt(err))*fabs(((rsun_obs/rsun_ref)*(0.00010)*(1/MUNAUGHT)*(1000.))/(count_mask)); // error in the quantity MEANJZD

*mean_jz_err_ptr = (sqrt(err)/count_mask)*((1/cdelt1)*(rsun_obs/rsun_ref)*(0.00010)*(1/MUNAUGHT)*(1000.)); // error in the quantity MEANJZD

*us_i_ptr = (us_i); /* us_i gets populated as TOTUSJZ */

*us_i_err_ptr = (sqrt(err))*fabs((cdelt1/1)*(rsun_ref/rsun_obs)*(0.00010)*(1/MUNAUGHT)); // error in the quantity TOTUSJZ

*us_i_err_ptr = (sqrt(err))*((cdelt1/1)*(rsun_ref/rsun_obs)*(0.00010)*(1/MUNAUGHT)); // error in the quantity TOTUSJZ

printf("MEANJZD=%f\n",*mean_jz_ptr);

//printf("MEANJZD=%f\n",*mean_jz_ptr);

printf("MEANJZD_err=%f\n",*mean_jz_err_ptr);

//printf("MEANJZD_err=%f\n",*mean_jz_err_ptr);

printf("TOTUSJZ=%g\n",*us_i_ptr);

//printf("TOTUSJZ=%g\n",*us_i_ptr);

printf("TOTUSJZ_err=%g\n",*us_i_err_ptr);

//printf("TOTUSJZ_err=%g\n",*us_i_err_ptr);

return 0;

Line 879 int computeJzsmooth(float *bx, float *by

Line 702 int computeJzsmooth(float *bx, float *by

/* Example function 10: Twist Parameter, alpha */

// The twist parameter, alpha, is defined as alpha = Jz/Bz. In this case, the calculation

// for alpha is calculated in the following way (different from Leka and Barnes' approach):

// for alpha is weighted by Bz (following Hagino et al., http://adsabs.harvard.edu/abs/2004PASJ...56..831H):

// (sum of all positive Bz + abs(sum of all negative Bz)) = avg Bz

// numerator = sum of all Jz*Bz

// (abs(sum of all Jz at positive Bz) + abs(sum of all Jz at negative Bz)) = avg Jz

// denominator = sum of Bz*Bz

// avg alpha = avg Jz / avg Bz

// alpha = numerator/denominator

// The sign is assigned as follows:

// If the sum of all Bz is greater than 0, then evaluate the sum of Jz at the positive Bz pixels.

// If this value is > 0, then alpha is > 0.

// If this value is < 0, then alpha is <0.

// If the sum of all Bz is less than 0, then evaluate the sum of Jz at the negative Bz pixels.

// If this value is > 0, then alpha is < 0.

// If this value is < 0, then alpha is > 0.

// The units of alpha are in 1/Mm

// The units of Jz are in Gauss/pix; the units of Bz are in Gauss.

Line 904 int computeJzsmooth(float *bx, float *by

Line 718 int computeJzsmooth(float *bx, float *by

int computeAlpha(float *jz_err, float *bz_err, float *bz, int *dims, float *jz, float *jz_smooth, float *mean_alpha_ptr, float *mean_alpha_err_ptr, int *mask, int *bitmask, float cdelt1, double rsun_ref, double rsun_obs)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask, a,b,c,d=0;

int ny = dims[1];

int i = 0;

int j = 0;

double alpha_total = 0.0;

double C = ((1/cdelt1)*(rsun_obs/rsun_ref)*(1000000.));

double total = 0.0;

double A = 0.0;

double B = 0.0;

if (nx <= 0 || ny <= 0) return 1;

float aa, bb, cc, bznew, alpha2, sum1, sum2, sum3, sum4, sum, sum5, sum6, sum_err=0.0;

for (i = 1; i < nx-1; i++)

{

for (j = 1; j < ny-1; j++)

{

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

//if isnan(jz_smooth[j * nx + i]) continue;

if isnan(jz[j * nx + i]) continue;

if isnan(bz[j * nx + i]) continue;

//if (jz_smooth[j * nx + i] == 0) continue;

if (jz[j * nx + i] == 0.0) continue;

if (bz_err[j * nx + i] == 0.0) continue;

if (bz[j * nx + i] == 0.0) continue;

if (bz[j * nx + i] > 0) sum1 += ( bz[j * nx + i] ); a++;

A += jz[j*nx+i]*bz[j*nx+i];

if (bz[j * nx + i] <= 0) sum2 += ( bz[j * nx + i] ); b++;

B += bz[j*nx+i]*bz[j*nx+i];

//if (bz[j * nx + i] > 0) sum3 += ( jz_smooth[j * nx + i]);

//if (bz[j * nx + i] <= 0) sum4 += ( jz_smooth[j * nx + i]);

if (bz[j * nx + i] > 0) sum3 += ( jz[j * nx + i] ); c++;

if (bz[j * nx + i] <= 0) sum4 += ( jz[j * nx + i] ); d++;

sum5 += bz[j * nx + i];

/* sum_err is a fractional uncertainty */

sum_err += sqrt(((jz_err[j * nx + i]*jz_err[j * nx + i])/(jz[j * nx + i]*jz[j * nx + i])) + ((bz_err[j * nx + i]*bz_err[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i]))) * fabs( ( (jz[j * nx + i]) / (bz[j * nx + i]) ) *(1/cdelt1)*(rsun_obs/rsun_ref)*(1000000.));

count_mask++;

}

sum = (((fabs(sum3))+(fabs(sum4)))/((fabs(sum2))+sum1))*((1/cdelt1)*(rsun_obs/rsun_ref)*(1000000.)); /* the units for (jz/bz) are 1/Mm */

for (i = 1; i < nx-1; i++)

{

/* Determine the sign of alpha */

for (j = 1; j < ny-1; j++)

if ((sum5 > 0) && (sum3 > 0)) sum=sum;

{

if ((sum5 > 0) && (sum3 <= 0)) sum=-sum;

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if ((sum5 < 0) && (sum4 <= 0)) sum=sum;

if isnan(jz[j * nx + i]) continue;

if ((sum5 < 0) && (sum4 > 0)) sum=-sum;

if isnan(bz[j * nx + i]) continue;

if (jz[j * nx + i] == 0.0) continue;

*mean_alpha_ptr = sum; /* Units are 1/Mm */

if (bz[j * nx + i] == 0.0) continue;

*mean_alpha_err_ptr = (sqrt(sum_err*sum_err)) / ((a+b+c+d)*100.); // error in the quantity (sum)/(count_mask); factor of 100 comes from converting percent

total += bz[j*nx+i]*bz[j*nx+i]*jz_err[j*nx+i]*jz_err[j*nx+i] + (jz[j*nx+i]-2*bz[j*nx+i]*A/B)*(jz[j*nx+i]-2*bz[j*nx+i]*A/B)*bz_err[j*nx+i]*bz_err[j*nx+i];

}

printf("a=%d\n",a);

}

printf("b=%d\n",b);

printf("d=%d\n",d);

printf("c=%d\n",c);

printf("MEANALP=%f\n",*mean_alpha_ptr);

/* Determine the absolute value of alpha. The units for alpha are 1/Mm */

printf("MEANALP_err=%f\n",*mean_alpha_err_ptr);

alpha_total = ((A/B)*C);

*mean_alpha_ptr = alpha_total;

*mean_alpha_err_ptr = (C/B)*(sqrt(total));

return 0;

}

Line 973 int computeHelicity(float *jz_err, float

Line 779 int computeHelicity(float *jz_err, float

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

int j = 0;

int count_mask = 0;

double sum = 0.0;

double sum2 = 0.0;

double err = 0.0;

if (nx <= 0 || ny <= 0) return 1;

float sum,sum2,sum_err=0.0;

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

{

for (j = 0; j < ny; j++)

Line 987 int computeHelicity(float *jz_err, float

Line 797 int computeHelicity(float *jz_err, float

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if isnan(jz[j * nx + i]) continue;

if isnan(bz[j * nx + i]) continue;

if isnan(jz_err[j * nx + i]) continue;

if isnan(bz_err[j * nx + i]) continue;

if (bz[j * nx + i] == 0.0) continue;

if (jz[j * nx + i] == 0.0) continue;

sum += (jz[j * nx + i]*bz[j * nx + i])*(1/cdelt1)*(rsun_obs/rsun_ref); // contributes to MEANJZH and ABSNJZH

sum2 += fabs(jz[j * nx + i]*bz[j * nx + i])*(1/cdelt1)*(rsun_obs/rsun_ref); // contributes to TOTUSJH

sum_err += sqrt(((jz_err[j * nx + i]*jz_err[j * nx + i])/(jz[j * nx + i]*jz[j * nx + i])) + ((bz_err[j * nx + i]*bz_err[j * nx + i])/(bz[j * nx + i]*bz[j * nx + i]))) * fabs(jz[j * nx + i]*bz[j * nx + i]*(1/cdelt1)*(rsun_obs/rsun_ref));

err += (jz_err[j * nx + i]*jz_err[j * nx + i]*bz[j * nx + i]*bz[j * nx + i]) + (bz_err[j * nx + i]*bz_err[j * nx + i]*jz[j * nx + i]*jz[j * nx + i]);

count_mask++;

}

Line 1000 int computeHelicity(float *jz_err, float

Line 812 int computeHelicity(float *jz_err, float

*total_us_ih_ptr = sum2 ; /* Units are G^2 / m ; keyword is TOTUSJH */

*total_abs_ih_ptr = fabs(sum) ; /* Units are G^2 / m ; keyword is ABSNJZH */

*mean_ih_err_ptr = (sqrt(sum_err*sum_err)) / (count_mask*100.) ; // error in the quantity MEANJZH

*mean_ih_err_ptr = (sqrt(err)/count_mask)*(1/cdelt1)*(rsun_obs/rsun_ref) ; // error in the quantity MEANJZH

*total_us_ih_err_ptr = (sqrt(sum_err*sum_err)) / (100.) ; // error in the quantity TOTUSJH

*total_us_ih_err_ptr = (sqrt(err))*(1/cdelt1)*(rsun_obs/rsun_ref) ; // error in the quantity TOTUSJH

*total_abs_ih_err_ptr = (sqrt(sum_err*sum_err)) / (100.) ; // error in the quantity ABSNJZH

*total_abs_ih_err_ptr = (sqrt(err))*(1/cdelt1)*(rsun_obs/rsun_ref) ; // error in the quantity ABSNJZH

printf("MEANJZH=%f\n",*mean_ih_ptr);

//printf("MEANJZH=%f\n",*mean_ih_ptr);

printf("MEANJZH_err=%f\n",*mean_ih_err_ptr);

//printf("MEANJZH_err=%f\n",*mean_ih_err_ptr);

printf("TOTUSJH=%f\n",*total_us_ih_ptr);

//printf("TOTUSJH=%f\n",*total_us_ih_ptr);

printf("TOTUSJH_err=%f\n",*total_us_ih_err_ptr);

//printf("TOTUSJH_err=%f\n",*total_us_ih_err_ptr);

printf("ABSNJZH=%f\n",*total_abs_ih_ptr);

//printf("ABSNJZH=%f\n",*total_abs_ih_ptr);

printf("ABSNJZH_err=%f\n",*total_abs_ih_err_ptr);

//printf("ABSNJZH_err=%f\n",*total_abs_ih_err_ptr);

return 0;

}

Line 1031 int computeSumAbsPerPolarity(float *jz_e

Line 843 int computeSumAbsPerPolarity(float *jz_e

int *mask, int *bitmask, float cdelt1, double rsun_ref, double rsun_obs)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i=0;

int j=0;

int count_mask=0;

double sum1=0.0;

double sum2=0.0;

double err=0.0;

*totaljzptr=0.0;

if (nx <= 0 || ny <= 0) return 1;

*totaljzptr=0.0;

float sum1,sum2,err=0.0;

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

{

for (j = 0; j < ny; j++)

{

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if isnan(bz[j * nx + i]) continue;

if isnan(jz[j * nx + i]) continue;

if (bz[j * nx + i] > 0) sum1 += ( jz[j * nx + i])*(1/cdelt1)*(0.00010)*(1/MUNAUGHT)*(rsun_ref/rsun_obs);

if (bz[j * nx + i] <= 0) sum2 += ( jz[j * nx + i])*(1/cdelt1)*(0.00010)*(1/MUNAUGHT)*(rsun_ref/rsun_obs);

err += (jz_err[j * nx + i]*jz_err[j * nx + i]);

Line 1054 int computeSumAbsPerPolarity(float *jz_e

Line 871 int computeSumAbsPerPolarity(float *jz_e

*totaljzptr = fabs(sum1) + fabs(sum2); /* Units are A */

*totaljz_err_ptr = sqrt(err)*(1/cdelt1)*fabs((0.00010)*(1/MUNAUGHT)*(rsun_ref/rsun_obs));

printf("SAVNCPP=%g\n",*totaljzptr);

//printf("SAVNCPP=%g\n",*totaljzptr);

printf("SAVNCPP_err=%g\n",*totaljz_err_ptr);

//printf("SAVNCPP_err=%g\n",*totaljz_err_ptr);

return 0;

}

Line 1063 int computeSumAbsPerPolarity(float *jz_e

Line 880 int computeSumAbsPerPolarity(float *jz_e

/*===========================================*/

/* Example function 13: Mean photospheric excess magnetic energy and total photospheric excess magnetic energy density */

// The units for magnetic energy density in cgs are ergs per cubic centimeter. The formula B^2/8*PI integrated over all space, dV

// automatically yields erg per cubic centimeter for an input B in Gauss.

// automatically yields erg per cubic centimeter for an input B in Gauss. Note that the 8*PI can come out of the integral; thus,

// the integral is over B^2 dV and the 8*PI is divided at the end.

// Total magnetic energy is the magnetic energy density times dA, or the area, and the units are thus ergs/cm. To convert

// ergs per centimeter cubed to ergs per centimeter, simply multiply by the area per pixel in cm:

Line 1077 int computeFreeEnergy(float *bx_err, flo

Line 895 int computeFreeEnergy(float *bx_err, flo

float cdelt1, double rsun_ref, double rsun_obs)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j, count_mask=0;

int ny = dims[1];

int i = 0;

if (nx <= 0 || ny <= 0) return 1;

int j = 0;

int count_mask = 0;

double sum = 0.0;

double sum1 = 0.0;

double err = 0.0;

*totpotptr=0.0;

*meanpotptr=0.0;

float sum,err=0.0;

if (nx <= 0 || ny <= 0) return 1;

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

{

Line 1093 int computeFreeEnergy(float *bx_err, flo

Line 915 int computeFreeEnergy(float *bx_err, flo

if ( mask[j * nx + i] < 70 || bitmask[j * nx + i] < 30 ) continue;

if isnan(bx[j * nx + i]) continue;

if isnan(by[j * nx + i]) continue;

sum += ( ((bpx[j * nx + i] - bx[j * nx + i])*(bpx[j * nx + i] - bx[j * nx + i])) + ((bpy[j * nx + i] - by[j * nx + i])*(bpy[j * nx + i] - by[j * nx + i])) ) / 8.*PI;

sum += ( ((bx[j * nx + i] - bpx[j * nx + i])*(bx[j * nx + i] - bpx[j * nx + i])) + ((by[j * nx + i] - bpy[j * nx + i])*(by[j * nx + i] - bpy[j * nx + i])) )*(cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0);

err += (4.0*bx[j * nx + i]*bx[j * nx + i]*bx_err[j * nx + i]*bx_err[j * nx + i]) + (4.0*by[j * nx + i]*by[j * nx + i]*by_err[j * nx + i]*by_err[j * nx + i]);

sum1 += ( ((bx[j * nx + i] - bpx[j * nx + i])*(bx[j * nx + i] - bpx[j * nx + i])) + ((by[j * nx + i] - bpy[j * nx + i])*(by[j * nx + i] - bpy[j * nx + i])) );

//err += 2.0*bz_err[j * nx + i]*bz_err[j * nx + i];

err += 4.0*(bx[j * nx + i] - bpx[j * nx + i])*(bx[j * nx + i] - bpx[j * nx + i])*(bx_err[j * nx + i]*bx_err[j * nx + i]) +

4.0*(by[j * nx + i] - bpy[j * nx + i])*(by[j * nx + i] - bpy[j * nx + i])*(by_err[j * nx + i]*by_err[j * nx + i]);

count_mask++;

}

*meanpotptr = (sum) / (count_mask); /* Units are ergs per cubic centimeter */

/* Units of meanpotptr are ergs per centimeter */

*meanpotptr = (sum1) / (count_mask*8.*PI) ; /* Units are ergs per cubic centimeter */

*meanpot_err_ptr = (sqrt(err)) / (count_mask*8.*PI); // error in the quantity (sum)/(count_mask)

//*mean_derivative_bz_err_ptr = (sqrt(err))/(count_mask); // error in the quantity (sum)/(count_mask)

/* Units of sum are ergs/cm^3, units of factor are cm^2/pix^2; therefore, units of totpotptr are ergs per centimeter */

*totpotptr = sum*(cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0*(1/8.*PI)) ;

*totpotptr = (sum)/(8.*PI);

*totpot_err_ptr = (sqrt(err))*fabs(cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0*(1/8.*PI));

*totpot_err_ptr = (sqrt(err))*fabs(cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0*(1/(8.*PI)));

printf("MEANPOT=%g\n",*meanpotptr);

//printf("MEANPOT=%g\n",*meanpotptr);

printf("MEANPOT_err=%g\n",*meanpot_err_ptr);

//printf("MEANPOT_err=%g\n",*meanpot_err_ptr);

printf("TOTPOT=%g\n",*totpotptr);

//printf("TOTPOT=%g\n",*totpotptr);

printf("TOTPOT_err=%g\n",*totpot_err_ptr);

//printf("TOTPOT_err=%g\n",*totpot_err_ptr);

return 0;

}

Line 1120 int computeFreeEnergy(float *bx_err, flo

Line 943 int computeFreeEnergy(float *bx_err, flo

/*===========================================*/

/* Example function 14: Mean 3D shear angle, area with shear greater than 45, mean horizontal shear angle, area with horizontal shear angle greater than 45 */

int computeShearAngle(float *bx_err, float *by_err, float *bh_err, float *bx, float *by, float *bz, float *bpx, float *bpy, float *bpz, int *dims,

int computeShearAngle(float *bx_err, float *by_err, float *bz_err, float *bx, float *by, float *bz, float *bpx, float *bpy, float *bpz, int *dims,

float *meanshear_angleptr, float *meanshear_angle_err_ptr, float *area_w_shear_gt_45ptr, int *mask, int *bitmask)

{

int nx = dims[0], ny = dims[1];

int nx = dims[0];

int i, j;

int ny = dims[1];

int i = 0;

int j = 0;

float count_mask = 0;

float count = 0;

double dotproduct = 0.0;

double magnitude_potential = 0.0;

double magnitude_vector = 0.0;

double shear_angle = 0.0;

double denominator = 0.0;

double term1 = 0.0;

double term2 = 0.0;

double term3 = 0.0;

double sumsum = 0.0;

double err = 0.0;

double part1 = 0.0;

double part2 = 0.0;

double part3 = 0.0;

*area_w_shear_gt_45ptr = 0.0;

*meanshear_angleptr = 0.0;

if (nx <= 0 || ny <= 0) return 1;

//*area_w_shear_gt_45ptr=0.0;

//*meanshear_angleptr=0.0;

float dotproduct, magnitude_potential, magnitude_vector, shear_angle,err=0.0, sum = 0.0, count=0.0, count_mask=0.0;

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

{

for (j = 0; j < ny; j++)

Line 1143 int computeShearAngle(float *bx_err, flo

Line 983 int computeShearAngle(float *bx_err, flo

if isnan(bz[j * nx + i]) continue;

if isnan(bx[j * nx + i]) continue;

if isnan(by[j * nx + i]) continue;

/* For mean 3D shear angle, area with shear greater than 45*/

if isnan(bx_err[j * nx + i]) continue;

if isnan(by_err[j * nx + i]) continue;

if isnan(bz_err[j * nx + i]) continue;

/* For mean 3D shear angle, percentage with shear greater than 45*/

dotproduct = (bpx[j * nx + i])*(bx[j * nx + i]) + (bpy[j * nx + i])*(by[j * nx + i]) + (bpz[j * nx + i])*(bz[j * nx + i]);

magnitude_potential = sqrt( (bpx[j * nx + i]*bpx[j * nx + i]) + (bpy[j * nx + i]*bpy[j * nx + i]) + (bpz[j * nx + i]*bpz[j * nx + i]));

magnitude_vector = sqrt( (bx[j * nx + i]*bx[j * nx + i]) + (by[j * nx + i]*by[j * nx + i]) + (bz[j * nx + i]*bz[j * nx + i]) );

//printf("dotproduct=%f\n",dotproduct);

//printf("magnitude_potential=%f\n",magnitude_potential);

//printf("magnitude_vector=%f\n",magnitude_vector);

shear_angle = acos(dotproduct/(magnitude_potential*magnitude_vector))*(180./PI);

sumsum += shear_angle;

//printf("shear_angle=%f\n",shear_angle);

count ++;

sum += shear_angle ;

err += -(1./(1.- sqrt(bx_err[j * nx + i]*bx_err[j * nx + i]+by_err[j * nx + i]*by_err[j * nx + i]+bh_err[j * nx + i]*bh_err[j * nx + i])));

if (shear_angle > 45) count_mask ++;

// For the error analysis

term1 = bx[j * nx + i]*by[j * nx + i]*bpy[j * nx + i] - by[j * nx + i]*by[j * nx + i]*bpx[j * nx + i] + bz[j * nx + i]*bx[j * nx + i]*bpz[j * nx + i] - bz[j * nx + i]*bz[j * nx + i]*bpx[j * nx + i];

term2 = bx[j * nx + i]*bx[j * nx + i]*bpy[j * nx + i] - bx[j * nx + i]*by[j * nx + i]*bpx[j * nx + i] + bx[j * nx + i]*bz[j * nx + i]*bpy[j * nx + i] - bz[j * nx + i]*by[j * nx + i]*bpz[j * nx + i];

term3 = bx[j * nx + i]*bx[j * nx + i]*bpz[j * nx + i] - bx[j * nx + i]*bz[j * nx + i]*bpx[j * nx + i] + by[j * nx + i]*by[j * nx + i]*bpz[j * nx + i] - by[j * nx + i]*bz[j * nx + i]*bpy[j * nx + i];

part1 = bx[j * nx + i]*bx[j * nx + i] + by[j * nx + i]*by[j * nx + i] + bz[j * nx + i]*bz[j * nx + i];

part2 = bpx[j * nx + i]*bpx[j * nx + i] + bpy[j * nx + i]*bpy[j * nx + i] + bpz[j * nx + i]*bpz[j * nx + i];

part3 = bx[j * nx + i]*bpx[j * nx + i] + by[j * nx + i]*bpy[j * nx + i] + bz[j * nx + i]*bpz[j * nx + i];

// denominator is squared

denominator = part1*part1*part1*part2*(1.0-((part3*part3)/(part1*part2)));

err = (term1*term1*bx_err[j * nx + i]*bx_err[j * nx + i])/(denominator) +

(term1*term1*bx_err[j * nx + i]*bx_err[j * nx + i])/(denominator) +

(term1*term1*bx_err[j * nx + i]*bx_err[j * nx + i])/(denominator) ;

}

/* For mean 3D shear angle, area with shear greater than 45*/

*meanshear_angleptr = (sum)/(count); /* Units are degrees */

*meanshear_angleptr = (sumsum)/(count); /* Units are degrees */

*meanshear_angle_err_ptr = (sqrt(err*err))/(count); // error in the quantity (sum)/(count_mask)

*meanshear_angle_err_ptr = (sqrt(err)/count_mask)*(180./PI);

*area_w_shear_gt_45ptr = (count_mask/(count))*(100.);/* The area here is a fractional area -- the % of the total area */

/* The area here is a fractional area -- the % of the total area. This has no error associated with it. */

*area_w_shear_gt_45ptr = (count_mask/(count))*(100.0);

//printf("MEANSHR=%f\n",*meanshear_angleptr);

//printf("MEANSHR_err=%f\n",*meanshear_angle_err_ptr);

//printf("SHRGT45=%f\n",*area_w_shear_gt_45ptr);

return 0;

}

/*===========================================*/

/* Example function 15: R parameter as defined in Schrijver, 2007 */

// Note that there is a restriction on the function fsample()

// If the following occurs:

// nx_out > floor((ny_in-1)/scale + 1)

// ny_out > floor((ny_in-1)/scale + 1),

// where n*_out are the dimensions of the output array and n*_in

// are the dimensions of the input array, fsample() will usually result

// in a segfault (though not always, depending on how the segfault was accessed.)

int computeR(float *bz_err, float *los, int *dims, float *Rparam, float cdelt1,

float *rim, float *p1p0, float *p1n0, float *p1p, float *p1n, float *p1,

float *pmap, int nx1, int ny1,

int scale, float *p1pad, int nxp, int nyp, float *pmapn)

{

int nx = dims[0];

int ny = dims[1];

int i = 0;

int j = 0;

int index, index1;

double sum = 0.0;

double err = 0.0;

*Rparam = 0.0;

struct fresize_struct fresboxcar, fresgauss;

struct fint_struct fints;

float sigma = 10.0/2.3548;

// set up convolution kernels

init_fresize_boxcar(&fresboxcar,1,1);

init_fresize_gaussian(&fresgauss,sigma,20,1);

// =============== [STEP 1] ===============

// bin the line-of-sight magnetogram down by a factor of scale

fsample(los, rim, nx, ny, nx, nx1, ny1, nx1, scale, 0, 0, 0.0);

// =============== [STEP 2] ===============

// identify positive and negative pixels greater than +/- 150 gauss

// and label those pixels with a 1.0 in arrays p1p0 and p1n0

for (i = 0; i < nx1; i++)

{

for (j = 0; j < ny1; j++)

{

index = j * nx1 + i;

if (rim[index] > 150)

p1p0[index]=1.0;

else

p1p0[index]=0.0;

if (rim[index] < -150)

p1n0[index]=1.0;

else

p1n0[index]=0.0;

}

// =============== [STEP 3] ===============

// smooth each of the negative and positive pixel bitmaps

fresize(&fresboxcar, p1p0, p1p, nx1, ny1, nx1, nx1, ny1, nx1, 0, 0, 0.0);

fresize(&fresboxcar, p1n0, p1n, nx1, ny1, nx1, nx1, ny1, nx1, 0, 0, 0.0);

// =============== [STEP 4] ===============

// find the pixels for which p1p and p1n are both equal to 1.

// this defines the polarity inversion line

for (i = 0; i < nx1; i++)

{

for (j = 0; j < ny1; j++)

{

index = j * nx1 + i;

if ((p1p[index] > 0.0) && (p1n[index] > 0.0))

p1[index]=1.0;

else

p1[index]=0.0;

}

// pad p1 with zeroes so that the gaussian colvolution in step 5

// does not cut off data within hwidth of the edge

// step i: zero p1pad

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

{

for (j = 0; j < nyp; j++)

{

index = j * nxp + i;

p1pad[index]=0.0;

}

// step ii: place p1 at the center of p1pad

for (i = 0; i < nx1; i++)

{

for (j = 0; j < ny1; j++)

{

index = j * nx1 + i;

index1 = (j+20) * nxp + (i+20);

p1pad[index1]=p1[index];

}

// =============== [STEP 5] ===============

// convolve the polarity inversion line map with a gaussian

// to identify the region near the plarity inversion line

// the resultant array is called pmap

fresize(&fresgauss, p1pad, pmap, nxp, nyp, nxp, nxp, nyp, nxp, 0, 0, 0.0);

// select out the nx1 x ny1 non-padded array within pmap

for (i = 0; i < nx1; i++)

{

for (j = 0; j < ny1; j++)

{

index = j * nx1 + i;

index1 = (j+20) * nxp + (i+20);

pmapn[index]=pmap[index1];

}

// =============== [STEP 6] ===============

// the R parameter is calculated

for (i = 0; i < nx1; i++)

{

for (j = 0; j < ny1; j++)

{

index = j * nx1 + i;

sum += pmapn[index]*abs(rim[index]);

}

printf("MEANSHR=%f\n",*meanshear_angleptr);

if (sum < 1.0)

printf("MEANSHR_err=%f\n",*meanshear_angle_err_ptr);

*Rparam = 0.0;

else

*Rparam = log10(sum);

free_fresize(&fresboxcar);

free_fresize(&fresgauss);

return 0;

}

/*===========================================*/

/* Example function 16: Lorentz force as defined in Fisher, 2012 */

// This calculation is adapted from Xudong's code

// at /proj/cgem/lorentz/apps/lorentz.c

int computeLorentz(float *bx, float *by, float *bz, float *fx, float *fy, float *fz, int *dims,

float *totfx_ptr, float *totfy_ptr, float *totfz_ptr, float *totbsq_ptr,

float *epsx_ptr, float *epsy_ptr, float *epsz_ptr, int *mask, int *bitmask,

float cdelt1, double rsun_ref, double rsun_obs)

{

int nx = dims[0];

int ny = dims[1];

int nxny = nx*ny;

int j = 0;

int index;

double totfx = 0, totfy = 0, totfz = 0;

double bsq = 0, totbsq = 0;

double epsx = 0, epsy = 0, epsz = 0;

double area = cdelt1*cdelt1*(rsun_ref/rsun_obs)*(rsun_ref/rsun_obs)*100.0*100.0;

double k_h = -1.0 * area / (4. * PI) / 1.0e20;

double k_z = area / (8. * PI) / 1.0e20;

/* Multiplier */

float vectorMulti[] = {1.,-1.,1.};

if (nx <= 0 || ny <= 0) return 1;

for (int i = 0; i < nxny; i++)

{

if ( mask[i] < 70 || bitmask[i] < 30 ) continue;

if isnan(bx[i]) continue;

if isnan(by[i]) continue;

if isnan(bz[i]) continue;

fx[i] = (bx[i] * vectorMulti[0]) * (bz[i] * vectorMulti[2]) * k_h;

fy[i] = (by[i] * vectorMulti[1]) * (bz[i] * vectorMulti[2]) * k_h;

fz[i] = (bx[i] * bx[i] + by[i] * by[i] - bz[i] * bz[i]) * k_z;

bsq = bx[i] * bx[i] + by[i] * by[i] + bz[i] * bz[i];

totfx += fx[i]; totfy += fy[i]; totfz += fz[i];

totbsq += bsq;

}

*totfx_ptr = totfx;

*totfy_ptr = totfy;

*totfz_ptr = totfz;

*totbsq_ptr = totbsq;

*epsx_ptr = (totfx / k_h) / totbsq;

*epsy_ptr = (totfy / k_h) / totbsq;

*epsz_ptr = (totfz / k_z) / totbsq;

return 0;

}

/*==================KEIJI'S CODE =========================*/

Line 1282 void greenpot(float *bx, float *by, floa

Line 1347 void greenpot(float *bx, float *by, floa

/*===========END OF KEIJI'S CODE =========================*/

char *sw_functions_version() // Returns CVS version of sw_functions.c

{

return strdup("$Id");

}

/* ---------------- end of this file ----------------*/

Legend:

Removed from v.1.9
changed lines
	Added in v.1.31

Karen Tian