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fillpriormat_gauss.m
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fillpriormat_gauss.m
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function prior = fillpriormat_gauss(Nobs,ons,offs,Nstates)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% prior = fillpriormat_gauss(Nobs,ons,offs,Nstates)
%
% Description:
% Creates a prior matrix based on the DTW alignment (supplied by the input
% variables ons and offs. A rectangular window with half a Gaussian on
% each side over the onsets and offsets estimated by the DTW alignment.
%
% Inputs:
% Nobs - number of observations
% ons - vector of onset times predicted by DTW alignment
% offs - vector of offset times predicted by DTW alignment
% Nstates - number of states in the hidden Markov model
%
% Outputs:
% prior - prior matrix based on DTW alignment
%
% Automatic Music Performance Analysis and Analysis Toolkit (AMPACT)
% http://www.ampact.org - Johanna Devaney, 2011
% (c) copyright 2011 Johanna Devaney (j@devaney.ca) and Michael Mandel
% (mim@mr-pc.org), all rights reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~exist('Nstates', 'var'), Nstates = 5; end
Nnotes = length(ons);
prior = sparse(Nnotes*(Nstates-1)+1,Nobs);
frames = 1:Nobs;
for i=1:Nnotes
row = (i-1)*(Nstates-1);
insert = Nstates-5;
% Silence
prior(row+1,:) = flatTopGaussian(frames, gh(ons,i-1,offs,i-1,frames,.5), ...
g(offs,i-1,frames), g(ons,i,frames), gh(ons,i,offs,i,frames,.5));
prior(row+2:row+2+insert-1,:) = repmat(prior(row+1,:),insert,1);
% Transient, steady state, transient
prior(row+2+insert,:) = ...
flatTopGaussian(frames, g(offs,i-1,frames), ...
gh(offs,i-1,ons,i,frames,.75), gh(ons,i,offs,i,frames,.25), g(offs,i,frames));
prior(row+3+insert,:) = ...
flatTopGaussian(frames, g(offs,i-1,frames), ...
g(ons,i,frames), g(offs,i,frames), g(ons,i+1,frames));
prior(row+4+insert,:) = ...
flatTopGaussian(frames, g(ons,i,frames), ...
gh(ons,i,offs,i,frames,.75), gh(offs,i,ons,i+1,frames,.25), g(ons,i+1,frames));
end
% The last silence
i = i+1;
prior(row+5+insert,:) = flatTopGaussIdx(frames, ons,i-1, offs,i-1, ...
offs,i, ons,i+1);
function x = gh(v1, i1, v2, i2, domain, frac)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% x = gh(v1, i1, v2, i2, domain, frac)
%
% Description:
% Get an element that is frac fraction of the way between v1(i1) and
% v2(i2), but check bounds on both vectors. Frac of 0 returns v1(i1),
% frac of 1 returns v2(i2), frac of 1/2 (the default) returns half way
% between them.
%
% Automatic Music Performance Analysis and Analysis Toolkit (AMPACT)
% http://www.ampact.org
% (c) copyright 2011 Johanna Devaney (j@devaney.ca) and Michael Mandel
% (mim@mr-pc.org), all rights reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~exist('frac', 'var'), frac = 0.5; end
x1 = g(v1, i1, domain);
x2 = g(v2, i2, domain);
x = floor(frac*x1 + (1-frac)*x2);
function w = flatTopGaussIdx(x, b1,bi1, t1,ti1, t2,ti2, b2,bi2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% flatTopGaussIdx(x, b1,bi1, t1,ti1, t2,ti2, b2,bi2)
%
% Description:
% Create a window function that is zeros, going up to 1s with the left
% half of a gaussian, then ones, then going back down to zeros with
% the right half of another gaussian. b1(bi1) is the x coordinate 2
% stddevs out from the mean, which is at t1(ti1). t2(ti2) is the x
% coordinate of the mean of the second gaussian and b2(bi2) is 2
% stddevs out from that. The points should be in that order. Vectors
% are indexed intelligently, so you don't have to worry about
% overflows or underflows. X is the set of points over which this is
% to be calculated.
%
% Automatic Music Performance Analysis and Analysis Toolkit (AMPACT)
% http://www.ampact.org
% (c) copyright 2011 Johanna Devaney (j@devaney.ca) and Michael Mandel
% (mim@mr-pc.org), all rights reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
b1 = g(b1, bi1, x);
t1 = g(t1, ti1, x);
t2 = g(t2, ti2, x);
b2 = g(b2, bi2, x);
w = flatTopGaussian(x, b1, t1, t2, b2);
function x = g(vec, idx, domain)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% x = g(vec, idx, domain)
%
% Description:
% Get an element from vec, checking bounds. Domain is the set of points
% that vec is a subset of.
%
% Automatic Music Performance Analysis and Analysis Toolkit (AMPACT)
% http://www.ampact.org
% (c) copyright 2011 Johanna Devaney (j@devaney.ca) and Michael Mandel
% (mim@mr-pc.org), all rights reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if idx < 1
x = 1;
elseif idx > length(vec)
x = domain(end);
else
x = vec(idx);
end
function w = flatTopGaussian(x, b1, t1, t2, b2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% flatTopGaussian(x, b1, t1, t2, b2)
%
% Description:
% Create a window function that is zeros, going up to 1s with the left
% half of a gaussian, then ones, then going back down to zeros with the
% right half of another gaussian. b1 is the x coordinate 2 stddevs out
% from the mean, which is at t1. t2 is the x coordinate of the mean of
% the second gaussian and b2 is 2 stddevs out from that. The points
% should be in that order. X is the set of points over which this is
% to be calculated.
%
% Automatic Music Performance Analysis and Analysis Toolkit (AMPACT)
% http://www.ampact.org
% (c) copyright 2011 Johanna Devaney (j@devaney.ca) and Michael Mandel
% (mim@mr-pc.org), all rights reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if any([b1 t1 t2] > [t1 t2 b2])
warning('Endpoints are not in order: %f %f %f %f', b1, t1, t2, b2)
end
left = normpdf(x, t1, (t1-b1)/2+1);
middle = ones(1,t2-t1-1);
right = normpdf(x, t2, (b2-t2)/2+1);
left = left ./ max(left);
right = right ./ max(right);
takeOneOut = (t1 == t2);
w = [left(1:t1) middle right(t2+takeOneOut:end)];