--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libinterp/corefcn/gsvd.cc	Sat Oct 01 17:02:51 2016 +0100
@@ -0,0 +1,465 @@
+// Copyright (C) 2016 Barbara Lócsi
+// Copyright (C) 2006, 2010 Pascal Dupuis <Pascal.Dupuis@uclouvain.be>
+// Copyright (C) 1996, 1997 John W. Eaton
+//
+// 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 3 of the License, 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 program; if not, see <http://www.gnu.org/licenses/>.
+
+#ifdef HAVE_CONFIG_H
+#  include <config.h>
+#endif
+
+#include "dMatrix.h"
+#include "CMatrix.h"
+#include "dDiagMatrix.h"
+#include "gsvd.h"
+
+#include "defun.h"
+#include "defun-int.h"
+#include "error.h"
+#include "errwarn.h"
+#include "utils.h"
+#include "ovl.h"
+#include "ov.h"
+
+
+template <typename T>
+static typename octave::math::gsvd<T>::Type
+gsvd_type (int nargout)
+{
+  return ((nargout == 0 || nargout == 1)
+          ? octave::math::gsvd<T>::Type::sigma_only
+          : (nargout > 5) ? octave::math::gsvd<T>::Type::std
+                          : octave::math::gsvd<T>::Type::economy);
+}
+
+// Named like this to avoid conflicts with the gsvd class.
+template <typename T>
+static octave_value_list
+function_gsvd (const T& A, const T& B, const octave_idx_type nargout)
+{
+  octave::math::gsvd<T> result (A, B, gsvd_type<T> (nargout));
+
+  octave_value_list retval (nargout);
+  if (nargout < 2)
+    {
+      DiagMatrix sigA = result.singular_values_A ();
+      DiagMatrix sigB = result.singular_values_B ();
+      for (int i = sigA.rows () - 1; i >= 0; i--)
+        sigA.dgxelem(i) /= sigB.dgxelem(i);
+      retval(0) = sigA.diag ();
+    }
+  else
+    {
+      retval(0) = result.left_singular_matrix_A ();
+      retval(1) = result.left_singular_matrix_B ();
+      if (nargout > 2)
+        retval(2) = result.right_singular_matrix ();
+      if (nargout > 3)
+        retval(3) = result.singular_values_A ();
+      if (nargout > 4)
+        retval(4) = result.singular_values_B ();
+      if (nargout > 5)
+        retval(5) = result.R_matrix ();
+    }
+  return retval;
+}
+
+DEFUN (gsvd, args, nargout,
+       doc: /* -*- texinfo -*-
+@deftypefn  {} {@var{s} =} gsvd (@var{a}, @var{b})
+@deftypefnx {} {[@var{u}, @var{v}, @var{x}, @var{c}, @var{s}, @var{r}] =} gsvd (@var{a}, @var{b})
+@cindex generalized singular value decomposition
+Compute the generalized singular value decomposition of (@var{a}, @var{b}):
+@tex
+$$
+ U^H A X = [I 0; 0 C] [0 R]
+ V^H B X = [0 S; 0 0] [0 R]
+ C*C + S*S = eye (columns (A))
+ I and 0 are padding matrices of suitable size
+ R is upper triangular
+$$
+@end tex
+@ifinfo
+
+@example
+@group
+u' * a * x = [I 0; 0 c] * [0 r]
+v' * b * x = [0 s; 0 0] * [0 r]
+c * c + s * s = eye (columns (a))
+I and 0 are padding matrices of suitable size
+r is upper triangular
+@end group
+@end example
+
+@end ifinfo
+
+The function @code{gsvd} normally returns the vector of generalized singular
+values
+@tex
+diag (C) ./ diag (S).
+@end tex
+@ifinfo
+diag (r) ./ diag (s).
+@end ifinfo
+If asked for five return values, it computes
+@tex
+$U$, $V$, and $X$.
+@end tex
+@ifinfo
+U, V, and X.
+@end ifinfo
+With a sixth output argument, it also returns
+@tex
+R,
+@end tex
+@ifinfo
+r,
+@end ifinfo
+The common upper triangular right term.  Other authors, like
+@nospell{S. Van Huffel}, define this transformation as the simultaneous
+diagonalization of the input matrices, this can be achieved by multiplying
+@tex
+X
+@end tex
+@ifinfo
+x
+@end ifinfo
+by the inverse of
+@tex
+[I 0; 0 R].
+@end tex
+@ifinfo
+[I 0; 0 r].
+@end ifinfo
+
+For example,
+
+@example
+gsvd (hilb (3), [1 2 3; 3 2 1])
+
+@result{}
+  0.1055705
+  0.0031759
+@end example
+
+@noindent
+and
+
+@example
+[u, v, c, s, x, r] = gsvd (hilb (3), [1 2 3; 3 2 1])
+@result{}
+
+u =
+
+  -0.965609   0.240893   0.097825
+  -0.241402  -0.690927  -0.681429
+  -0.096561  -0.681609   0.725317
+
+v =
+
+  -0.41974   0.90765
+  -0.90765  -0.41974
+
+x =
+
+   0.408248   0.902199   0.139179
+  -0.816497   0.429063  -0.386314
+   0.408248  -0.044073  -0.911806
+
+c =
+
+   0.10499   0.00000
+   0.00000   0.00318
+
+s =
+   0.99447   0.00000
+   0.00000   0.99999
+
+r =
+  -0.14093  -1.24345   0.43737
+   0.00000  -3.90043   2.57818
+   0.00000   0.00000  -2.52599
+
+@end example
+
+The code is a wrapper to the corresponding @sc{lapack} dggsvd and zggsvd
+routines.
+
+@end deftypefn */)
+{
+  if (args.length () !=  2)
+    print_usage ();
+
+  octave_value_list retval;
+
+  octave_value argA = args(0);
+  octave_value argB = args(1);
+
+  octave_idx_type nr = argA.rows ();
+  octave_idx_type nc = argA.columns ();
+
+  octave_idx_type np = argB.columns ();
+
+  // This "special" case should be handled in the gsvd class, not here
+  if (nr == 0 || nc == 0)
+    {
+      retval = octave_value_list (nargout);
+      if (nargout < 2) // S = gsvd (A, B)
+        retval(0) = Matrix (0, 1);
+      else // [U, V, X, C, S, R] = gsvd (A, B)
+        {
+          retval(0) = identity_matrix (nc, nc);
+          retval(1) = identity_matrix (nc, nc);
+          if (nargout > 2)
+            retval(2) = identity_matrix (nr, nr);
+          if (nargout > 3)
+            retval(3) = Matrix (nr, nc);
+          if (nargout > 4)
+            retval(4) = identity_matrix (nr, nr);
+          if (nargout > 5)
+            retval(5) = identity_matrix (nr, nr);
+        }
+    }
+  else
+    {
+      if (nc != np)
+        print_usage ();
+
+      if (argA.is_real_type () && argB.is_real_type ())
+        {
+          Matrix tmpA = argA.matrix_value ();
+          Matrix tmpB = argB.matrix_value ();
+
+          // FIXME: This code is still using error_state
+          if (! error_state)
+            {
+              if (tmpA.any_element_is_inf_or_nan ())
+                error ("gsvd: B cannot have Inf or NaN values");
+              if (tmpB.any_element_is_inf_or_nan ())
+                error ("gsvd: B cannot have Inf or NaN values");
+
+              retval = function_gsvd (tmpA, tmpB, nargout);
+            }
+        }
+      else if (argA.is_complex_type () || argB.is_complex_type ())
+        {
+          ComplexMatrix ctmpA = argA.complex_matrix_value ();
+          ComplexMatrix ctmpB = argB.complex_matrix_value ();
+
+          if (! error_state)
+            {
+              if (ctmpA.any_element_is_inf_or_nan ())
+                error ("gsvd: A cannot have Inf or NaN values");
+              if (ctmpB.any_element_is_inf_or_nan ())
+                error ("gsvd: B cannot have Inf or NaN values");
+
+              retval = function_gsvd (ctmpA, ctmpB, nargout);
+            }
+        }
+      else
+        {
+          // Actually, can't tell which arg is at fault
+          err_wrong_type_arg ("gsvd", argA);
+          //err_wrong_type_arg ("gsvd", argB);
+        }
+    }
+
+  return retval;
+}
+
+/*
+## a few tests for gsvd.m
+%!shared A, A0, B, B0, U, V, C, S, X, R, D1, D2
+%! A0 = randn (5, 3);
+%! B0 = diag ([1 2 4]);
+%! A = A0;
+%! B = B0;
+
+## A (5x3) and B (3x3) are full rank
+%!test
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros (5, 3);  D1(1:3, 1:3) = C;
+%! D2 = S;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 5x3 full rank, B: 3x3 rank deficient
+%!test
+%! B(2, 2) = 0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros (5, 3);  D1(1, 1) = 1;  D1(2:3, 2:3) = C;
+%! D2 = [zeros(2, 1) S; zeros(1, 3)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 5x3 rank deficient, B: 3x3 full rank
+%!test
+%! B = B0;
+%! A(:, 3) = 2*A(:, 1) - A(:, 2);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 3);  D1(1:3, 1:3) = C;
+%! D2 = S;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A and B are both rank deficient
+%!test
+%! B(:, 3) = 2*B(:, 1) - B(:, 2);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 2);  D1(1:2, 1:2) = C;
+%! D2 = [S; zeros(1, 2)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*[zeros(2, 1) R]) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*[zeros(2, 1) R]) <= 1e-6);
+
+## A (now 3x5) and B (now 5x5) are full rank
+%!test
+%! A = A0.';
+%! B0 = diag ([1 2 4 8 16]);
+%! B = B0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = [C zeros(3,2)];
+%! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 3x5 full rank, B: 5x5 rank deficient
+%!test
+%! B(2, 2) = 0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(3, 5); D1(1, 1) = 1; D1(2:3, 2:3) = C;
+%! D2 = zeros(5, 5); D2(1:2, 2:3) = S; D2(3:4, 4:5) = eye (2);
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 3x5 rank deficient, B: 5x5 full rank
+%!test
+%! B = B0;
+%! A(3, :) = 2*A(1, :) - A(2, :);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros (3, 5);  D1(1:3, 1:3) = C;
+%! D2 = zeros (5, 5);  D2(1:3, 1:3) = S;  D2(4:5, 4:5) = eye (2);
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A and B are both rank deficient
+%!test
+%! A = A0.'; B = B0.';
+%! A(:, 3) = 2*A(:, 1) - A(:, 2);
+%! B(:, 3) = 2*B(:, 1) - B(:, 2);
+%! [U, V, X, C, S, R]=gsvd (A, B);
+%! D1 = zeros(3, 4); D1(1:3, 1:3) = C;
+%! D2 = eye (4); D2(1:3, 1:3) = S; D2(5,:) = 0;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*[zeros(4, 1) R]) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*[zeros(4, 1) R]) <= 1e-6);
+
+## A: 5x3 complex full rank, B: 3x3 complex full rank
+%!test
+%! A0 = A0 + j*randn (5, 3);
+%! B0 = diag ([1 2 4]) + j*diag ([4 -2 -1]);
+%! A = A0;
+%! B = B0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 3);  D1(1:3, 1:3) = C;
+%! D2 = S;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 5x3 complex full rank, B: 3x3 complex rank deficient
+%!test
+%! B(2, 2) = 0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 3);  D1(1, 1) = 1;  D1(2:3, 2:3) = C;
+%! D2 = [zeros(2, 1) S; zeros(1, 3)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 5x3 complex rank deficient, B: 3x3 complex full rank
+%!test
+%! B = B0;
+%! A(:, 3) = 2*A(:, 1) - A(:, 2);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 3);  D1(1:3, 1:3) = C;
+%! D2 = S;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A (5x3) and B (3x3) are both complex rank deficient
+%!test
+%! B(:, 3) = 2*B(:, 1) - B(:, 2);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(5, 2);  D1(1:2, 1:2) = C;
+%! D2 = [S; zeros(1, 2)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*[zeros(2, 1) R]) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*[zeros(2, 1) R]) <= 1e-6);
+
+## A (now 3x5) complex and B (now 5x5) complex are full rank
+## now, A is 3x5
+%!test
+%! A = A0.';
+%! B0 = diag ([1 2 4 8 16]) + j*diag ([-5 4 -3 2 -1]);
+%! B = B0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = [C zeros(3,2)];
+%! D2 = [S zeros(3,2); zeros(2, 3) eye(2)];
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 3x5 complex full rank, B: 5x5 complex rank deficient
+%!test
+%! B(2, 2) = 0;
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(3, 5);  D1(1, 1) = 1;  D1(2:3, 2:3) = C;
+%! D2 = zeros(5,5);  D2(1:2, 2:3) = S;  D2(3:4, 4:5) = eye (2);
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A: 3x5 complex rank deficient, B: 5x5 complex full rank
+%!test
+%! B = B0;
+%! A(3, :) = 2*A(1, :) - A(2, :);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(3, 5);  D1(1:3, 1:3) = C;
+%! D2 = zeros(5,5);  D2(1:3, 1:3) = S;  D2(4:5, 4:5) = eye (2);
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*R) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*R) <= 1e-6);
+
+## A and B are both complex rank deficient
+%!test
+%! A = A0.';
+%! B = B0.';
+%! A(:, 3) = 2*A(:, 1) - A(:, 2);
+%! B(:, 3) = 2*B(:, 1) - B(:, 2);
+%! [U, V, X, C, S, R] = gsvd (A, B);
+%! D1 = zeros(3, 4);  D1(1:3, 1:3) = C;
+%! D2 = eye (4);  D2(1:3, 1:3) = S;  D2(5,:) = 0;
+%! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6);
+%! assert (norm ((U'*A*X) - D1*[zeros(4, 1) R]) <= 1e-6);
+%! assert (norm ((V'*B*X) - D2*[zeros(4, 1) R]) <= 1e-6);
+*/
+