From ff12815d21222c795b9842ff1b1b8af6193c4af3 Mon Sep 17 00:00:00 2001
From: Nicola Vigano <nicola.vigano@esrf.fr>
Date: Tue, 30 May 2017 19:21:26 +0200
Subject: [PATCH] Eigenvalues and Eigenvectors of 3x3 symm matrices, added
degeneracy handling
Signed-off-by: Nicola Vigano <nicola.vigano@esrf.fr>
---
zUtil_Maths/gtMathsEig3x3SymmPosDef.m | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/zUtil_Maths/gtMathsEig3x3SymmPosDef.m b/zUtil_Maths/gtMathsEig3x3SymmPosDef.m
index 037d4c2a..5839d708 100644
--- a/zUtil_Maths/gtMathsEig3x3SymmPosDef.m
+++ b/zUtil_Maths/gtMathsEig3x3SymmPosDef.m
@@ -1,4 +1,7 @@
-function [e, V] = gtMathsEig3x3SymmPosDef(M)
+function [e, V] = gtMathsEig3x3SymmPosDef(M, toll_deg)
+ if (~exist('toll_deg', 'var') || isempty(toll_deg))
+ toll_deg = 1e5;
+ end
num_matrs = size(M, 3);
e = zeros(1, 3, num_matrs, class(M));
@@ -47,6 +50,8 @@ function [e, V] = gtMathsEig3x3SymmPosDef(M)
e(1, 2, others) = q_3 - e(1, 1, others) - e(1, 3, others);
end
+ e = abs(e);
+
V = zeros(3, 3, num_matrs, 'like', M);
M23M12 = M(2, 3, :) .* M(1, 2, :);
@@ -59,6 +64,15 @@ function [e, V] = gtMathsEig3x3SymmPosDef(M)
V(2, :, :) = bsxfun(@minus, bsxfun(@times, M(2, 3, :), M11), M12M13);
V(3, :, :) = bsxfun(@minus, M12_2, M11 .* M22);
+ % Let's take care of the degeneracies
+ deg_12 = abs(e(1, 1, :) - e(1, 2, :)) < toll_deg;
+ deg_13 = abs(e(1, 1, :) - e(1, 3, :)) < toll_deg;
+ deg_23 = abs(e(1, 2, :) - e(1, 3, :)) < toll_deg;
+
+ V(:, 2, deg_12) = gtMathsCross(V(:, 1, deg_12), V(:, 3, deg_12), 1);
+ V(:, 3, deg_13) = gtMathsCross(V(:, 1, deg_13), V(:, 2, deg_13), 1);
+ V(:, 3, deg_23) = gtMathsCross(V(:, 1, deg_23), V(:, 2, deg_23), 1);
+
norm_V = sqrt(sum(V .^ 2, 1));
norm_V = 1 ./ (norm_V + (norm_V == 0));
V = bsxfun(@times, V, norm_V);
--
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