From b325933591cd1d0d534a90ad5a417c2d03a0c6f3 Mon Sep 17 00:00:00 2001
From: Pasca <edoardo.pasca@stfc.ac.uk>
Date: Wed, 29 Mar 2017 16:46:28 +0100
Subject: Initial revision

---
 main_func/studentst.m | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 main_func/studentst.m

(limited to 'main_func/studentst.m')

diff --git a/main_func/studentst.m b/main_func/studentst.m
new file mode 100644
index 0000000..99fed1e
--- /dev/null
+++ b/main_func/studentst.m
@@ -0,0 +1,47 @@
+function [f,g,h,s,k] = studentst(r,k,s)
+% Students T penalty with 'auto-tuning'
+%
+% use:
+%   [f,g,h,{k,{s}}] = studentst(r)     - automatically fits s and k
+%   [f,g,h,{k,{s}}] = studentst(r,k)   - automatically fits s
+%   [f,g,h,{k,{s}}] = studentst(r,k,s) - use given s and k
+%
+% input:
+%   r - residual as column vector
+%   s - scale (optional)
+%   k - degrees of freedom (optional)
+% 
+% output:
+%   f - misfit (scalar)
+%   g - gradient (column vector)
+%   h - positive approximation of the Hessian (column vector, Hessian is a diagonal matrix)
+%   s,k - scale and degrees of freedom
+%
+% Tristan van Leeuwen, 2012.
+% tleeuwen@eos.ubc.ca
+
+% fit both s and k
+if nargin == 1
+    opts = optimset('maxFunEvals',1e2);
+    tmp = fminsearch(@(x)st(r,x(1),x(2)),[1;2],opts);
+    s   = tmp(1);
+    k   = tmp(2);
+end
+
+
+if nargin == 2
+    opts = optimset('maxFunEvals',1e2);
+    tmp = fminsearch(@(x)st(r,x,k),[1],opts);
+    s   = tmp(1);
+end
+
+% evaulate penalty
+[f,g,h] = st(r,s,k);
+
+
+function [f,g,h] = st(r,s,k)
+n = length(r);
+c = -n*(gammaln((k+1)/2) - gammaln(k/2) - .5*log(pi*s*k));
+f = c + .5*(k+1)*sum(log(1 + conj(r).*r/(s*k)));
+g = (k+1)*r./(s*k + conj(r).*r);
+h = (k+1)./(s*k + conj(r).*r);
-- 
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