MatLabPolynomial

How to create symbolic polynomial  with specific vector of coefficients of symbolic variables in MatLab? - poly2sym -- MatLab How to create symbolic polynomial  with specific vector of coefficients of symbolic variables in MatLab? [Ans] poly2sym [description] sym coeefficients -> poly more details on: Create symbolic polynomial from vector of coefficients - MATLAB poly2sym (mathworks.com) code: clear clc syms a b c d p = poly2sym([a, b, c, d]) fprintf( "1\n" ); p = poly2sym(sym([1/2, -1/3, 1/4])) fprintf( "2\n" ); p = poly2sym([0.75, -0.5, 0.25]) fprintf( "3\n" ); syms a b c d t p = poly2sym([a, b, c, d], t) fprintf( "4\n" ); p1 = subs(p, t, t^2 + 1) p2 = subs(p, t, exp(t)) fprintf( "5\n" ); result: p = a*x^3 + b*x^2 + c*x + d 1 p = x^2/2 - x/3 + 1/4 2 p = (3*x^2)/4 - x/2 + 1/4 3 p = a*t^3 + b*t^2 + c*t + d 4 p1 = d + a*(t^2 + 1)^3 + b*(t^2 + 1)^2 + c*(t^2 + 1) p2 = d + c*exp(t) + a*exp(3*t) + b*exp(2*t) 5  

How to extract coefficients from given symbolic polynomial in MatLab? sym2poly -- MatLab How to extract coefficients from given symbolic polynomial in MatLab?  [Ans] sym2poly  [description] extract coefficients from given polynomial. more details on: Extract vector of all numeric coefficients, including zeros, from symbolic polynomial - MATLAB sym2poly (mathworks.com) code: clear clc syms x c = sym2poly(x^3 - 2*x - 5) fprintf( "1\n" ); c = sym2poly(1/2*x^3 - 2/3*x - 5) fprintf( "2\n" ); result: c = 1 0 -2 -5 1 c = 0.5000 0 -0.6667 -5.0000

 How to find coefficient of a polynomial in MatLab? - coeffs -- MatLab  How to find coefficient of a polynomial in MatLab?  [Ans] coeffs [description] Find all coefficient of a polynomial with symbolic variables. more details on: Coefficients of polynomial - MATLAB coeffs (mathworks.com) code: clear clc syms x ; c = coeffs(16*x^2 + 19*x + 11) fprintf( "1\n" ) syms x y cx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x) cy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y) fprintf( "2\n" ) syms x y cxy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x y]) cyx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y x]) fprintf( "3\n" ) syms x [c,t] = coeffs(16*x^2 + 19*x + 11) fprintf( "4\n" ) syms x y [cx,tx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x) [cy,ty] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y) fprintf( "5\n" ) syms x y [cxy, txy] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x,y]) [cyx, tyx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y,x]) fprintf( ...

 eg10_1 code1: clear clc a=[0.1 1;0.2 1.1;0.3 1.2;0.4 1.3;0.5 1.1;0.6 0.9;0.7 0.7;0.8 1.0;0.9 1.2;1 1.3]; plot(a(:,1),a(:,2), '*' );%fig(b) axis([0.1 1 0.5 1.5]); pause p=polyfit(a(:,1),a(:,2),4); fprintf( 'order of polynomial is 4' ); p t=[0.1:0.001:0.95]; nev=polyval(p,t); plot(t,nev,a(:,1),a(:,2), '*' );%fig(c) axis([0 1.1 0.6 1.4]); grid title( 'order of polynomial is 4' ); xlabel( 'input data' ); ylabel( 'output data' ); pause fig(a) fig(b) fig(c)

 How to get interploated values corresponding to the query point in MatLab? - spline -- MatLab How to get interploated values corresponding to the query point in MatLab?  [Ans] spline [Description] spline is abbrevaition of sample point linearly interpolation. (I guess.) (1) s  = spline( x , y , xq ) ; It will return  a vector of interpolated values  s  corresponding to the query points in  xq . The values of  s  are determined by cubic spline interpolation of  x  and  y . (2) pp = spline(x,y) ; It will return a piecewise polynomial structure for use by  ppval  and the spline utility  unmkpp . more details on: Cubic spline data interpolation - MATLAB spline (mathworks.com) code clear clc help spline ; %spline example1 %fig(a) x = [0 1 2.5 3.6 5 7 8.1 10]; y = sin(x); xx = 0:.25:10; yy = spline(x,y,xx); plot(x,y, 'o' ,xx,yy) %spline example2 %fig(b) x = -4:4; y = [0 .15 1.12 2.36 2.36 1.46 .49 .06 0]; cs = spline...

 How to  get an approximately value with number data with specified polynomial in MatLab? - polyfit -- MatLab How to  get an apprixmate value with number data with specified polynomial in MatLab? [Ans] polyfit [syntax] [<p>,<S>,<mu>] = polyfit(<x>,<y>,<n>) ; [description] [<p>,<S>,<mu>] = polyfit(<x>,<y>,<n>) ; It will return approximately value with x-axis data <x> and y-axis data <y> which is represented with degree n of the polynomial. <p> coefficient of polynomial <S> structure of polynomial <mu> population of mean in distribution more details about mu (one of Greek Letters) on: μ - Wiktionary Mu (letter) - Wikipedia statistics - How do I calculate mu and sigma? - Mathematics Stack Exchange more details on: Polynomial curve fitting - MATLAB polyfit (mathworks.com) code clear clc x = linspace(0,4*pi,10); y = sin(x); p = polyfit(x,y,7) %{ p = -0.0001 0.0028 -0.0...

How to multiple or divide two polynomials in MatLab? - conv - deconv -- MatLab How to multiple or divide two polynomials in MatLab? [Ans] conv:multiple deconv:divide [Description] conv Convolution and polynomial multiplication w = conv( u,v )   It will return the  convolution  of vectors  u  and  v . If  u  and  v  are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials. w = conv( u,v , shape )   It will return a subsection of the convolution, as specified by  shape . For example,  conv(u,v,'same')  returns only the central part of the convolution, the same size as  u , and  conv(u,v,'valid')  returns only the part of the convolution computed without the zero-padded edges. deconv Deconvolution and polynomial division [ q , r ] = deconv( u,v )   It will deconvolve a vector  v  out of a vector  u  using long division, and returns th...

 How to calculate a polynomial with specified point in MatLab? - polyval -- MatLab How to calculate a polynomial with specified point in MatLab? [Ans] polyval [description] Evaluate polynomial <Y> = polyval (<P>,<X>) It will return the value of a polynomial P evaluated at X. <P>   is a vector of length N+1 whose elements are the coefficients of the polynomial in descending powers: Y = P(1)*X^N + P(2)*X^(N-1) + ... + P(N)*X + P(N+1) P is vector type. <X> is a given value double or single or int type. more details on: Polynomial evaluation - MATLAB polyval (mathworks.com) code clear clc c=[1 0]; d=1:1:10; polyval(c,d) fprintf( "1\n" ); %{ output: 1 2 3 4 5 6 7 8 9 10 %} c=[1 0]; d=1:1:10; polyval(c,d) fprintf( "2\n" ); %{ output: 1 2 3 4 5 6 7 8 9 10 %}

 How to get polynomial by the given root in MatLab? - poly -- MatLab How to get polynomial by the given root in MatLab? [Ans] poly [description] (1) <pr_coef>=poly(<pr_vec>); It  will return coefficients of polynomial with specified roots of polynomial. <pr_coef>  coefficients of polynomial. vector type. <pr_vec> specified roots of polynomial. vector type. (2) <pr_M>=poly(<M>) Let M is be a N by N matrix. pr_M is a row vector with N+1 elements which are the coefficients of the characteristic polynomial. It is computed by det(lambda*eye(size(M)) - M). <pr_M> pr_M is coefficients of characterist polynomial. vector type. <M> roots of polynomial Square-Matrix type. more details on: Polynomial with specified roots or characteristic polynomial - MATLAB poly (mathworks.com) code: clear clc pr=[1:6] %root of polynomial poly1=poly(pr) %cooefficient of polynomial given by pr. fprintf( "1\n" ); %{ output: pr = 1 2 3 4 ...