Add core/indef.

Author: higham

core/private/Contents.m

@@ -15,6 +15,7 @@
 %   hessfull01 - Totally nonnegative lower Hessenberg Toeplitz matrix.
 %   hessmaxdet - Upper Hessenberg matrix with maximal determinant.
 %   hess_sublu - Upper Hessengerg matrix giving subnormal numbers in LU factor.
+%   indef      -  Symmetric indefinite matrix with known inertia.
 %   kms_nonsymm - Nonsymmetric Kac-Murdock-Szego Toeplitz matrix.
 %   milnes     -  Upper triangle 1s and constant columnss in lower triangle.
 %   nilpot_tridiag - Nilpotent tridiagonal matrix (sparse).

core/private/indef.m

@@ -0,0 +1,29 @@
+function [A,properties] = indef(n,r)
+%INDEF   Symmetric indefinite matrix with known inertia.
+%   A = INDEF(n,r) is the n-by-n matrix with (i,j) element
+%   (p(i) + p(j))^r, where r is nonnegative and p(i) = i/n.
+%   r defaults to 2.
+%   A = INDEF(p,r) has (i,j) element (p(i) + p(j))^r, where
+%   p is an input vector of distinct positive entries.
+%   If r is an integer with 0 <= r <= n-1 then A has
+%     - ceil( (r+1)/2 ) positive eigenvalues,     
+%     - floor( (r+1)/2 ) negative eigenvalues, and    
+%     - n - r - 1 zero eigenvalues.
+%   If r >= n-1 then A has
+%     - ceil(n/2) positive eigenvalues,     
+%     - floor(n/2) negative eigenvalues.
+%   The inertia is also known for real r with 0 < r < n-2.
+
+%   Reference: 
+%   Rajendra Bhatia and Tanvi Jain, Inertia of the Matrix (p_i+p_j)^r],
+%   J. Spectr. Theory, 5(1), 71-78, 2015.
+
+properties = {'symmetric', 'indefinite', 'positive'};
+if nargin == 0, A = []; return, end
+
+p = n;
+if length(p) == 1
+   p = (1:n)'/n;
+end
+if nargin < 2, r = 2; end
+A = (p + p').^r;

readme.md

@@ -26,6 +26,7 @@ The following matrices have been added since v1.0.
 - core/collatz
 - core/cross
 - core/hess_sublu
+- core/indef
 - core/milnes
 - core/orthog_cauchy 
 - core/pick