h2metrics/constructKnots.m - ERROR - matlab

I'm trying to run the following code:
"https://github.com/h2metrics/h2metrics/blob/master/constructKnots.m"
%% constructEmptySplineData
%
% Function constructs an empty splineData struct. Some default parameters
% are being set; others are set to empty arrays.
%
% Default parameters
% dSpace = 2
% phiEps = 1e-12
% a = [1 0 1]
%
% Output
% splineData
% The created struct.
%
function [ splineData ] = constructEmptySplineData
splineData = struct('nS', [],...
'nT', [], ...
'nPhi', [], ...
'N', [], ...
'Nt', [], ...
'Nphi', [], ...
'quadDegree', [], ...
'dSpace', 2, ...
'phiEps', 1e-12, ...
'a', [1 0 1], ...
'knotsS', [], ...
'knotsT', [], ...
'knotsPhi', [], ...
'innerKnotsS', [], ...
'innerKnotsT', [], ...
'innerKnotsPhi', [], ...
'periodic', 1, ...
'noInterpolS', [], ...
'interpolS', [], ...
'stepsT', [], ...
'quadData', [], ...
'quadDataTensor', [] );
end
but I obtained the following error(s):
>> Error using constructKnots (line 20)
Not enough input arguments.
>> constructKnots(splineData)
Undefined function or variable 'splineData'
Also, I observed SplineData function is created here:
"https://github.com/h2metrics/h2metrics/blob/master/constructEmptySplineData.m".
%% constructKnots
%
% Function constructs the knot sequences with the given parameters from
% splineData. The knot sequences are uniform in space and time, periodic in
% space and with full multiplicity at the boundary in time.
%
% interpolS is set automatically using N and nS.
%
% Input
% splineData
% Contains information about spline degree and number of control
% points.
%
% Output
% splineData
% Same as input with knot sequences.
%
function [ splineData ] = constructKnots( splineData )
if ~isempty(splineData.N) && ~isempty(splineData.nS)
N = splineData.N;
nS = splineData.nS;
% Normalize, domain of definition is [0,2*pi]
splineData.knotsS = [(-nS):(N+nS)]/N*2*pi;
splineData.innerKnotsS = splineData.knotsS(nS+1:end-nS);
splineData.noInterpolS = splineData.N;
innerKnotsS = splineData.innerKnotsS;
if mod(splineData.nS, 2) == 0 % See deBoor for reasons for this.
splineData.interpolS = innerKnotsS(1:end-1)' + ...
0.5*diff(innerKnotsS)';
else
splineData.interpolS = innerKnotsS(1:end-1)';
end
end
if ~isempty(splineData.Nt) && ~isempty(splineData.nT)
Nt = splineData.Nt;
nT = splineData.nT;
splineData.knotsT = [ zeros(1,nT), linspace(0,1,Nt-nT+1), ...
ones(1,nT) ];
splineData.innerKnotsT = splineData.knotsT(nT+1:end-nT);
end
if ~isempty(splineData.Nphi) && ~isempty(splineData.nPhi)
Nphi = splineData.Nphi;
nPhi = splineData.nPhi;
% Normalize, domain of definition is [0,2*pi]
splineData.knotsPhi = [(-nPhi):(Nphi+nPhi)]/Nphi*2*pi;
splineData.innerKnotsPhi = splineData.knotsPhi(nPhi+1:end-nPhi);
end
end
I do not know how to create a connection between those 2 links.
From my point of view it seems to be ok... Could you help me, please to find the bug.

Related

Encrypt/decrypt image with AES256 in Matlab

I have to encrypt and decrypt an image with AES256. I'm working on the program below, which encrypts plaintext.
AES is an algorithm that has fixed length input in 128 bit. It work in four different steps every round; AES256 has 14 rounds, as the program shows for a different kind of this algorithm.
I'm looking to adapt the main program for any image that surely will have a length larger than 128bit. Should I divide it into many blocks that have the same size, or do you have other suggestions?
function [output] = aes(s, oper, mode, input, iv, sbit)
% AES Encrypt/decrypt array of bytes by AES.
% output = aes(s, oper, mode, input, iv, sbit)
% Encrypt/decrypt array of bytes by AES-128, AES-192, AES-256.
% All NIST SP800-38A cipher modes supported (e.g. ECB, CBC, OFB, CFB, CTR).
% Usage example: out = aesdecrypt(s, 'dec', 'ecb', data)
% s: AES structure (generated by aesinit)
% oper: operation:
% 'e', 'enc', 'encrypt', 'E',... = encrypt
% 'd', 'dec', 'decrypt', 'D',... = decrypt
% mode: operation mode
% 'ecb' = Electronic Codebook Mode
% 'cbc' = Cipher Block Chaining Mode
% 'cfb' = Cipher Feedback Mode
% 'ofb' = Output Feedback Mode
% 'ctr' = Counter Mode
% For counter mode you need external AES_GET_COUNTER()
% counter function.
% input: plaintext/ciphertext byte-vector with length
% multiple of 16
% iv: initialize vector - some modes need it
% ending initialize vector is stored in s.iv, so you
% can use aes() repetitively to encode/decode
% large vector:
% out = aes(s, 'enc', 'cbc', input1, iv);
% out = [out aes(s, 'enc', 'cbc', input1, s.iv)];
% ...
% sbit: bit-width parameter for CFB mode
% output: ciphertext/plaintext byte-vector
%
% See
% Morris Dworkin, Recommendation for Block Cipher Modes of Operation
% Methods and Techniques
% NIST Special Publication 800-38A, 2001 Edition
% for details.
error(nargchk(4, 6, nargin));
validateattributes(s, {'struct'}, {});
validateattributes(oper, {'char'}, {});
validateattributes(mode, {'char'}, {});
validateattributes(input, {'numeric'}, {'real', 'vector', '>=', 0, '<', 256});
if (nargin >= 5)
validateattributes(iv, {'numeric'}, {'real', 'vector', '>=', 0, '<', 256});
if (length(iv) ~= 16)
error('Length of ''iv'' must be 16.');
end
end
if (nargin >= 6)
validateattributes(sbit, {'numeric'}, {'real', 'scalar', '>=', 1, '<=', 128});
end
if (mod(length(input), 16))
error('Length of ''input'' must be multiple of 16.');
end
switch lower(oper)
case {'encrypt', 'enc', 'e'}
oper = 0;
case {'decrypt', 'dec', 'd'}
oper = 1;
otherwise
error('Bad ''oper'' parameter.');
end
blocks = length(input)/16;
input = input(:);
switch lower(mode)
case {'ecb'}
% Electronic Codebook Mode
% ------------------------
output = zeros(1,length(input));
idx = 1:16;
for i = 1:blocks
if (oper)
% decrypt
output(idx) = aesdecrypt(s,input(idx));
else
% encrypt
output(idx) = aesencrypt(s,input(idx));
end
idx = idx + 16;
end
case {'cbc'}
% Cipher Block Chaining Mode
% --------------------------
if (nargin < 5)
error('Missing initialization vector ''iv''.');
end
output = zeros(1,length(input));
ob = iv;
idx = 1:16;
for i = 1:blocks
if (oper)
% decrypt
in = input(idx);
output(idx) = bitxor(ob(:), aesdecrypt(s,in)');
ob = in;
else
% encrypt
ob = bitxor(ob(:), input(idx));
ob = aesencrypt(s, ob);
output(idx) = ob;
end
idx = idx + 16;
end
% store iv for block passing
s.iv = ob;
case {'cfb'}
% Cipher Feedback Mode
% --------------------
% Special mode with bit manipulations
% sbit = 1..128
if (nargin < 6)
error('Missing ''sbit'' parameter.');
end
% get number of bits
bitlen = 8*length(input);
% loop counter
rounds = round(bitlen/sbit);
% check
if (rem(bitlen, sbit))
error('Message length in bits is not multiple of ''sbit''.');
end
% convert input to bitstream
inputb = reshape(de2bi(input,8,2,'left-msb')',1,bitlen);
% preset init. vector
ib = iv;
ibb = reshape(de2bi(ib,8,2,'left-msb')',1,128);
% preset output binary stream
outputb = zeros(size(inputb));
for i = 1:rounds
iba = aesencrypt(s, ib);
% convert to bit, MSB first
ibab = reshape(de2bi(iba,8,2,'left-msb')',1,128);
% strip only sbit MSB bits
% this goes to xor
ibab = ibab(1:sbit);
% strip bits from input
inpb = inputb((i - 1)*sbit + (1:sbit));
% make xor
outb = bitxor(ibab, inpb);
% write to output
outputb((i - 1)*sbit + (1:sbit)) = outb;
if (oper)
% decrypt
% prepare new iv - bit shift
ibb = [ibb((1 + sbit):end) inpb];
else
% encrypt
% prepare new iv - bit shift
ibb = [ibb((1 + sbit):end) outb];
end
% back to byte ary
ib = bi2de(vec2mat(ibb,8),'left-msb');
% loop
end
output = bi2de(vec2mat(outputb,8),'left-msb');
% store iv for block passing
s.iv = ib;
case {'ofb'}
% Output Feedback Mode
% --------------------
if (nargin < 5)
error('Missing initialization vector ''iv''.');
end
output = zeros(1,length(input));
ib = iv;
idx = 1:16;
for i = 1:blocks
% encrypt, decrypt
ib = aesencrypt(s, ib);
output(idx) = bitxor(ib(:), input(idx));
idx = idx + 16;
end
% store iv for block passing
s.iv = ib;
case {'ctr'}
% Counter Mode
% ------------
if (nargin < 5)
iv = 1;
end
output = zeros(1,length(input));
idx = 1:16;
for i = (iv):(iv + blocks - 1)
ib = AES_GET_COUNTER(i);
ib = aesencrypt(s, ib);
output(idx) = bitxor(ib(:), input(idx));
idx = idx + 16;
end
s.iv = iv + blocks;
otherwise
error('Bad ''oper'' parameter.');
end
the aesencrypt function :
function [out] = aesencrypt(s, in)
% AESENCRYPT Encrypt 16-bytes vector.
% Usage: out = aesencrypt(s, in)
% s: AES structure
% in: input 16-bytes vector (plaintext)
% out: output 16-bytes vector (ciphertext)
if (nargin ~= 2)
error('Bad number of input arguments.');
end
validateattributes(s, {'struct'}, {});
validateattributes(in, {'numeric'}, {'real','uint8'});
% copy input to local
% 16 -> 4 x 4
state = reshape(in, 4, 4);
% Initial round
% AddRoundKey keyexp(1:4)
state = bitxor(state, (s.keyexp(1:4, :))');
% Loop over (s.rounds - 1) rounds
for i = 1:(s.rounds - 1)
% SubBytes - lookup table
state = s.s_box(state + 1);
% ShiftRows
state = shift_rows(state, 0);
% MixColumns
state = mix_columns(state, s);
% AddRoundKey keyexp(i*4 + (1:4))
state = bitxor(state, (s.keyexp((1:4) + 4*i, :))');
end
% Final round
% SubBytes - lookup table
state = s.s_box(state + 1);
% ShiftRows
state = shift_rows(state, 0);
% AddRoundKey keyexp(4*s.rounds + (1:4))
state = bitxor(state, (s.keyexp(4*s.rounds + (1:4), :))');
% copy local to output
% 4 x 4 -> 16
out = reshape(state, 1, 16);
function aesinit:
function s = aesinit(key)
% AESINIT Generate structure with s-boxes, expanded key, etc.
% Usage: s = aesinit([23 34 168 ... 39])
% key: 16 (AES-128), 24 (AES-192), and 32 (AES-256)
% items array with bytes of key
% s: AES structure for AES parameters and tables
% Stepan Matejka, 2011, matejka[at]feld.cvut.cz
% $Revision: 1.1.0 $ $Date: 2011/10/12 $
validateattributes(key,...
{'numeric'},...
{'real', 'vector', '>=', 0, '<=', 255});
key = key(:);
lengthkey = length(key);
switch (lengthkey)
case 16
rounds = 10;
case 24
rounds = 12;
case 32
rounds = 14;
otherwise
error('Only AES-128, AES-192, and AES-256 are supported.');
end
% fill s structure
s = {};
s.key = key;
s.bytes = lengthkey;
s.length = lengthkey * 8;
s.rounds = rounds;
% irreducible polynomial for multiplication in a finite field 0x11b
% bin2dec('100011011');
s.mod_pol = 283;
% s-box method 1 (slow)
% ---------------------
% % multiplicative inverse table
% % first is zero, calculate rest
% inverse = zeros(1,256);
% for i = 2:256
% inverse(i) = find_inverse(i - 1, s.mod_pol);
% end
%
% % generate s-box
% s_box = zeros(1,256);
% for i = 1:256
% % affine transformation
% s_box(i) = aff_trans(inverse(i));
% end
% s.s_box = s_box;
%
% % generate inverse s-box
% inv_s_box(s_box(1:256) + 1) = (1:256) - 1;
% s.inv_s_box = inv_s_box;
% s-box method 2 (faster)
% -----------------------
% first build logarithm lookup table and it's inverse
aes_logt = zeros(1,256);
aes_ilogt = zeros(1,256);
gen = 1;
for i = 0:255
aes_logt(gen + 1) = i;
aes_ilogt(i + 1) = gen;
gen = poly_mult(gen, 3, s.mod_pol);
end
% store log tables
s.aes_logt = aes_logt;
s.aes_ilogt = aes_ilogt;
% build s-box and it's inverse
s_box = zeros(1,256);
loctable = [1 2 4 8 16 32 64 128 1 2 4 8 16 32 64 128];
for i = 0:255
if (i == 0)
inv = 0;
else
inv = aes_ilogt(255 - aes_logt(i + 1) + 1);
end
temp = 0;
for bi = 0:7
temp2 = sign(bitand(inv, loctable(bi + 1)));
temp2 = temp2 + sign(bitand(inv, loctable(bi + 4 + 1)));
temp2 = temp2 + sign(bitand(inv, loctable(bi + 5 + 1)));
temp2 = temp2 + sign(bitand(inv, loctable(bi + 6 + 1)));
temp2 = temp2 + sign(bitand(inv, loctable(bi + 7 + 1)));
temp2 = temp2 + sign(bitand(99, loctable(bi + 1)));
if (rem(temp2,2))
temp = bitor(temp, loctable(bi + 1));
end
end
s_box(i + 1) = temp;
end
inv_s_box(s_box(1:256) + 1) = (0:255);
% table correction (must be)
s_box(1 + 1) = 124;
inv_s_box(124 + 1) = 1;
inv_s_box(99 + 1) = 0;
s.s_box = s_box;
s.inv_s_box = inv_s_box;
% tables for fast MixColumns
mix_col2 = zeros(1,256);
mix_col3 = mix_col2;
mix_col9 = mix_col2;
mix_col11 = mix_col2;
mix_col13 = mix_col2;
mix_col14 = mix_col2;
for i = 1:256
mix_col2(i) = poly_mult(2, i - 1, s.mod_pol);
mix_col3(i) = poly_mult(3, i - 1, s.mod_pol);
mix_col9(i) = poly_mult(9, i - 1, s.mod_pol);
mix_col11(i) = poly_mult(11, i - 1, s.mod_pol);
mix_col13(i) = poly_mult(13, i - 1, s.mod_pol);
mix_col14(i) = poly_mult(14, i - 1, s.mod_pol);
end
s.mix_col2 = mix_col2;
s.mix_col3 = mix_col3;
s.mix_col9 = mix_col9;
s.mix_col11 = mix_col11;
s.mix_col13 = mix_col13;
s.mix_col14 = mix_col14;
% expanded key
s.keyexp = key_expansion(s.key, s.s_box, s.rounds, s.mod_pol, s.aes_logt, s.aes_ilogt);
% poly & invpoly
s.poly_mat = [...
2 3 1 1;...
1 2 3 1;...
1 1 2 3;...
3 1 1 2];
s.inv_poly_mat =[...
14 11 13 9;...
9 14 11 13;...
13 9 14 11;...
11 13 9 14];
% end of aesinit.m
% ------------------------------------------------------------------------
function p = poly_mult(a, b, mod_pol)
% Multiplication in a finite field
% For loop multiplication - slower than log/ilog tables
% but must be used for log/ilog tables generation
p = 0;
for counter = 1 : 8
if (rem(b, 2))
p = bitxor(p, a);
b = (b - 1)/2;
else
b = b/2;
end
a = 2*a;
if (a > 255)
a = bitxor(a, mod_pol);
end
end
% ------------------------------------------------------------------------
function inv = find_inverse(in, mod_pol)
% Multiplicative inverse for an element a of a finite field
% very bad calculate & test method
% Not used in faster version
% loop over all possible bytes
for inv = 1 : 255
% calculate polynomial multiplication and test to be 1
if (1 == poly_mult(in, inv, mod_pol))
% we find it
break
end
end
inv = 0;
% ------------------------------------------------------------------------
function out = aff_trans(in)
% Affine transformation over GF(2^8)
% Not used for faster s-box generation
% modulo polynomial for multiplication in a finite field
% bin2dec('100000001');
mod_pol = 257;
% multiplication polynomial
% bin2dec('00011111');
mult_pol = 31;
% addition polynomial
% bin2dec('01100011');
add_pol = 99;
% polynomial multiplication
temp = poly_mult(in, mult_pol, mod_pol);
% xor with addition polynomial
out = bitxor(temp, add_pol);
% ------------------------------------------------------------------------
function expkey = key_expansion(key, s_box, rounds, mod_pol, aes_logt, aes_ilogt)
% Expansion of key
% This is old version for AES-128 (192?, 256? not tested):
% rcon = ones(1,rounds);
% for i = 2:rounds
% rcon(i) = poly_mult(rcon(i - 1), 2, mod_pol);
% end
% % fill bytes 2, 3, and 4 by 0
% rcon = [rcon(:), zeros(rounds, 3)];
%
% kcol = length(key)/4;
% expkey = (reshape(key, kcol, 4))';
% for i = (kcol + 1):(4*rounds + 4)
% % copy the previous row of the expanded key into a buffer
% temp = expkey(i - 1, :);
% % each fourth row
% if (mod(i, 4) == 1)
% % shift temp
% temp = temp([2 3 4 1]);
% % s-box transform
% temp = s_box(temp + 1);
% % compute the current round constant
% r = rcon((i - 1)/4, :);
% % xor
% temp = bitxor(temp, r);
% else
% if ((kcol > 6) && (mod(i, kcol) == 0))
% temp = s_box(temp);
% end
% end
% % generate new row of the expanded key
% expkey(i, :) = bitxor(expkey(i - 4, :), temp);
% end
% This is new faster version for all AES:
rcon = 1;
kcol = length(key)/4;
expkey = (reshape(key,4,kcol))';
% traverse for all rounds
for i = kcol:(4*(rounds + 1) - 1)
% copy the previous row of the expanded key into a buffer
temp = expkey(i, :);
% each kcol row
if (mod(i, kcol) == 0)
% rotate word
temp = temp([2 3 4 1]);
% s-box transform
temp = s_box(temp + 1);
% xor
temp(1) = bitxor(temp(1), rcon);
% new rcon
% 1. classic poly_mult
% rcon = poly_mult(rcon, 2, mod_pol);
% 2. or faster version with log/ilog tables
% note rcon is never zero here
% rcon = aes_ilogt(mod((aes_logt(rcon + 1) + aes_logt(2 + 1)), 255) + 1);
rcon = aes_ilogt(mod((aes_logt(rcon + 1) + 25), 255) + 1);
else
if ((kcol > 6) && (mod(i, kcol) == 4))
temp = s_box(temp + 1);
end
end
% generate new row of the expanded key
expkey(i + 1, :) = bitxor(expkey(i - kcol + 1, :), temp);
end
You are limited to 128 bits because you tried to encrypt using aesencrypt, one of the low level functions which work on 4x4 blocks. If you instead use the aes function you can encode any "byte-vector with length multiple of 16". It will repeatedly call aesenrypt for you until all 4x4 blocks are processed.

ode45 solving of diff.equation with further fitting to exp.results

I am building a code to solve a diff. equation:
function dy = KIN1PARM(t,y,k)
%
% version : first order reaction
% A --> B
% dA/dt = -k*A
% integrated form A = A0*exp(-k*t)
%
dy = -k.*y;
end
I want this equation to be solved numerically and the results (y as a function of t, and k) to be used for minimization with respect to the experimental values to get the optimal value of parameter k.
function SSE = SSE_minimization_1parm(tspan_inp,val_exp,k_inp,y0_inp)
f = #(Tt,Ty) KIN1PARM(Tt,Ty,k_inp); %function to call ode45
size_limit = length(y0_inp);
options = odeset('NonNegative',1:size_limit,'RelTol',1e-4,'AbsTol', 1e-4);
[ts,val_theo] = ode45(f, tspan_inp, y0_inp,options); %Cexp is the state variable predicted by the model
err = val_exp - val_theo;
SSE = sum(err.^2); %sum squared-error
The main code to plot the experimental and calculated data is:
% Analyzing first order kinetics
clear all; clc;
figure_title = 'Experimental Data';
label_abscissa = 'Time [s]';
label_ordinatus = 'Concentration [mol/L]';
%
abscissa = [ 0;
240;
480;
720;
960;
1140;
1380;
1620;
1800;
2040;
2220;
2460;
2700;
2940];
ordinatus = [ 0;
19.6;
36.7;
49.0;
57.1;
64.5;
71.4;
75.2;
78.7;
81.3;
83.3;
85.5;
87.0;
87.7];
%
title_string = [' Time [s]', ' | ', ' Complex [mol/L] ', ' '];
disp(title_string);
for i=1:length(abscissa)
report_raw_data{i} = sprintf('%1.3E\t',abscissa(i),ordinatus(i));
disp([report_raw_data{i}]);
end;
%---------------------/plotting dot data/-------------------------------------
%
f = figure('Position', [100 100 700 500]);
title(figure_title,'FontName','arial','FontWeight','bold', 'FontSize', 12);
xlabel(label_abscissa, 'FontSize', 12);
ylabel(label_ordinatus, 'FontSize', 12);
%
grid on; hold on;
%
marker_style = { 's'};
%
plot(abscissa,ordinatus, marker_style{1},...
'MarkerFaceColor', 'black',...
'MarkerEdgeColor', 'black',...
'MarkerSize',4);
%---------------------/Analyzing/----------------------------------------
%
options = optimset('Display','iter','TolFun',1e-4,'TolX',1e-4);
%
CPUtime0 = cputime;
Time_M = abscissa;
Concentration_M = ordinatus;
tspan = Time_M;
y0 = 0;
k0 = rand(1);
[k, fval, exitflag, output] = fminsearch(#(k) SSE_minimization_1parm(tspan,Concentration_M,k,y0),k0,options);
CPUtimex = cputime;
CPUtime_delay = CPUtimex - CPUtime0;
%
%---------------------/plotting calculated data/-------------------------------------
%
xupperlimit = Time_M(length(Time_M));
xval = ([0:1:xupperlimit])';
%
yvector = data4plot_1parm(xval,k,y0);
plot(xval,yvector, 'r');
hold on;
%---------------------/printing calculated data/-------------------------------------
%
disp('RESULTS:');
disp(['CPU time: ',sprintf('%0.5f\t',CPUtime_delay),' sec']);
disp(['k: ',sprintf('%1.3E\t',k')]);
disp(['fval: ',sprintf('%1.3E\t',fval)]);
disp(['exitflag: ',sprintf('%1.3E\t',exitflag)]);
disp(output);
disp(['Output: ',output.message]);
The corresponding function, which uses the optimized parameter k to yield the calculated y = f(t) data :
function val = data4plot_1parm(tspan_inp,k_inp,y0_inp)
f = #(Tt,Ty) KIN1PARM(Tt,Ty,k_inp);
size_limit = length(y0_inp);
options = odeset('NonNegative',1:size_limit,'RelTol',1e-4,'AbsTol',1e-4);
[ts,val_theo] = ode45(f, tspan_inp, y0_inp, options);
The code runs optimization cycles always giving different values of parameter k, which are different from the value calculated using ln(y) vs t (should be around 7.0e-4 for that series of exp. data).
Looking at the outcome of the ode solver (SSE_minimization_1parm => val_theo) I found that the ode function gives me a vector of zeroes.
Could someone help me , please, to figure out what's going with the ode solver ?
Thanks much in advance !
So here comes the best which I can get right now. For my way I tread ordinatus values as time and the abscissa values as measured quantity which you try to model. Also, you seem to have set alot of options for the solver, which I all omitted. First comes your proposed solution using ode45(), but with a non-zero y0 = 100, which I just "guessed" from looking at the data (in a semilogarithmic plot).
function main
abscissa = [0;
240;
480;
720;
960;
1140;
1380;
1620;
1800;
2040;
2220;
2460;
2700;
2940];
ordinatus = [ 0;
19.6;
36.7;
49.0;
57.1;
64.5;
71.4;
75.2;
78.7;
81.3;
83.3;
85.5;
87.0;
87.7];
tspan = [min(ordinatus), max(ordinatus)]; % // assuming ordinatus is time
y0 = 100; % // <---- Probably the most important parameter to guess
k0 = -0.1; % // <--- second most important parameter to guess (negative for growth)
k_opt = fminsearch(#minimize, k0) % // optimization only over k
% nested minimization function
function e = minimize(k)
sol = ode45(#KIN1PARM, tspan, y0, [], k);
y_hat = deval(sol, ordinatus); % // evaluate solution at given times
e = sum((y_hat' - abscissa).^2); % // compute squarederror
end
% // plot with optimal parameter
[T,Y] = ode45(#KIN1PARM, tspan, y0, [], k_opt);
figure
plot(ordinatus, abscissa,'ko', 'markersize',10,'markerfacecolor','black')
hold on
plot(T,Y, 'r--', 'linewidth', 2)
% // Another attempt with fminsearch and the integral form
t = ordinatus;
t_fit = linspace(min(ordinatus), max(ordinatus))
y = abscissa;
% create model function with parameters A0 = p(1) and k = p(2)
model = #(p, t) p(1)*exp(-p(2)*t);
e = #(p) sum((y - model(p, t)).^2); % minimize squared errors
p0 = [100, -0.1]; % an initial guess (positive A0 and probably negative k for exp. growth)
p_fit = fminsearch(e, p0); % Optimize
% Add to plot
plot(t_fit, model(p_fit, t_fit), 'b-', 'linewidth', 2)
legend('location', 'best', 'data', 'ode45 with fixed y0', ...
sprintf ('integral form: %5.1f*exp(-%.4f)', p_fit))
end
function dy = KIN1PARM(t,y,k)
%
% version : first order reaction
% A --> B
% dA/dt = -k*A
% integrated form A = A0*exp(-k*t)
%
dy = -k.*y;
end
The result can be seen below. Quit surprisingly to me, the initial guess of y0 = 100 fits quite well with the optimal A0 found. The result can be seen below:

How does the choice of the wavelet function impact the speed of cwt()?

In cwt() I can specify which wavelet function to use. How does that impact the speed of cwt()?
Here is a benchmark, which I run with the -singleCompThread option when starting MATLAB to force it to use a single computational thread. cwt() was passed a 1,000,000-sample signal and asked to compute scales 1 to 10. My CPU is an i7-3610QM.
Code used:
clear all
%% Benchmark parameters
results_file_name = 'results_scale1-10.csv';
number_of_random_runs = 10;
scales = 1:10;
number_of_random_samples = 1000000;
%% Construct a cell array containing all the wavelet names
wavelet_haar_names = {'haar'};
wavelet_db_names = {'db1'; 'db2'; 'db3'; 'db4'; 'db5'; 'db6'; 'db7'; 'db8'; 'db9'; 'db10'};
wavelet_sym_names = {'sym2'; 'sym3'; 'sym4'; 'sym5'; 'sym6'; 'sym7'; 'sym8'};
wavelet_coif_names = {'coif1'; 'coif2'; 'coif3'; 'coif4'; 'coif5'};
wavelet_bior_names = {'bior1.1'; 'bior1.3'; 'bior1.5'; 'bior2.2'; 'bior2.4'; 'bior2.6'; 'bior2.8'; 'bior3.1'; 'bior3.3'; 'bior3.5'; 'bior3.7'; 'bior3.9'; 'bior4.4'; 'bior5.5'; 'bior6.8'};
wavelet_rbior_names = {'rbio1.1'; 'rbio1.3'; 'rbio1.5'; 'rbio2.2'; 'rbio2.4'; 'rbio2.6'; 'rbio2.8'; 'rbio3.1'; 'rbio3.3'; 'rbio3.5'; 'rbio3.7'; 'rbio3.9'; 'rbio4.4'; 'rbio5.5'; 'rbio6.8'};
wavelet_meyer_names = {'meyr'};
wavelet_dmeyer_names = {'dmey'};
wavelet_gaus_names = {'gaus1'; 'gaus2'; 'gaus3'; 'gaus4'; 'gaus5'; 'gaus6'; 'gaus7'; 'gaus8'};
wavelet_mexh_names = {'mexh'};
wavelet_morl_names = {'morl'};
wavelet_cgau_names = {'cgau1'; 'cgau2'; 'cgau3'; 'cgau4'; 'cgau5'};
wavelet_shan_names = {'shan1-1.5'; 'shan1-1'; 'shan1-0.5'; 'shan1-0.1'; 'shan2-3'};
wavelet_fbsp_names = {'fbsp1-1-1.5'; 'fbsp1-1-1'; 'fbsp1-1-0.5'; 'fbsp2-1-1'; 'fbsp2-1-0.5'; 'fbsp2-1-0.1'};
wavelet_cmor_names = {'cmor1-1.5'; 'cmor1-1'; 'cmor1-0.5'; 'cmor1-1'; 'cmor1-0.5'; 'cmor1-0.1'};
% Concatenate all wavelet names into a single cell array
wavelet_categories_names = who('wavelet*names');
wavelet_names = {};
for wavelet_categories_number=1:size(wavelet_categories_names,1)
temp = wavelet_categories_names(wavelet_categories_number);
temp = eval(temp{1});
wavelet_names = vertcat(wavelet_names, temp);
end
%% Prepare data
random_signal = rand(number_of_random_runs,number_of_random_samples);
%% Run benchmarks
result_file_ID = fopen(results_file_name, 'w');
for wavelet_number = 1:size(wavelet_names,1)
wavelet_name = wavelet_names(wavelet_number,:)
% Compute wavelet on a random signal
tic
for run = 1:number_of_random_runs
cwt(random_signal(run, :),scales,wavelet_name{1});
end
run_time_random_test = toc
fprintf(result_file_ID, '%s,', wavelet_name{1})
fprintf(result_file_ID, '%d\n', run_time_random_test)
end
size(wavelet_names,1)
fclose(result_file_ID);
If you want to see the impact of the choice of the scale:
Code used:
clear all
%% Benchmark parameters
results_file_name = 'results_sym2_change_scale.csv';
number_of_random_runs = 10;
scales = 1:10;
number_of_random_samples = 10000000;
% wavelet_names = {'sym2', 'sym3'}%, 'sym4'};
output_directory = 'output';
wavelet_names = get_all_wavelet_names();
%% Prepare data
random_signal = rand(number_of_random_runs,number_of_random_samples);
%% Prepare result folder
if ~exist(output_directory, 'dir')
mkdir(output_directory);
end
%% Run benchmarks
result_file_ID = fopen(results_file_name, 'w');
for wavelet_number = 1:size(wavelet_names,1)
wavelet_name = wavelet_names{wavelet_number}
if wavelet_number > 1
fprintf(result_file_ID, '%s\n', '');
end
fprintf(result_file_ID, '%s', wavelet_name)
run_time_random_test_scales = zeros(size(scales,2),1);
for scale_number = 1:size(scales,2)
scale = scales(scale_number);
% Compute wavelet on a random signal
tic
for run = 1:number_of_random_runs
cwt(random_signal(run, :),scale,wavelet_name);
end
run_time_random_test = toc
fprintf(result_file_ID, ',%d', run_time_random_test)
run_time_random_test_scales(scale_number) = run_time_random_test;
end
figure
bar(run_time_random_test_scales)
title(['Run time on random signal for ' wavelet_name])
xlabel('Scale')
ylabel('Run time (seconds)')
save_figure( fullfile(output_directory, ['run_time_random_test_' wavelet_name]) )
close all
end
size(wavelet_names,1)
fclose(result_file_ID);
With 3 functions:
get_all_wavelet_names.m:
function [ wavelet_names ] = get_all_wavelet_names( )
%GET_ALL_WAVELET_NAMES Get a list of available wavelet functions
%% Construct a cell array containing all the wavelet names
wavelet_haar_names = {'haar'};
wavelet_db_names = {'db1'; 'db2'; 'db3'; 'db4'; 'db5'; 'db6'; 'db7'; 'db8'; 'db9'; 'db10'};
wavelet_sym_names = {'sym2'; 'sym3'; 'sym4'; 'sym5'; 'sym6'; 'sym7'; 'sym8'};
wavelet_coif_names = {'coif1'; 'coif2'; 'coif3'; 'coif4'; 'coif5'};
wavelet_bior_names = {'bior1.1'; 'bior1.3'; 'bior1.5'; 'bior2.2'; 'bior2.4'; 'bior2.6'; 'bior2.8'; 'bior3.1'; 'bior3.3'; 'bior3.5'; 'bior3.7'; 'bior3.9'; 'bior4.4'; 'bior5.5'; 'bior6.8'};
wavelet_rbior_names = {'rbio1.1'; 'rbio1.3'; 'rbio1.5'; 'rbio2.2'; 'rbio2.4'; 'rbio2.6'; 'rbio2.8'; 'rbio3.1'; 'rbio3.3'; 'rbio3.5'; 'rbio3.7'; 'rbio3.9'; 'rbio4.4'; 'rbio5.5'; 'rbio6.8'};
wavelet_meyer_names = {'meyr'};
wavelet_dmeyer_names = {'dmey'};
wavelet_gaus_names = {'gaus1'; 'gaus2'; 'gaus3'; 'gaus4'; 'gaus5'; 'gaus6'; 'gaus7'; 'gaus8'};
wavelet_mexh_names = {'mexh'};
wavelet_morl_names = {'morl'};
wavelet_cgau_names = {'cgau1'; 'cgau2'; 'cgau3'; 'cgau4'; 'cgau5'};
wavelet_shan_names = {'shan1-1.5'; 'shan1-1'; 'shan1-0.5'; 'shan1-0.1'; 'shan2-3'};
wavelet_fbsp_names = {'fbsp1-1-1.5'; 'fbsp1-1-1'; 'fbsp1-1-0.5'; 'fbsp2-1-1'; 'fbsp2-1-0.5'; 'fbsp2-1-0.1'};
wavelet_cmor_names = {'cmor1-1.5'; 'cmor1-1'; 'cmor1-0.5'; 'cmor1-1'; 'cmor1-0.5'; 'cmor1-0.1'};
% Concatenate all wavelet names into a single cell array
wavelet_categories_names = who('wavelet*names');
wavelet_names = {};
for wavelet_categories_number=1:size(wavelet_categories_names,1)
temp = wavelet_categories_names(wavelet_categories_number);
temp = eval(temp{1});
wavelet_names = vertcat(wavelet_names, temp);
end
end
save_figure.m:
function [ ] = save_figure( output_graph_filename )
% Record aa figure as PNG and fig files
% Create the folder if it doesn't exist already.
[pathstr, name, ext] = fileparts(output_graph_filename);
if ~exist(pathstr, 'dir')
mkdir(pathstr);
end
h = gcf;
set(0,'defaultAxesFontSize',18) % http://www.mathworks.com/support/solutions/en/data/1-8XOW94/index.html?solution=1-8XOW94
boldify(h);
print('-dpng','-r600', [output_graph_filename '.png']);
print(h,[output_graph_filename '.pdf'],'-dpdf','-r600')
saveas(gcf,[output_graph_filename '.fig'], 'fig')
end
and boldify.m:
function boldify(h,g)
%BOLDIFY Make lines and text bold for standard viewgraph style.
% BOLDIFY boldifies the lines and text of the current figure.
% BOLDIFY(H) applies to the graphics handle H.
%
% BOLDIFY(X,Y) specifies an X by Y inch graph of the current
% figure. If text labels have their 'UserData' data property
% set to 'slope = ...', then the 'Rotation' property is set to
% account for changes in the graph's aspect ratio. The
% default is MATLAB's default.
% S. T. Smith
% The name of this function does not represent an endorsement by the author
% of the egregious grammatical trend of verbing nouns.
if nargin < 1, h = gcf;, end
% Set (and get) the default MATLAB paper size and position
set(gcf,'PaperPosition','default');
units = get(gcf,'PaperUnits');
set(gcf,'PaperUnits','inches');
fsize = get(gcf,'PaperPosition');
fsize = fsize(3:4); % Figure size (X" x Y") on paper.
psize = get(gcf,'PaperSize');
if nargin == 2 % User specified graph size
fsize = [h,g];
h = gcf;
end
% Set the paper position of the current figure
set(gcf,'PaperPosition', ...
[(psize(1)-fsize(1))/2 (psize(2)-fsize(2))/2 fsize(1) fsize(2)]);
fsize = get(gcf,'PaperPosition');
fsize = fsize(3:4); % Graph size (X" x Y") on paper.
set(gcf,'PaperUnits',units); % Back to original
% Get the normalized axis position of the current axes
units = get(gca,'Units');
set(gca,'Units','normalized');
asize = get(gca,'Position');
asize = asize(3:4);
set(gca,'Units',units);
ha = get(h,'Children');
for i=1:length(ha)
% if get(ha(i),'Type') == 'axes'
% changed by B. A. Miller
if strcmp(get(ha(i), 'Type'), 'axes') == 1
units = get(ha(i),'Units');
set(ha(i),'Units','normalized');
asize = get(ha(i),'Position'); % Axes Position (normalized)
asize = asize(3:4);
set(ha(i),'Units',units);
[m,j] = max(asize); j = j(1);
scale = 1/(asize(j)*fsize(j)); % scale*inches -normalized units
set(ha(i),'FontWeight','Bold');
set(ha(i),'LineWidth',2);
[m,k] = min(asize); k = k(1);
if asize(k)*fsize(k) > 1/2
set(ha(i),'TickLength',[1/8 1.5*1/8]*scale); % Gives 1/8" ticks
else
set(ha(i),'TickLength',[3/32 1.5*3/32]*scale); % Gives 3/32" ticks
end
set(get(ha(i),'XLabel'),'FontSize',18); % 14-pt labels
set(get(ha(i),'XLabel'),'FontWeight','Bold');
set(get(ha(i),'XLabel'),'VerticalAlignment','top');
set(get(ha(i),'YLabel'),'FontSize',18); % 14-pt labels
set(get(ha(i),'YLabel'),'FontWeight','Bold');
%set(get(ha(i),'YLabel'),'VerticalAlignment','baseline');
set(get(ha(i),'Title'),'FontSize',18); % 16-pt titles
set(get(ha(i),'Title'),'FontWeight','Bold');
% set(get(ha(i), 'FontSize',20, 'XTick',[]));
end
hc = get(ha(i),'Children');
for j=1:length(hc)
chtype = get(hc(j),'Type');
if chtype(1:4) == 'text'
set(hc(j),'FontSize',17); % 12 pt descriptive labels
set(hc(j),'FontWeight','Bold');
ud = get(hc(j),'UserData'); % User data
if length(ud) 8
if ud(1:8) == 'slope = ' % Account for change in actual slope
slope = sscanf(ud,'slope = %g');
slope = slope*(fsize(2)/fsize(1))/(asize(2)/asize(1));
set(hc(j),'Rotation',atan(slope)/pi*180);
end
end
elseif chtype(1:4) == 'line'
set(hc(j),'LineWidth',2);
end
end
end
Bonus: correlation between all wavelets on a random signal with 1000000 samples with the first 10 scales:
Code used:
%% PRE-REQUISITE: You need to download http://www.mathworks.com/matlabcentral/fileexchange/24253-customizable-heat-maps , which gives the function heatmap()
%% Benchmark parameters
scales = 1:10;
number_of_random_samples = 1000000;
% wavelet_names = {'sym2'; 'sym3'; 'sym4'; 'sym5'; 'sym6'; 'sym7'; 'sym8'};
% wavelet_names = {'cgau1'; 'cgau2'; 'cgau3'; 'cgau4'; 'cgau5'};
wavelet_names = {'db2'; 'sym2'};
OUTPUT_FOLDER = 'output_corr';
% wavelet_names = get_all_wavelet_names(); % WARNING: you need to remove all complex wavelets, viz. cgau1, shan, fbsp and cmor, and the heatmap will be pissed to see complex values coming to her.
%% Prepare data
random_signal = rand(1,number_of_random_samples);
results = zeros(size(wavelet_names,1), number_of_random_samples);
%% Prepare result folder
if ~exist(OUTPUT_FOLDER, 'dir')
mkdir(OUTPUT_FOLDER);
end
%% Run benchmarks
for scale_number = 1:size(scales,2)
scale = scales(scale_number);
for wavelet_number = 1:size(wavelet_names,1)
wavelet_name = wavelet_names{wavelet_number}
% Compute wavelet on a random signal
run = 1;
results(wavelet_number, :) = cwt(random_signal(run, :),scale,wavelet_name);
if wavelet_number == 999
break
end
end
correlation_results = corrcoef(results')
heatmap(correlation_results, [], [], '%0.2f', 'MinColorValue', -1.0, 'MaxColorValue', 1.0, 'Colormap', 'jet',...
'Colorbar', true, 'ColorLevels', 64, 'UseFigureColormap', false);
title(['Correlation matrix for scale ' num2str(scale)]);
xlabel(['Wavelet 1 to ' num2str(size(wavelet_names,1)) ' for scale ' num2str(scale)]);
ylabel(['Wavelet 1 to ' num2str(size(wavelet_names,1)) ' for scale ' num2str(scale)]);
snapnow
print('-dpng','-r600',fullfile(OUTPUT_FOLDER, ['scalecorr' num2str(scale) '.png']))
end
Correlation for each wavelet between different scales (1 to 100):
Code used:
%% PRE-REQUISITE: You need to download http://www.mathworks.com/matlabcentral/fileexchange/24253-customizable-heat-maps , which gives the function heatmap()
%% Benchmark parameters
scales = 1:100;
number_of_random_samples = 1000000;
% wavelet_name = 'gaus2';
% wavelet_names = {'sym2', 'sym3'}%, 'sym4'};
OUTPUT_FOLDER = 'output_corr';
wavelet_names = get_all_wavelet_names(); % WARNING: you need to remove all complex wavelets, viz. cgau1, shan, fbsp and cmor, and the heatmap will be pissed to see complex values coming to her.
%% Prepare data
random_signal = rand(1,number_of_random_samples);
results = zeros(size(scales,2), number_of_random_samples);
%% Prepare result folder
if ~exist(OUTPUT_FOLDER, 'dir')
mkdir(OUTPUT_FOLDER);
end
%% Run benchmarks
for wavelet_number = 1:size(wavelet_names,1)
wavelet_name = wavelet_names{wavelet_number}
run_time_random_test_scales = zeros(size(scales,2),1);
for scale_number = 1:size(scales,2)
scale = scales(scale_number);
run = 1;
% Compute wavelet on a random signal
results(scale_number, :) = cwt(random_signal(run, :),scale,wavelet_name);
end
correlation_results = corrcoef(results')
heatmap(correlation_results, [], [], '%0.2f', 'MinColorValue', -1.0, 'MaxColorValue', 1.0, 'Colormap', 'jet',...
'Colorbar', true, 'ColorLevels', 64, 'UseFigureColormap', false);
title(['Correlation matrix for wavelet ' wavelet_name]);
xlabel(['Scales 1 to ' num2str(max(scales)) ' for wavelet ' wavelet_name]);
ylabel(['Scales 1 to ' num2str(max(scales)) ' for wavelet ' wavelet_name]);
snapnow
print('-dpng','-r600',fullfile(OUTPUT_FOLDER, [wavelet_name '_scalecorr_scale1to' num2str(max(scales)) '.png']))
end

Converting Matlab to Octave is there a containers.Map equivalent?

I am trying to convert some matlab code from the Maia package into something that will work with Octave. I am currently getting stuck because one of the files has several calls to containers.Map which is apparently something that has not yet been implemented in octave. Does anyone have any ideas for easily achieving similar functionality without doing a whole lot of extra work in octave? Thanks all for your time.
function [adj_direct contig_direct overlap names longest_path_direct...
weigth_direct deltafiles deltafiles_ref ReferenceAlignment ...
contig_ref overlap_ref name_hash_ref] = ...
assembly_driver(assemblies,ref_genome,target_chromosome, ...
deltafiles_ref,contig_ref, overlap_ref, ...
name_hash_ref, varargin)
% ASSEMBLY_DRIVER Combines contig sets into one assembled chromosome
%
% INPUT
% assemblies
% ref_chromosome
% Startnode_name
% Endnode_name
% OPTIONAL DEFAULT
% 'z_weigths' [.25 .25 .25 .25]
% 'clipping_thrs' 10
% 'ref_distance' -10
% 'ref_quality' 1E-5
% 'max_chromosome_dist' 100
% 'quit_treshold' 15
% 'tabu_time' 3
% 'minimum_improvement' -inf
% 'ref_node_assemblies' all assemblies (slow)
% 'endextend' true
%
%
% SET DEFAULTS
% General parameters
z_weights = [.25 .25 .25 .25];
clipping_thrs = 10;
mapfilter = '-rq';
alignlen = 75;
ident = 85;
% Reference nod parameters
ref_distance = -10;
ref_quality = 1E-5;
max_chromosome_dist = 100;
% TABU parameters
quit_treshold = 15;
tabu_time = 3;
minimum_improvement = -inf;
ref_node_assemblies = assemblies;
% Extending the assembly outwards from the start and en node
endextend = true;
AllowReverse = true;
% If no start and end node are given, they will be determined from tiling
Startnode_name = '';
Endnode_name = '';
containment_edge = true;
ref_first = true;
% If contigs have already been aligned to the reference, give the
% deltafile
ReferenceAlignment = 'NotYetDoneByMaia';
% Get VARARGIN user input
if length(varargin) > 0
while 1
switch varargin{1}
case 'Startnode_name'
Startnode_name = varargin{2};
case 'Endnode_name'
Endnode_name = varargin{2};
case 'z_weigths'
z_weights = varargin{2};
case 'clipping_thrs'
clipping_thrs = varargin{2};
case 'ref_distance'
ref_distance = varargin{2};
case 'ref_quality'
ref_quality = varargin{2};
case 'max_chromosome_dist'
max_chromosome_dist = varargin{2};
case 'quit_treshold'
quit_treshold = varargin{2};
case 'tabu_time'
tabu_time = varargin{2};
case 'minimum_improvement'
minimum_improvement = varargin{2};
case 'ref_node_assemblies'
ref_node_assemblies = assemblies(varargin{2},:);
case 'extend_ends'
endextend = assemblies(varargin{2},:);
case 'AllowReverse'
AllowReverse = varargin{2};
case 'ReferenceAlignment'
ReferenceAlignment = varargin{2};
case 'containment_edge'
containment_edge = varargin{2};
case 'ref_first'
ref_first = varargin{2};
case 'mapfilter'
mapfilter = varargin{2};
case 'alignlen'
alignlen = varargin{2};
case 'ident'
ident = varargin{2};
otherwise
error(['Input ' varargin{2} ' is not known']);
end
if length(varargin) > 2
varargin = varargin(3:end);
else
break;
end
end
end
% Read input assemblies
assembly_names = assemblies(:,1);
assembly_locs = assemblies(:,2);
assembly_quality = containers.Map(assemblies(:,1),assemblies(:,3));
assembly_quality('reference') = ref_quality;
% Read input assemblies for creation of reference nodes
ref_node_assembly_names = ref_node_assemblies(:,1);
ref_node_assembly_locs = ref_node_assemblies(:,2);
ref_node_assembly_quality = containers.Map(ref_node_assemblies(:,1),ref_node_assemblies(:,3));
ref_node_assembly_quality('reference') = ref_quality;
% If there is only one assembly there is nothing to align
if size(assemblies,1) >= 2
% Align assemblies against each other
assembly_pairs = {};
coordsfiles = [];
deltafiles = [];
for i = 1:length(assembly_locs)-1
for j = i+1:length(assembly_locs)
[coordsfile,deltafile] = align_assemblies({assembly_locs{i},assembly_locs{j}},{assembly_names{i}, assembly_names{j}}, ...
mapfilter, alignlen, ident);
coordsfiles = [coordsfiles; coordsfile];
%deltafiles = [deltafiles deltafile];
deltafiles = [deltafiles; {deltafile}];
assembly_pairs = [assembly_pairs;[assembly_names(i) assembly_names(j)]];
end
end
% fprintf('Loading alignment files.\n');
% load alignments_done;
% Put the nucmer alignments in an adjency matrix
%[adj, names, name_hash, contig, overlap] = get_adj_matrix(coordsfiles, assembly_pairs, assembly_quality, z_weights, 'clipping_thrs', clipping_thrs, 'dove_tail', 'double','edge_weight','z-scores', 'containment_edge', true);
[adj, names, name_hash, contig, overlap] = get_adj_matrix(deltafiles, assembly_pairs, assembly_quality, z_weights, 'clipping_thrs', clipping_thrs, 'dove_tail', 'double','edge_weight','z-scores', 'containment_edge', containment_edge);
% Merge deltafiles
deltafilesnew = deltafiles{1};
if size(deltafiles,1) > 1
for di = 2:size(deltafiles,1)
deltafilesnew = [deltafilesnew deltafiles{di}];
end
end
deltafiles = deltafilesnew;
else
assembly_pairs = {};
coordsfiles = [];
deltafiles = [];
adj = [];
names = {};
name_hash = containers.Map;
contig = struct('name',{},'size',[],'chromosome',[],'number',[], 'assembly', [], 'assembly_quality', []);
overlap = struct('Q',{},'R',[],'S1',[],'E1', [], 'S2', [], 'E2', [], 'LEN1', [], 'LEN2', [], 'IDY', [], 'COVR', [], 'COVQ', [],'LENR',[], 'LENQ',[]);
end
% Ad the pseudo nodes to the graph. If the contigs have already been
% aligned to the reference genome, just select the alignments that
% correspond to the target chromosome
if isequal(ReferenceAlignment,'NotYetDoneByMaia')
% Align all contigs in 'contig_sets_fasta' to the reference chromosome
[contig_ref, overlap_ref, name_hash_ref, deltafiles_ref] = align_contigs_sets(...
ref_genome, ref_node_assembly_locs, ref_node_assembly_names, ...
ref_node_assembly_quality, clipping_thrs, z_weights, ...
ref_distance,max_chromosome_dist);
ReferenceAlignment = 'out2.delta';
end
% Select only the entries in the deltafile for the current target chromosome
[contig_target_ref, overlap_target_ref, name_hash_target_ref, delta_target_ref] = ...
GetVariablesForTargetChromosome(...
contig_ref, overlap_ref, deltafiles_ref);
% Ref clipping should be high in case of tiling
%if isequal(max_chromosome_dist,'tiling')
% clipping_thrs = 10000
%end
% Add reference nodes to the adjency matrix
[adj, names, name_hash, contig, overlap, delta_target_ref, Startnode_name, Endnode_name] = get_reference_nodes( ...
adj, names, name_hash, contig, overlap, target_chromosome, ...
contig_target_ref, overlap_target_ref, name_hash_target_ref, delta_target_ref, ...
max_chromosome_dist, ref_distance, clipping_thrs, ref_first,...
Startnode_name, Endnode_name, AllowReverse);
% Give reference edges some small extra value to distict between
% assemblies to which a reference node leads
% adj = rank_reference_edges(adj,contig,assembly_quality);
% Specify a start and an end node for the assembly
Startnode = name_hash(Startnode_name);
Endnode = name_hash(Endnode_name);
% Find the best scoring path
fprintf('Directing the final graph\n');
% Calculate path on undirected graph to get an idea on how to direct the graph
[longest_path weigth] = longest_path_tabu(adj, Startnode, Endnode, quit_treshold, tabu_time, minimum_improvement);
% Make the graph directed (greedy)
[adj_direct contig_direct] = direct_graph(adj,overlap, contig, names, name_hash,clipping_thrs, Startnode, longest_path, true, ref_first);
% Calcultate final layout-path
fprintf('Find highest scoring path\n');
[longest_path_direct weigth_direct] = longest_path_tabu(adj_direct, Startnode, Endnode, quit_treshold, tabu_time, minimum_improvement);
function [contig_target_ref, overlap_target_ref, name_hash_target_ref, delta_target_ref] = ...
GetVariablesForTargetChromosome(...
contig_ref, overlap_ref, deltafiles_ref)
% Select only the entries in the deltafile for the current target chromosome
delta_target_ref = deltafiles_ref;
for di = size(delta_target_ref,2):-1:1
if ~isequal(delta_target_ref(di).R,target_chromosome)
delta_target_ref(di) = [];
end
end
overlap_target_ref = overlap_ref;
for oi = size(overlap_target_ref,2):-1:1
if ~isequal(overlap_target_ref(oi).R,target_chromosome)
overlap_target_ref(oi) = [];
end
end
contig_target_ref = contig_ref;
for ci = size(contig_target_ref,1):-1:1
if isequal(contig_target_ref(ci).assembly, 'reference') && ~isequal(contig_target_ref(ci).name,target_chromosome)
contig_target_ref(ci) = [];
end
end
name_hash_target_ref = make_hash({contig_target_ref.name}');
end
end
There is no exact equivalent of containers.Map in Octave that I know of...
One option is to use the java package to create java.util.Hashtable. Using this example:
pkg load java
d = javaObject("java.util.Hashtable");
d.put('a',1)
d.put('b',2)
d.put('c',3)
d.get('b')
If you are willing to do a bit of rewriting, you can use the builtin struct as a rudimentary hash table with strings (valid variable names) as keys, and pretty much anything stored in values.
For example, given the following:
keys = {'Mon','Tue','Wed'}
values = {10, 20, 30}
you could replace this:
map = containers.Map(keys,values);
map('Mon')
by:
s = struct();
for i=1:numel(keys)
s.(keys{i}) = values{i};
end
s.('Mon')
You might need to use genvarname to produce valid keys, or maybe a proper hashing function that produces valid key strings.
Also look into struct-related functions: getfield, setfield, isfield, fieldnames, rmfield, etc..

Cubic spline in matlab

i have trouble getting a matlab code to work properly! i found a cubic spline code in matlab to give me the interpolated polynomial. and i simply give it an example to work:
Xi = [0 0.05 0.1]
Fi = [1 1.105171 1.221403]
Fi' = [2 _ 2.442806]
but it gives me this error:
??? Attempted to access du(1); index out of bounds because numel(du)=0.
Error in ==> cubic_nak at 53
du(1) = du(1) - hi(1)^2 / hi(2);
here is the full code for not a knot condition
function csn = cubic_nak ( xi, fi )
%CUBIC_NAK compute the cubic spline interpolant, subject to
% "not-a-knot" boundary conditions, associated with a
% given set of interpolating points and function values
%
% calling sequences:
% csn = cubic_nak ( xi, fi )
% cubic_nak ( xi, fi )
%
% inputs:
% xi vector containing the interpolating points
% (must be sorted in ascending order)
% fi vector containing function values
% the i-th entry in this vector is the function
% value associated with the i-th entry in the 'xi'
% vector
%
% output:
% csn five column matrix containing the information which
% defines the "not-a-knot" cubic spline interpolant
% - first column: interpolating points
% - second column: function values
% - third column: coefficients of linear terms
% - fourth column: coefficients of quadratic terms
% - fifth column: coefficients of cubic terms
%
% NOTE:
% to evaluate the "not-a-knot" cubic spline interpolant apply
% the routine SPLINE_EVAL to the output of this routine
%
n = length ( xi );
m = length ( fi );
if ( n ~= m )
disp ( 'number of ordinates and number of function values must be equal' )
return
end
for i = 1 : n-1
hi(i) = xi(i+1) - xi(i);
end
for i = 1 : n-2
dd(i) = 2.0 * ( hi(i) + hi(i+1) );
ri(i) = (3.0/hi(i+1))*(fi(i+2)-fi(i+1))-(3.0/hi(i))*(fi(i+1)-fi(i));
end
dd(1) = dd(1) + hi(1) + hi(1)^2 / hi(2);
dd(n-2) = dd(n-2) + hi(n-1) + hi(n-1)^2 / hi(n-2);
du = hi(2:n-2);
dl = du;
du(1) = du(1) - hi(1)^2 / hi(2);
dl(n-3) = dl(n-3) - hi(n-1)^2 / hi(n-2);
temp = tridiagonal ( dl, dd, du, ri );
c = zeros ( n,1 );
d = c; b = c;
c(2:n-1) = temp;
c(1) = ( 1 + hi(1) / hi(2) ) * c(2) - hi(1) / hi(2) * c(3);
c(n) = ( 1 + hi(n-1) / hi(n-2) ) * c(n-1) - hi(n-1) / hi(n-2) * c(n-2);
for i = 1 : n-1
d(i) = (c(i+1)-c(i))/(3.0*hi(i));
b(i) = (fi(i+1)-fi(i))/hi(i) - hi(i)*(c(i+1)+2.0*c(i))/3.0;
end
if ( nargout == 0 )
disp ( [ xi' fi' b c d ] )
else
csn = [ xi' fi' b c d ];
end
also for the clamped condition it gives me this error:
??? Undefined function or method 'tridiagonal' for input arguments of type 'double'.
Error in ==> cubic_clamped at 55
c = tridiagonal ( hi(1:n-1), dd, hi(1:n-1), ri );
??? Input argument "xi" is undefined.
Error in ==> cubic_clamped at 35
n = length ( xi );
the full code for clamped mode:
function csc = cubic_clamped ( xi, fi, fpa, fpb )
%CUBIC_CLAMPED compute the cubic spline interpolant, subject to
% "clamped" boundary conditions, associated with a
% given set of interpolating points and function values
%
% calling sequences:
% csc = cubic_clamped ( xi, fi, fpa, fpb )
% cubic_clamped ( xi, fi, fpa, fpb )
%
% inputs:
% xi vector containing the interpolating points
% (must be sorted in ascending order)
% fi vector containing function values
% the i-th entry in this vector is the function
% value associated with the i-th entry in the 'xi'
% vector
% fpa derivative value at left endpoint; i.e., xi(1)
% fpb derivative value at right endpoint; i.e., xi(n)
%
% output:
% csn five column matrix containing the information which
% defines the "clamped" cubic spline interpolant
% - first column: interpolating points
% - second column: function values
% - third column: coefficients of linear terms
% - fourth column: coefficients of quadratic terms
% - fifth column: coefficients of cubic terms
%
% NOTE:
% to evaluate the "clamped" cubic spline interpolant apply
% the routine SPLINE_EVAL to the output of this routine
%
n = length ( xi );
m = length ( fi );
if ( n ~= m )
disp ( 'number of ordinates and number of function values must be equal' )
return
end
for i = 1 : n-1
hi(i) = xi(i+1) - xi(i);
end
dd(1) = 2.0*hi(1); dd(n) = 2.0*hi(n-1);
ri(1) = (3.0/hi(1))*(fi(2)-fi(1)) - 3.0 * fpa;
ri(n) = 3.0 * fpb - (3.0/hi(n-1))*(fi(n)-fi(n-1));
for i = 1 : n-2
dd(i+1) = 2.0 * ( hi(i) + hi(i+1) );
ri(i+1) = (3.0/hi(i+1))*(fi(i+2)-fi(i+1))-(3.0/hi(i))*(fi(i+1)-fi(i));
end
disp ( [dd' ri'] )
c = tridiagonal ( hi(1:n-1), dd, hi(1:n-1), ri );
d = zeros ( n,1 );
b = d;
for i = 1 : n-1
d(i) = (c(i+1)-c(i))/(3.0*hi(i));
b(i) = (fi(i+1)-fi(i))/hi(i) - hi(i)*(c(i+1)+2.0*c(i))/3.0;
end
if ( nargout == 0 )
disp ( [ xi' fi' b c' d ] )
else
csc = [ xi' fi' b c' d ];
end
for this one it only gives me the first 2 columns!
so anyone knows how i can make these 2 work?
Your data only has 3 points. You need 4 (or more) points to fit a cubic, so your out-of-bounds error probably comes from the code looking for another point in the array.