Performs conversion of geomagnetic potential coeffficients

plm2mag.m

@@ -1,49 +1,64 @@
-function lmcosip=plm2mag(lmcosiS,r,a,wat)
-% lmcosip=plm2mag(lmcosiS,r,a,wat)
+function lmcosip=plm2mag(lmcosi,r,a,wat,schm)
+% lmcosip=PLM2MAG(lmcosi,r,a,wat,schm)
+%
+% Converts a (Schmidt-normalized) real-spherical-harmonic array of
+% magnetic-potential cosine and sine coefficients into a same-size
+% spherical harmonic array with modified coefficients, depending on given
+% input and requested output, e.g. for upward and downward continuation,
+% differentiation to individual components, and the like. 
 %
 % INPUT:
 %
-% lmcosiS       [l m Ccos Csin] degrees, order, coefficients in the
-%               Schmidt semi-normalized basis
-% r             Requested radius, in m [default: a]
-% a             Reference radius [default: 6371200]
-% wat           1 radial-component magnetic field u_r [default]
-%               2 colatitudinal tangential-component u_th
-%               3 longitudinal tangential-component u_ph
+% lmcosi        [l m Ccos Csin] degrees, order, cos/sin potential coefficients
+% r             Requested radius for the input, in m [default: a]
+% a             Reference radius for the output [default: 6371200]
+% wat           1 output is radial-component field [default]
+%               2 output is colatitudinal tangential-component field [default]
+%               3 output is longitudinal tangential-component field [default]
+% schm          1 change normalization from being appropriate for expansion
+%                 into Schmidt semi-normalized harmonics to being
+%                 appropriate for expansion into 4pi-normalized ones [default] 
+%                 Otherwise, keep the normalization as it is.
 %
 % OUPUT:
 %
-% lmcosip       [l m Ccos Csin] degrees, order, coefficients of output in
-%               the 4pi fully normalized basis good for PLM2XYZ
+% lmcosip       [l m Ccos Csin] degrees, order, cos/sin coefficients of output
 %
+% Written by by fjsimons-at-alum.mit.edu, 03/05/2009
+% Modified by Jarno Saarimaki, 07/01/2011
 % Last modified by fjsimons-at-alum.mit.edu, 05/04/2018
 
-% Default values
+% Deafult input values
 defval('a',6371200)
 defval('r',a)
 defval('wat',1)
+defval('schm',1)
 
 % Get the spherical harmonic degree
-el=lmcosiS(:,1);
+el=lmcosi(:,1);
+
+% Precalculate a certain upward-continuation factor
 arl2=(a/r).^(el+2);
 
-% Convert from Schmidt semi-normalized to 4pi-normalized
-lmcosiS(:,3:4)=lmcosiS(:,3:4)./sqrt(2*[el el]+1);
-lmcosip=lmcosiS;
+if schm == 1
+  % Convert coefficients from being expanded into Schmidt semi-normalized
+  % to being expanded into 4pi-normalized real spherical harmonics
+  lmcosi(:,3:4)=lmcosi(:,3:4)./sqrt(2*[el el]+1);
+end
 
-% Convert
+% Perform the upward or downward continuation portion first
+lmcosi(:,3:4)=lmcosi(:,3:4).*arl2*[1 1];
+
+% Convert to other things
 switch wat
  case 1
-  % Blakely p. 169 (8.20)
-  fact=(el+1).*arl2*[1 1];
+  % [Blakely 1995 p. 169 after eq. (8.20)]
   disp('Calculating radial field from potential')
+  lmcosip(:,3:4)=lmcosi(:,3:4).*(el+1)*[1 1];
  case 2
   % Kono 
   disp('Calculating colatitudinal tangential field from potential')
  case 3
   % Kono
   disp('Calculating longitudinal tangential field from potential')
 end
-
-% Factor in the factor
-lmcosip(:,3:4)=fact.*lmcosiS(:,3:4);