--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/gearm.m	Wed May 06 14:56:53 2015 +0200
@@ -0,0 +1,26 @@
+function A = gearm(n, i, j)
+%GEARM   Gear matrix.
+%        A = GEARM(N,I,J) is the N-by-N matrix with ones on the sub- and
+%        super-diagonals, SIGN(I) in the (1,ABS(I)) position, SIGN(J)
+%        in the (N,N+1-ABS(J)) position, and zeros everywhere else.
+%        Defaults: I = N, j = -N.
+%        All eigenvalues are of the form 2*COS(a) and the eigenvectors
+%        are of the form [SIN(w+a), SIN(w+2a), ..., SIN(w+Na)].
+%        The values of a and w are given in the reference below.
+%        A can have double and triple eigenvalues and can be defective.
+%        GEARM(N) is singular.
+
+%        (GEAR is a Simulink function, hence GEARM for Gear matrix.)
+%        Reference:
+%        C.W. Gear, A simple set of test matrices for eigenvalue programs,
+%        Math. Comp., 23 (1969), pp. 119-125.
+
+if nargin == 1, i = n; j = -n; end
+
+if ~(i~=0 & abs(i)<=n & j~=0 & abs(j)<=n)
+     error('Invalid I and J parameters')
+end
+
+A = diag(ones(n-1,1),-1) + diag(ones(n-1,1),1);
+A(1, abs(i)) = sign(i);
+A(n, n+1-abs(j)) = sign(j);