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changeset 8702:3c4628550318

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eigs.cc: increase tolerance
author John W. Eaton <jwe@octave.org>
date Mon, 09 Feb 2009 12:29:30 -0500
parents 1652e39b934e
children c953a6977be6
files src/ChangeLog src/DLD-FUNCTIONS/eigs.cc
diffstat 2 files changed, 158 insertions(+), 156 deletions(-) [+]
line wrap: on
line diff
--- a/src/ChangeLog	Mon Feb 09 12:23:12 2009 -0500
+++ b/src/ChangeLog	Mon Feb 09 12:29:30 2009 -0500
@@ -1,5 +1,7 @@
 2009-02-09  John W. Eaton  <jwe@octave.org>
 
+	* DLD-FUNCTIONS/eigs.cc: Increase tolerance to 1e-11 on all tests.
+
 	* lex.l (lexical_feedback::looking_at_decl_list): New data member.
 	* lex.l (lexical_feedback::init): Initialize it.
 	(handle_identifier): Also force local variable if looking_at_decl_list.
--- a/src/DLD-FUNCTIONS/eigs.cc	Mon Feb 09 12:23:12 2009 -0500
+++ b/src/DLD-FUNCTIONS/eigs.cc	Mon Feb 09 12:29:30 2009 -0500
@@ -763,104 +763,104 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (d1, d0(end:-1:(end-k)),1e-12);
+%! assert (d1, d0(end:-1:(end-k)),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (d1, d0(k:-1:1), 1e-12);
+%! assert (d1, d0(k:-1:1), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'la');
-%! assert (d1, d2(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sa');
-%! assert (d1, d2(1:k), 1e-12);
+%! assert (d1, d2(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'be');
-%! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-12);
+%! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k+1, 'be');
-%! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-12);
+%! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (d1(idx1), d0(idx0(1:k)), 1e-12);
+%! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, speye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (eigs(A,k,4.1), eigs(A,speye(n),k,4.1), 1e-12);
+%! assert (eigs(A,k,4.1), eigs(A,speye(n),k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (eigs(A,k,4.1), eigs(A,speye(n),k,4.1), 1e-12);
+%! assert (eigs(A,k,4.1), eigs(A,speye(n),k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (d1, d0(k:-1:1), 1e-12);
+%! assert (d1, d0(k:-1:1), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (d1, eigs(A,k,4.1), 1e-12);
+%! assert (d1, eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'la');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sa');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'be');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */
@@ -877,119 +877,119 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (abs(d1), abs(d0(1:k)), 1e-12);
+%! assert (abs(d1), abs(d0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lr');
 %! [dum, idx] = sort (real(d0));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-12);
+%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(1:k)), 1e-12);
+%! assert (real(d1), real(d2(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'li');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'si');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-12);
-%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-12);
+%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-11);
+%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, speye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,speye(n),k,4.1)), 1e-12);
+%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,speye(n),k,4.1)), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,speye(n),k,4.1))), 1e-12);
+%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,speye(n),k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (abs(d1), d0(1:k), 1e-12);
+%! assert (abs(d1), d0(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'li');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'si');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */
@@ -1006,121 +1006,121 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (abs(d1), abs(d0(1:k)), 1e-12);
+%! assert (abs(d1), abs(d0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-12);
+%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(1:k)), 1e-12);
+%! assert (real(d1), real(d2(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'li');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'si');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-12);
-%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-12);
+%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-11);
+%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, speye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, speye(n), k, 4.1, opts);
-%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-12);
-%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-12);
+%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-11);
+%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, speye(n)(q,q), k, 4.1, opts);
-%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-12);
-%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-12);
+%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-11);
+%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,speye(n),k,4.1)), 1e-12);
+%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,speye(n),k,4.1)), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,speye(n),k,4.1))), 1e-12);
+%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,speye(n),k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (abs(d1), d0(1:k), 1e-12);
+%! assert (abs(d1), d0(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'li');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'si');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */
@@ -1140,104 +1140,104 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (d1, d0(end:-1:(end-k)),1e-12);
+%! assert (d1, d0(end:-1:(end-k)),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (d1, d0(k:-1:1), 1e-12);
+%! assert (d1, d0(k:-1:1), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'la');
-%! assert (d1, d2(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sa');
-%! assert (d1, d2(1:k), 1e-12);
+%! assert (d1, d2(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'be');
-%! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-12);
+%! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k+1, 'be');
-%! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-12);
+%! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (d1(idx1), d0(idx0(1:k)), 1e-12);
+%! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, eye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (eigs(A,k,4.1), eigs(A,eye(n),k,4.1), 1e-12);
+%! assert (eigs(A,k,4.1), eigs(A,eye(n),k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (eigs(A,k,4.1), eigs(A,eye(n),k,4.1), 1e-12);
+%! assert (eigs(A,k,4.1), eigs(A,eye(n),k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (d1, d0(end:-1:(end-k+1)), 1e-12);
+%! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (d1, d0(k:-1:1), 1e-12);
+%! assert (d1, d0(k:-1:1), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 1; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (d1, eigs(A,k,4.1), 1e-12);
+%! assert (d1, eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'la');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sa');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'be');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */
@@ -1254,119 +1254,119 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (abs(d1), abs(d0(1:k)), 1e-12);
+%! assert (abs(d1), abs(d0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lr');
 %! [dum, idx] = sort (real(d0));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-12);
+%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(1:k)), 1e-12);
+%! assert (real(d1), real(d2(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'li');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'si');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-12);
-%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-12);
+%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-11);
+%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, eye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,eye(n),k,4.1)), 1e-12);
+%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,eye(n),k,4.1)), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,eye(n),k,4.1))), 1e-12);
+%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,eye(n),k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (abs(d1), d0(1:k), 1e-12);
+%! assert (abs(d1), d0(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 0; opts.isreal = 1;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'li');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'si');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */
@@ -1383,121 +1383,121 @@
 %! d0 = d0(idx);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A,k+1);
-%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k))),1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sm');
-%! assert (abs(d1), abs(d0(1:k)), 1e-12);
+%! assert (abs(d1), abs(d0(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'lr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-12);
+%! assert (real(d1), real(d2(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'sr');
 %! [dum, idx] = sort (real(abs(d0)));
 %! d2 = d0(idx);
-%! assert (real(d1), real(d2(1:k)), 1e-12);
+%! assert (real(d1), real(d2(1:k)), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'li');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(end:-1:(end-k+1)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 'si');
 %! [dum, idx] = sort (imag(abs(d0)));
 %! d2 = d0(idx);
-%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-12);
+%! assert (sort(imag(d1)), sort(imag(d2(1:k))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs (A, k, 4.1);
 %! [dum,idx0] = sort (abs(d0 - 4.1));
 %! [dum,idx1] = sort (abs(d1 - 4.1));
-%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-12);
-%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-12);
+%! assert (abs(d1(idx1)), abs(d0(idx0(1:k))), 1e-11);
+%! assert (sort(imag(d1(idx1))), sort(imag(d0(idx0(1:k)))), 1e-11);
 %!testif HAVE_ARPACK
 %! d1 = eigs(A, eye(n), k, 'lm');
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! d1 = eigs(A, eye(n), k, 4.1, opts);
-%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-12);
-%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-12);
+%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-11);
+%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! opts.cholB=true;
 %! q = [2:n,1];
 %! opts.permB=q;
 %! d1 = eigs(A, eye(n)(q,q), k, 4.1, opts);
-%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-12);
-%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-12);
+%! assert (abs(abs(d1)), abs(eigs(A,k,4.1)), 1e-11);
+%! assert (sort(imag(abs(d1))), sort(imag(eigs(A,k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,eye(n),k,4.1)), 1e-12);
+%! assert (abs(eigs(A,k,4.1)), abs(eigs(A,eye(n),k,4.1)), 1e-11);
 %!testif HAVE_ARPACK
-%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,eye(n),k,4.1))), 1e-12);
+%! assert (sort(imag(eigs(A,k,4.1))), sort(imag(eigs(A,eye(n),k,4.1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A * x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 'lm', opts);
-%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-12);
+%! assert (abs(d1), abs(d0(end:-1:(end-k+1))), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) A \ x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 'sm', opts);
-%! assert (abs(d1), d0(1:k), 1e-12);
+%! assert (abs(d1), d0(1:k), 1e-11);
 %!testif HAVE_ARPACK
 %! fn = @(x) (A - 4.1 * eye(n)) \ x;
 %! opts.issym = 0; opts.isreal = 0;
 %! d1 = eigs (fn, n, k, 4.1, opts);
-%! assert (abs(d1), eigs(A,k,4.1), 1e-12);
+%! assert (abs(d1), eigs(A,k,4.1), 1e-11);
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sm');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'lr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'sr');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'li');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 %!testif HAVE_ARPACK
 %! [v1,d1] = eigs(A, k, 'si');
 %! d1 = diag(d1);
 %! for i=1:k
-%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-12)
+%!  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 %! endfor
 
 */