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[project @ 1996-11-20 00:20:12 by jwe]
author jwe
date Wed, 20 Nov 1996 00:21:25 +0000
parents 1dca28c213f0
children 80a42c3fefc9
files scripts/ChangeLog scripts/linear-algebra/commutation_matrix.m scripts/linear-algebra/cross.m scripts/linear-algebra/duplication_matrix.m scripts/linear-algebra/vec.m scripts/linear-algebra/vech.m
diffstat 6 files changed, 257 insertions(+), 0 deletions(-) [+]
line wrap: on
line diff
--- a/scripts/ChangeLog
+++ b/scripts/ChangeLog
@@ -1,3 +1,21 @@
+Tue Nov 19 15:13:35 1996  John W. Eaton  <jwe@bevo.che.wisc.edu>
+
+	* linear-algebra/commutation_matrix.m, linear-algebra/cross.m,
+	linear-algebra/duplication_matrix.m, linear-algebra/vec.m,
+	linear-algebra/vech.m: New files from Kurt Hornik.
+
+	* general/nextpow2.m, general/shift.m, general/diff.m,
+	general/common_size.m: New files from Kurt Hornik.
+
+	* miscellaneous/bincoeff.m, miscellaneous/xor.m:
+	New files from Kurt Hornik.
+
+	* signal/detrend.m: New file from Kurt Hornik.
+
+	* specfun/betai.m, specfun/gammai.m, specfun/erfinv.m,
+	specfun/pow2.m, specfun/log2.m:
+	New files and updates from Kurt Hornik.
+
 Fri Nov 15 18:13:00 1996  John W. Eaton  <jwe@bevo.che.wisc.edu>
 
 	* plot/__plt__.m: Add explicit replot after last command is
new file mode 100644
--- /dev/null
+++ b/scripts/linear-algebra/commutation_matrix.m
@@ -0,0 +1,55 @@
+## Copyright (C) 1995, 1996  Kurt Hornik
+## 
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+## 
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details. 
+## 
+## You should have received a copy of the GNU General Public License
+## along with this file.  If not, write to the Free Software Foundation,
+## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+
+## usage:  commutation_matrix (m [, n])
+## 
+## Returns the commutation matrix K_{m,n} which is the unique m*n by
+## m*n matrix such that K_{m,n} * vec (A) = vec (A') for all m by n
+## matrices A.
+##
+## If only one argument m is given, K_{m,m} is returned.
+##
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+
+## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
+## Created: 8 May 1995
+## Adapted-By: jwe
+
+function k = commutation_matrix (m, n)
+  
+  if (nargin < 1 || nargin > 2)
+    usage ("commutation_matrix (m [, n])");
+  else
+    if (! (is_scalar (m) && m == round (m) && m > 0))
+      error ("commutation_matrix: m must be a positive integer");
+    endif
+    if (nargin == 1)
+      n = m;
+    elseif (! (is_scalar (n) && n == round (n) && n > 0))
+      error ("commutation_matrix: n must be a positive integer");
+    endif
+  endif
+  
+  ## It is clearly possible to make this a LOT faster!
+  k = zeros (m * n, m * n);
+  for i = 1 : m
+    for j = 1 : n
+      k ((i - 1) * n + j, (j - 1) * m + i) = 1;
+    endfor
+  endfor
+
+endfunction
new file mode 100644
--- /dev/null
+++ b/scripts/linear-algebra/cross.m
@@ -0,0 +1,44 @@
+## Copyright (C) 1995, 1996  Kurt Hornik
+## 
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+## 
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details. 
+## 
+## You should have received a copy of the GNU General Public License
+## along with this file.  If not, write to the Free Software Foundation,
+## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+
+## usage:  cross (x, y)
+##
+## Computes the vector cross product of the two 3-dimensional vectors
+## x and y.
+
+## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
+## Created: 15 October 1994
+## Adapted-By: jwe
+
+function z = cross (x, y)
+  
+  if (nargin != 2)
+    usage ("cross (x, y)");
+  endif
+
+  if (! (is_vector (x) && length (x) == 3
+	 && is_vector (y) && length (y) == 3))
+    error ("cross: both x and y must be 3-dimensional vectors");
+  endif
+  
+  x = reshape (x, 3, 1);
+  y = reshape (y, 3, 1);
+  e = eye (3, 3);
+  for k = 1 : 3
+    z(k) = det ([x y e(:, k)]);
+  endfor
+
+endfunction
new file mode 100644
--- /dev/null
+++ b/scripts/linear-algebra/duplication_matrix.m
@@ -0,0 +1,53 @@
+## Copyright (C) 1995, 1996  Kurt Hornik
+## 
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+## 
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details. 
+## 
+## You should have received a copy of the GNU General Public License
+## along with this file.  If not, write to the Free Software Foundation,
+## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+
+## usage: duplication_matrix (n)
+## 
+## Returns the duplication matrix D_n which is the unique n^2 by
+## n*(n+1)/2 matrix such that D_n * vech (A) = vec (A) for all
+## symmetric n by n matrices A.
+## 
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+
+## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
+## Created: 8 May 1995
+## Adapged-By: jwe
+
+function d = duplication_matrix (n)
+
+  if (nargin != 1)
+    usage ("duplication_matrix (n)");
+  endif
+
+  if (! (is_scalar (n) && n == round (n) && n > 0))
+    error ("duplication_matrix: n must be a positive integer");
+  endif
+
+  d = zeros (n * n, n * (n + 1) / 2);
+
+  ## It is clearly possible to make this a LOT faster!
+  count = 0;
+  for j = 1 : n
+    d ((j - 1) * n + j, count + j) = 1;
+    for i = (j + 1) : n
+      d ((j - 1) * n + i, count + i) = 1;
+      d ((i - 1) * n + j, count + i) = 1;
+    endfor
+    count = count + n - j;
+  endfor
+
+endfunction
new file mode 100644
--- /dev/null
+++ b/scripts/linear-algebra/vec.m
@@ -0,0 +1,37 @@
+## Copyright (C) 1995, 1996  Kurt Hornik
+## 
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+## 
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details. 
+## 
+## You should have received a copy of the GNU General Public License
+## along with this file.  If not, write to the Free Software Foundation,
+## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+
+## usage:  vec (x)
+##
+## Returns vec (x), the vector obtained by stacking the columns of x
+## one above the other.
+## 
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+
+## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
+## Created: 8 May 1995
+## Adapted-By: jwe
+
+function v = vec (x)
+  
+  if (nargin != 1)
+    usage ("vec (x)"); 
+  endif 
+  
+  v = reshape (x, prod (size (x)), 1);
+
+endfunction
new file mode 100644
--- /dev/null
+++ b/scripts/linear-algebra/vech.m
@@ -0,0 +1,50 @@
+## Copyright (C) 1995, 1996  Kurt Hornik
+## 
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+## 
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details. 
+## 
+## You should have received a copy of the GNU General Public License
+## along with this file.  If not, write to the Free Software Foundation,
+## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+
+## usage: vech (x)
+##
+## For square x, returns the vector vech (x) which is obtained from x
+## by eliminating all supradiagonal elements and stacking the result
+## one column above the other.
+## 
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+
+## Author KH <Kurt.Hornik@ci.tuwien.ac.at>
+## Created: 8 May 1995
+## Adapted-By: jwe
+
+function v = vech (x)
+  
+  if (nargin != 1)
+    usage ("vech (x)");
+  endif
+  
+  if (! is_square (x))
+    error ("vech:  x must be square");
+  endif
+  
+  ## This should be quicker than having an inner `for' loop as well.
+  ## Ideally, vech should be written in C++.
+  n = rows (x);
+  count = 0;
+  for j = 1 : n
+    i = j : n; 
+    v (count + i) = x (i, j);
+    count = count + n - j;
+  endfor
+
+endfunction