Mercurial > hg > octave-lojdl
changeset 2528:704d7e130e71
[project @ 1996-11-18 19:06:39 by jwe]
author | jwe |
---|---|
date | Mon, 18 Nov 1996 19:06:40 +0000 |
parents | e2a7c830472c |
children | 90fa35bd0216 |
files | scripts/polynomial/conv-amr.m scripts/polynomial/conv-tuwien.m scripts/polynomial/deconv-amr.m scripts/polynomial/deconv-tuwien.m scripts/polynomial/poly-amr.m scripts/polynomial/poly-tuwien.m scripts/polynomial/roots-amr.m scripts/polynomial/roots-tuwien.m |
diffstat | 8 files changed, 0 insertions(+), 371 deletions(-) [+] |
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deleted file mode 100644 --- a/scripts/polynomial/conv-amr.m +++ /dev/null @@ -1,52 +0,0 @@ -function y = conv(a,b) -#Convolve two vectors. -#y = conv(a,b) returns a vector of length equal to length(a)+length(b)-1. -#If a and b are polynomial coefficient vectors, conv returns the -#coefficients of the product polynomial. -# -#SEE ALSO: deconv, poly, roots, residue, polyval, polyderiv, polyinteg - -# Author: -# Tony Richardson -# amr@mpl.ucsd.edu -# June 1994 - - if(nargin != 2) - error("usage: conv(a,b)"); - endif - - if(is_matrix(a) || is_matrix(b)) - error("conv: both arguments must be vectors"); - endif - - la = length(a); - lb = length(b); - - ly = la + lb - 1; - - # Ensure that both vectors are row vectors. - if(rows(a) > 1) - a = reshape(a,1,la); - endif - if(rows(b) > 1) - b = reshape(b,1,lb); - endif - - # Use the shortest vector as the coefficent vector to filter. - if (la < lb) - if(ly>lb) - x = [b zeros(1,ly-lb)]; - else - x = b; - endif - y = filter(a,1,x); - else - if(ly>la) - x = [a zeros(1,ly-la)]; - else - x = a; - endif - y = filter(b,1,x); - endif - -endfunction
deleted file mode 100644 --- a/scripts/polynomial/conv-tuwien.m +++ /dev/null @@ -1,43 +0,0 @@ -function c=conv(a,b) -# -# usage: conv(a,b) -# -# Returns the convolution of vectors a and b. The resulting vector -# is of length(a)+length(b)-1. If a and b are polynomial coefficients -# conv(a,b) is equivalent to polynomial multiplication. - -# written by Gerhard Kircher on Aug 27, 1993 -# modified by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 23, 1993. - - l_a = length(a); - l_b = length(b); - return_row = 0; - if (l_a > l_b) - if (rows(a) == 1) - return_row = 1; - endif - else - if (rows(b) == 1) - return_row = 1; - endif - endif - a = reshape(a, l_a, 1); - b = reshape(b, l_b, 1); - if (l_a == 1 || l_b == 1) - c = a * b; - else - l_c = l_a + l_b - 1; - a(l_c) = 0; - b(l_c) = 0; - c = ifft(fft(a) .* fft(b)); - if !( any(imag(a)) || any(imag(b)) ) - c = real(c); - endif - if !( any(a-round(a)) || any(b-round(b)) ) - c = round(c); - endif - endif - if (return_row == 1) - c = c'; - end -endfunction
deleted file mode 100644 --- a/scripts/polynomial/deconv-amr.m +++ /dev/null @@ -1,51 +0,0 @@ -function [b, r] = deconv(y,a) -#Deconvolve two vectors. -# -#[b, r] = deconv(y,a) solves for b and r such that: -# -# y = conv(a,b) + r -# -#If y and a are polynomial coefficient vectors, b will contain the -#coefficients of the polynomial quotient and r will be a remander -#polynomial of lowest order. -# -#SEE ALSO: conv, poly, roots, residue, polyval, polyderiv, polyinteg - -# Author: -# Tony Richardson -# amr@mpl.ucsd.edu -# June 1994 - - if(nargin != 2) - error("usage: deconv(y,a)"); - endif - - if(is_matrix(y) || is_matrix(a)) - error("conv: both arguments must be vectors"); - endif - - la = length(a); - ly = length(y); - - lb = ly - la + 1; - - if (ly>la) - b = filter(y,a,[1 zeros(1,ly-la)]); - elseif (ly == la) - b = filter(y,a,1); - else - b = 0; - endif - - b = polyreduce(b); - - lc = la + length(b) - 1; - if(ly == lc) - r = y - conv(a,b); - else - r = [ zeros(1,lc-ly) y] - conv(a,b); - endif - - r = polyreduce(r); - -endfunction
deleted file mode 100644 --- a/scripts/polynomial/deconv-tuwien.m +++ /dev/null @@ -1,47 +0,0 @@ -function [x, r] = deconv(a, b) -# -# Returns x and r such that a = conv(b, x) + r. -# If a and b are vectors of polynomial coefficients, x and r are the -# vectors of coefficients of quotient and remainder in the polynomial -# division of a by b. - -# written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 27, 1993 -# copyright Dept of Probability Theory and Statistics TU Wien - - if !(nargin == 2) - error("usage: deconv(a, b)"); - endif - f = find(b); - l_b = length(f); - if (l_b == 0) - error("deconv(a, b): b has to be nonzero"); - endif - l_a = length(a); - if (l_a < l_b) - x = 0; - r = a; - else - b = reshape(b(f(1):f(l_b)), 1, l_b); - a = reshape(a, 1, l_a); - # the stupid way: - if (l_b == 1) - x = a / b; - else - x(1) = a(1) ./ b(1); - for i = 2:l_a-l_b+1; - x(i) = (a(i) - b(i:-1:2) * x(1:i-1)) ./ b(1); - endfor - endif - r = a - conv(b, x); - endif - -endfunction - - - - - - - - -
deleted file mode 100644 --- a/scripts/polynomial/poly-amr.m +++ /dev/null @@ -1,54 +0,0 @@ -function c = poly(r) -#Find the coefficients of a polynomial from its roots. -#Find the characteristic polynomial of a matrix. -# -#Given a vector r of length n containing the n roots of polynomial p(x) -# -# p(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(n)) -# -#poly(r) will return a coefficient vector c of length n+1 such that -# -# p(x) = c(1) x^n + ... + c(n) x + c(n+1). -# -#and c(1) will always be equal to one. -# -#Given a matrix A, poly(A) will return a vector containing the coefficients -#of the characteristic polynomial of A, det(xI - A). -# -#poly and roots are inverse functions to within a scaling factor. -# -#SEE ALSO: roots, conv, deconv, residue, filter, polyval, polyderiv, polyinteg - -# Author: -# Tony Richardson -# amr@mpl.ucsd.edu -# June 1994 - - if(nargin != 1) - error("usage: roots(argument)"); - endif - - l = length(r) + 1; - - if (is_scalar(r)) - c = [1 -r]; - return; - elseif(l == 1) - # r is an empty matrix. - # Matlab compatibility - c = 1; - return; - elseif (is_square(r)) - r = eig(r); - elseif (is_matrix(r)) - error("poly: matrix argument must be square."); - endif - - c = ones(1,l); - c(l) = -r(1); - for index = 2:(l-1) - m = l + 2 - index; - c((m-1):l) = [c(m:l) 0] - r(index)*[1 c(m:l)]; - endfor - -endfunction
deleted file mode 100644 --- a/scripts/polynomial/poly-tuwien.m +++ /dev/null @@ -1,32 +0,0 @@ -function y = poly (x) -# -# If A is a square matrix, poly (A) is the row vector of coefficients of -# the characteristic polynomial det (z * eye(A) - A). -# If x is a vector, poly (x) is a vector of coefficients of the polynomial -# whose roots are the elements of x. - -# written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 24, 1993 -# copyright Dept of Probability Theory and Statistics TU Wien - - m = min(size(x)); - n = max(size(x)); - if (m == 0) - y = 1; - elseif (m == 1) - v = x; - elseif (m == n) - v = eig(x); - else - error("usage: poly(x), where x is a vector or a square matrix"); - endif - - y = [ 1 zeros(1,n) ]; - for j = 1:n; - y(2:(j+1)) = y(2:(j+1)) - v(j) .* y(1:j); - endfor - - if all(imag(x) == 0) - y = real(y); - endif - -endfunction
deleted file mode 100644 --- a/scripts/polynomial/roots-amr.m +++ /dev/null @@ -1,55 +0,0 @@ -function r = roots(c) -#Find the roots of a polynomial. -# -#In octave, a polynomial is represented by it's coefficients (arranged -#in descending order). For example, a vector c of length n+1 corresponds -#to the following nth order polynomial -# -# p(x) = c(1) x^n + ... + c(n) x + c(n+1). -# -#roots(c) will return a vector r of length n such that -# -# p(x) = c(1) [ (x - r(1)) * (x - r(2)) * ... * (x - r(n)) ] -# -#roots and poly are inverse functions to within a scaling factor. -# -#SEE ALSO: poly, roots, conv, deconv, residue, filter, polyval, polyvalm, -# polyderiv, polyinteg - -# Author: -# Tony Richardson -# amr@mpl.ucsd.edu -# June 1994 - - if(nargin != 1) - error("usage: roots(vector)"); - endif - - if(is_matrix(c)) - error("argument must be a vector."); - endif - - n = length(c); - - if(is_scalar(c) || n == 0) - r = []; - return; - endif - - # Ensure that c is a row vector. - if(rows(c) > 1) - c = reshape(c,1,n); - endif - - # We could replace this with a call to compan, but it's faster to - # just reproduce the code here. - A = diag(ones(n-2,1),-1); - A(1,:) = -c(2:n)/c(1); - - r = eig(A); - - # Sort roots in order by decreasing magnitude. - [mr i] = sort(abs(r)); - r = r(i(length(i):-1:1)); - -endfunction
deleted file mode 100644 --- a/scripts/polynomial/roots-tuwien.m +++ /dev/null @@ -1,37 +0,0 @@ -function r = roots(v) -# -# For a vector v with n components, return the roots of the polynomial -# v(1)*z^(n-1) + ... + v(n-1) * z + v(n). - -# written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 24, 1993 -# copyright Dept of Probability Theory and Statistics TU Wien -# modified by KH on Jan 10, 1994 - - [nr, nc] = size(v); - if !((nr == 1 && nc > 1) || (nc == 1 && nr > 1)) - error("usage: roots(v), where v is a nonzero vector"); - endif - n = nr + nc - 1; - v = reshape(v,1,n); - # If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the - # leading k zeros and n-k-l roots of the polynomial are zero. - f = find(v); - m = max(size(f)); - if (m > 0) - v = v(f(1):f(m)); - l = max(size(v)); - if (l > 1) - A = diag(ones(1, l-2), -1); - A(1,:) = -v(2:l) ./ v(1); - r = eig(A); - if (f(m) < n) - r = [r; zeros(n-f(m), 1)]; - endif - else - r = zeros(n-f(m), 1); - endif - else - error("usage: roots(v), where v is a nonzero vector"); - endif - -endfunction