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Drastically reduce iterations for convexify for some matrices #3177

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Drastically reduce iterations for convexify for some matrices #3177

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41 changes: 24 additions & 17 deletions casadi/core/runtime/casadi_cvx.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -229,47 +229,54 @@ void casadi_cvx_implicit_qr(casadi_int n, T1* t_diag, T1* t_off, T1* cs) {
template<typename T1>
int casadi_cvx_symm_schur(casadi_int n, T1* t_diag, T1* t_off, T1 tol, casadi_int max_iter,
casadi_int* trace_meta, T1* trace) {
casadi_int i, p, q, sp, sq, trace_offset, nn;
casadi_int i, p, sp, sn, trace_offset, nn;
casadi_int* n_iter;
n_iter = trace_meta++;

trace_offset = 0;
q = 0;
p = 0;
*n_iter = 0;

while (q<n) {
if (*n_iter==max_iter) return 1;
while (p<n) {
// Clip converged entries
for (i=0;i<n-1;++i) {
if (fabs(t_off[i])<=tol*(fabs(t_diag[i])+fabs(t_diag[i+1]))) {
t_off[i] = 0;
}
}

// Determine p, q
// Detetermine unreduced block.
// Slightly different than in Golub & Van Loan
// Finding first unreduced block with connected components,
// i.e. the off diagonal element that would connect the unreduced blocks is 0: t_off[i]==0
p = 0;
q = 0;
nn = 1;
sp = 0;
sq = 0;
sn = 0;
for (i=0;i<n-1;++i) {
if (t_off[n-i-2]==0 && sq==0) {
q++;
} else {
sq = 1;
}
// Determine start p of block
if (t_off[i]==0 && sp==0) {
p++;
} else {
sp = 1;
}
if (q==n-1) {
q = n;
p = 0;
// Determine size nn of block
if (t_off[i]!=0 && sn==0 && sp==1) {
nn++;
} else if (sp==1) {
sn = 1;
}
}
// Increase p (by 1) to n to indicate that we have converged
if (p==n-1) {
nn = 0;
p = n;
}

nn = n-q-p;
if (q<n) {
if (p<n) {
// Fail if we run out of iterations (not enough memory in work vector trace_meta to continue)
if (*n_iter==max_iter) return 1;
// Take an implicit qr step
casadi_cvx_implicit_qr(nn, t_diag+p, t_off+p, trace ? trace+trace_offset : nullptr);
trace_offset += 2*(nn-1);

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19 changes: 19 additions & 0 deletions test/python/mx.py
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Expand Up @@ -3032,6 +3032,25 @@ def test_convexify_bugs(self):
Ac = evalf(convexify(A,{"strategy":"eigen-reflect"}))
self.checkarray(A,Ac,digits=8)

def test_convexify_hard(self):
# Test case where the convexify used to spend many iterations to converge
A = DM([
[ 0.092217, 0.001860, -0.003761, -0.003143, -0.002274, 0.000225, -0.000098, 0.000173],
[ 0.001860, 0.000269, -0.000110, -0.000100, -0.000069, 0.000003, -0.000001, 0.000002],
[-0.003761, -0.000110, 0.000123, 0.000037, 0.002089, -0.000011, 0.000005, -0.000008],
[-0.003143, -0.000100, 0.000037, 0.000093, -0.000138, 0.000053, 0.000007, -0.000016],
[-0.002274, -0.000069, 0.002089, -0.000138, -0.000252, -0.016051, 0.000459, -0.001413],
[ 0.000225, 0.000003, -0.000011, 0.000053, -0.016051, 0.001170, 0.000105, -0.000325],
[-0.000098, -0.000001, 0.000005, 0.000007, 0.000459, 0.000105, -0.000068, 0.000417],
[ 0.000173, 0.000002, -0.000008, -0.000016, -0.001413, -0.000325, 0.000417, -0.000035]
])
[D,V] = np.linalg.eig(np.array(A))
Dr= fmax(abs(D),1e-7)
Ar_ref = mtimes(mtimes(V,diag(Dr)),V.T)

Ar = evalf(convexify(A,{"strategy":"eigen-reflect"}))

self.checkarray(Ar,Ar_ref,digits=8)

def test_logsumexp(self):
x = MX.sym("x",3)
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