# HG changeset patch
# User jwe
# Date 848344000 0
# Node ID 704d7e130e71d3b3cab5cdffcb445da4fc162b70
# Parent  e2a7c830472ca52f8905b2af1ab47a5467f6ebf2
[project @ 1996-11-18 19:06:39 by jwe]

diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/conv-amr.m
--- a/scripts/polynomial/conv-amr.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/conv-tuwien.m
--- a/scripts/polynomial/conv-tuwien.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/deconv-amr.m
--- a/scripts/polynomial/deconv-amr.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/deconv-tuwien.m
--- a/scripts/polynomial/deconv-tuwien.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
-    
-
-
-
-
-
-
-
-
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/poly-amr.m
--- a/scripts/polynomial/poly-amr.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/poly-tuwien.m
--- a/scripts/polynomial/poly-tuwien.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/roots-amr.m
--- a/scripts/polynomial/roots-amr.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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
diff -r e2a7c830472c -r 704d7e130e71 scripts/polynomial/roots-tuwien.m
--- a/scripts/polynomial/roots-tuwien.m	Sun Nov 17 21:42:37 1996 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -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