function  [dev,d,h,i,f,x,y,z]=magdev(flat,flon,elevkm,year);

% function [dev,d,h,i,f,x,y,z]=magdev(flat,flon,elevkm,year);

% 

% compute magnetic deviation

%

% based on IGRF12 model (observed until end of 2014, predicted until end of 2019)

%

% input:  flat        - latitude (degree)

%         flon        - longitude (degree)

%         elevkm [0]  - elevation above mean geoid (km)

%         year        - decimal year

%

% output:	dev         - mag. deviation (degree)

% 

% 

% based of FORTRAN ROUTINE GEOMAG.FOR

% more info under  http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

% 

%

% version 0.5	last change 13.07.2015

% M. Visbeck, LDEO FEB 2000

% rewritten for other epochs, G. Krahmann, IFM-GEOMAR Mar 2007

%

% modified for >=R14                    GK, Jun 2007    0.1-->0.2

% switch to IGRF11                      GK, 08.11.2010  0.2-->0.3

% replaced sind/cosd with sind/cosd   GK, 31.05.2011  0.3-->0.4

% switch to IGRF12                      GK, 12.07.2015  0.4-->0.5

%======================================================================

%                    M A G D E V . M 

%                    doc: Wed Sep  4 18:17:31 2019

%                    dlm: Wed Sep  4 18:18:16 2019

%                    (c) 2019 G. Krahmann

%                    uE-Info: 40 49 NIL 0 0 72 0 2 8 NIL ofnI

%======================================================================

% CHANGES BY ANT:

%   SEp  4, 2019: - changed sin/cos_d to sin/cosd

%

% read the coefficients

%

fname = 'igrf12coeffs.xls';

warning off			% avoid non-sensical warning in >=R14

gh = xlsread(fname);

warning on

%

% determine the maximum order of polynomials

%

% this might need modification in future versions of the file

%

if year<2000 

  nmax = 10;

else

  nmax = 13;

end

%

% interpolate the coefficients in time

%

warning off	% another workaround for annoying >=R14 warnings

if year <= gh(1,end-1)

  gh2 = interp1( gh(1,3:end-1),gh(2:end,3:end-1)',year)';

else

  gh2 = interp1( gh(1,3:end-1),gh(2:end,3:end-1)',gh(1,end-1))';

  ghc = gh2*0;

  dummy = gh(2:end,end);

  good = find(~isnan(dummy));

  ghc(good) = dummy(good);

  gh2 = gh2+ghc*(year-gh(1,end-1));

end

warning on

% 

% set default elevation

%

if nargin<3

 elevkm=0;

end

%

% calculate field

%

[x,y,z] = shval3(flat,flon,elevkm,nmax,gh2);

[d,i,h,f]=dihf (x,y,z);

%

% convert units

%

dev=d*180/pi;

%

% more detailed screen output, if output is not stored

%

if nargout<1

 disp([' model ',fname,'  harmonics: ',int2str(nmax)])

 disp([' lat: ',num2str(flat)])

 disp([' lon: ',num2str(flon)])

 disp([' tim: ',num2str(year)])

 disp([' mag dev [deg]: ',num2str(d*180/pi)])

end

%=====================================================================

function [x,y,z] = shval3(flat,flon,elevkm,nmax,gh)

% function [x,y,z] = shval3(flat,flon,elevkm,nmax,gh)

% ================================================================

%

%       version 1.01

%

%       calculates field components from spherical harmonic (sh)

%       models.

%

%       input:

%           flat  - north latitude, in degrees

%           flon  - east longitude, in degrees

%           elevkm  - elevation above mean sea level 

%           nmax  - maximum degree and order of coefficients

%           gh    - schmidt quasi-normal internal spherical

%                   harmonic coefficients

%           iext  - external coefficients flag (= 0 if none)

%           ext   - the three 1st-degree external coefficients

%                   (not used if iext = 0)

%

%       output:

%           x     -  northward component

%           y     -  eastward component

%           z     -  vertically-downward component

%

%       based on subroutine 'igrf' by d. r. barraclough and

%       s. r. c. malin, report no. 71/1, institute of geological

%       sciences, u.k.

%

%       norman w. peddie, u.s. geological survey, mail stop 964,

%       federal center, box 25046, denver, colorado 80225

%

% ================================================================

%       the required sizes of the arrays used in this subroutine

%       depend on the value of nmax.  the minimum dimensions

%       needed are indicated in the table below.  (note that this

%       version is dimensioned for nmax of 14 or less).

%

% ================================================================

r=elevkm;

erad=6371.2;

a2=40680925.;

b2=40408588.;

slat = sind(flat);

aa = min(89.999,max(-89.999,flat));

clat = cosd(aa);

sl(1) = sind(flon);

cl(1) = cosd(flon);

x=0.0;

y=0.0;

z=0.0;

sd = 0.0;

cd = 1.0;

n=0;

l=1;

m=1;

npq = (nmax*(nmax+3))/2;

aa = a2*clat*clat;

bb = b2*slat*slat;

cc = aa+bb;

dd = sqrt(cc);

r=sqrt(elevkm*(elevkm+2.0*dd)+(a2*aa+b2*bb)/cc);

cd = (elevkm+dd)/r;

sd = (a2-b2)/dd*slat*clat/r;

aa = slat;

slat = slat*cd-clat*sd;

clat = clat*cd+aa*sd;

ratio = erad/r;

aa = sqrt(3.0);

p(1) = 2.0*slat;

p(2) = 2.0*clat;

p(3) = 4.5*slat*slat-1.5;

p(4) = 3.0*aa*clat*slat;

q(1) = -clat;

q(2) = slat;

q(3) = -3.0*clat*slat;

q(4) = aa*(slat*slat-clat*clat);

for k = 1: npq

if (n<m)

    m=0;

    n=n+1;

    rr = ratio^(n+2);

    fn=n;

end;

fm=m;

if (k>=5)

    if (m==n)

         aa = sqrt(1.0-.5/fm);

         j=k-n-1;

         p(k) = (1.0+1.0/fm)*aa*clat*p(j);

         q(k) = aa*(clat*q(j)+slat/fm*p(j));

         sl(m) = sl(m-1)*cl(1)+cl(m-1)*sl(1);

         cl(m) = cl(m-1)*cl(1)-sl(m-1)*sl(1);

    else 

         aa = sqrt(fn*fn-fm*fm);

         bb = sqrt((fn-1.0)^2-fm*fm)/aa;

         cc = (2.0*fn-1.0)/aa;

         i=k-n;

         j=k-2*n+1;

         p(k) = (fn+1.0)*(cc*slat/fn*p(i)-bb/(fn-1.0)*p(j));

         q(k) = cc*(slat*q(i)-clat/fn*p(i))-bb*q(j);

    end;

end;

aa = rr*gh(l);

if (m==0)

   x=x+aa*q(k);

   z=z-aa*p(k);

   l=l+1;

else 

   bb = rr*gh(l+1);

   cc = aa*cl(m)+bb*sl(m);

   x=x+cc*q(k);

   z=z-cc*p(k);

   if (clat>0.0)

     y=y+(aa*sl(m)-bb*cl(m))*fm*p(k)/((fn+1.0)*clat);

   else 

     y=y+(aa*sl(m)-bb*cl(m))*q(k)*slat;

   end;

   l=l+2;

end;

m=m+1;

end;

aa=x;

x=x*cd+z*sd;

z=z*cd-aa*sd;

return;

%==================================================================

function [d,i,h,f] = dihf(x,y,z)

% function [d,i,h,f] = dihf(x,y,z)

% ===============================================================

%

%       version 1.01

%

%       computes the geomagnetic elements d, i, h, and f from

%       x, y, and z.

%

%       input:

%           x   - northward component

%           y   - eastward component

%           z   - vertically-downward component

%

%       output:

%           d   - declination

%           i   - inclination

%           h   - horizontal intensity

%           f   - total intensity

%

%       a. zunde

%       usgs, ms 964, box 25046 federal center, denver, co  80225

%

% ===============================================================

sn=0.0001;

% ---------------------------------------------------------------

%       if d and i cannot be determined, set equal to NaN

% ---------------------------------------------------------------

h=sqrt(x*x+y*y);

f=sqrt(x*x+y*y+z*z);

if (f<sn)

  d=NaN;

  i=NaN;

else 

  i=atan2(z,h);

  if (h<sn)

    d=NaN;

  else 

    hpx = h+x;

    if (hpx<200)

      d=pi;

    else 

      d=2.0*atan2(y,hpx);

    end;

  end;

end;

return;