MATLAB: How to create a vector with a sequence 1, u, u(u-1), u(u-1)(u-2)….

create a vector of a sequence

How to create a vector with a sequence 1, u, u(u-1), u(u-1)(u-2)….

Best Answer

syms u
n = 7;
A = [1,cumprod(u - (0:n))];
A =
[ 1, u, u*(u - 1), u*(u - 1)*(u - 2), u*(u - 1)*(u - 2)*(u - 3), u*(u - 1)*(u - 2)*(u - 3)*(u - 4), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5)*(u - 6), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5)*(u - 6)*(u - 7)]

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MATLAB: Manipulating matrix in particular columns

final_result = {
'Genes'      'T0&T2'    'T1&T3'    'T2&T4'    'T3&T5'    'T4&T6'
'YAR029W'    'dd'       'uu'       'dd'       'uu'       'du'
'YBL095W'    'du'       'ud'       'ud'       'du'       'du'
'YBL111C'    'uu'       'uu'       'ud'       'ud'       'du'
'YBL113C'    'uu'       'uu'       'uu'       'ud'       'ud'
'YBR096W'    'uu'       'uu'       'ud'       'ud'       'dd'
'YBR138C'    'ud'       'ud'       'ud'       'du'       'du' };
final = {
'YAR029W'    'd'     []    'd'     []    'd'
'YBL095W'    'd'     []     []    'd'    'd'
'YBL111C'    'u'    'u'    'u'    'u'     []
'YBL113C'    'u'    'u'    'u'    'u'    'u'
'YBR096W'    'u'    'u'    'u'    'u'     []
'YBR138C'    'd'     []     []    'd'    'd'};
n = ~cellfun(@isempty,final(:,2:end));
fnl = arrayfun(@(x)final_result([1,x+1:end],[true,n(x,:)]),(1:size(n,1))','un',0);

MATLAB: Matlab solve indeterminate polynomial equations numerically

Finally, I find out the answer, it seems matlab will do some approximations, the true system is

eqstrue=[ u6*(3*u5 - 1) - u4 - u1 - 3*u2*u3 - 3*u5*u6 + 3*u3*(u2 - 1) + 1/24, u2^2*u3*(u2 - 1) - 2*u5^3*u6 - u2*u3*(u2 - 1)^2 - (2*u4)/27 - u5*u6*(3*u5 - 1)^2 + u5^2*u6*(3*u5 - 1) + 1/360, 1/1260 - 2*u5^4*u6 - 2*u5^2*u6*(3*u5 - 1)^2 - 2*u2^2*u3*(u2 - 1)^2 - (2*u4)/81, u5^2*u6*(3*u5 - 1)^3 - 3*u5^5*u6 - u4/81 - 4*u5^3*u6*(3*u5 - 1)^2 + 4*u5^4*u6*(3*u5 - 1) + 1/2880, 9*u5^4*u6*(3*u5 - 1) - 3*u5^3*u6*(3*u5 - 1)^2 + 1/6720, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 - 3*u5^4*u6*(3*u5 - 1)^3 - 6*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) - 3*u5^6*u6*(3*u5 - 1) + 1/21600, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 + u5^4*u6*(3*u5 - 1)^3 + 2*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) + u5^6*u6*(3*u5 - 1) + 11/226800]

after I make

a2 = 1; b2 = -1; b3 = 1;

matlab solves the approximatied system

eqs=[ u6*(3*u5 - 1) - u4 - u1 - 3*u2*u3 - 3*u5*u6 + 3*u3*(u2 - 1) + 1/24, u2^2*u3*(u2 - 1) - 2*u5^3*u6 - u2*u3*(u2 - 1)^2 - (2*u4)/27 - u5*u6*(3*u5 - 1)^2 + u5^2*u6*(3*u5 - 1) + 1/360, 1/1260 - 2*u5^4*u6 - 2*u5^2*u6*(3*u5 - 1)^2 - 2*u2^2*u3*(u2 - 1)^2 - (2*u4)/81, u5^2*u6*(3*u5 - 1)^3 - 3*u5^5*u6 - u4/81 - 4*u5^3*u6*(3*u5 - 1)^2 + 4*u5^4*u6*(3*u5 - 1) + 1/2880, 9*u5^4*u6*(3*u5 - 1) - 3*u5^3*u6*(3*u5 - 1)^2 + 1/6720, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 - 3*u5^4*u6*(3*u5 - 1)^3 - 6*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) - 3*u5^6*u6*(3*u5 - 1) + 34433922270924495617/743772721051969121157120, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 + u5^4*u6*(3*u5 - 1)^3 + 2*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) + u5^6*u6*(3*u5 - 1) + 37713343439583972437/743772721051969121157120];

so it gives me an answer, I don't know why it does this. In the last equation.

vpa(11/226800 - 37713343439583972437/743772721051969121157120)
ans = -0.0000022045855379188659798651850341144609

It's a bad approximation.

Best Answer

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MATLAB: Manipulating matrix in particular columns

MATLAB: Matlab solve indeterminate polynomial equations numerically

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