/
cvxquad_tests.m
387 lines (352 loc) · 14.8 KB
/
cvxquad_tests.m
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function cvxquad_tests()
% CVXQUAD_TESTS
% Run some unit tests on cvxquad's functions
% These are very simple tests and are designed to quickly detect any
% trivial problem with the code
rng(0);
test_matrix_geo_mean_hypo_cone();
test_lieb_ando();
test_op_rel_entr_epi_cone();
test_trace_logm();
test_quantum_entr();
test_quantum_rel_entr();
end
function test_matrix_geo_mean_hypo_cone()
fprintf('---- TESTING matrix_geo_mean_hypo_cone ----\n');
nvec = [3 5];
tvec = [1/2 1/4 1/8 1/16 3/4 7/8 15/16 2/3 6/7];
for n=nvec
for t=tvec
for cplx=[0 1]
A = randPSD(n,cplx);
B = randPSD(n,cplx);
cvx_quiet(true);
cvx_begin
if cplx
variable T(n,n) hermitian
else
variable T(n,n) symmetric
end
maximize trace(T)
{A,B,T} == matrix_geo_mean_hypo_cone(n,t,cplx,0);
cvx_end
ABt = A^(1/2)*mpower(A^(-1/2)*B*A^(-1/2),t)*A^(1/2);
[p,q] = rat(t);
fprintf('n=%d, t=%d/%d, cplx=%d: ', n,p,q,cplx);
assert(norm(ABt-T) <= 1e-6,'Test failed matrix_geo_mean_hypo_cone n=%d, t=%d/%d, cplx=%d', n,p,q,cplx);
fprintf('OK\n');
end
end
end
% Additional test for fullhyp=1
A = [6.25 0; 0 16];
B = [2 1; 1 2];
% These matrices satisfy A^(1/2) >= B and so (A,eye(2),B) \in hyp_{1/2}
% A and B however do not satisfy A >= B^2 and so [A B; B eye(2)] not
% psd, and using fullhyp=0 will give an infeasible SDP.
cvx_quiet(true)
cvx_begin
minimize 0
{A,eye(2),B} == matrix_geo_mean_hypo_cone(2,1/2,0,1);
cvx_end
fprintf('Testing fullhyp=1: ')
assert(cvx_optval == 0, 'Test matrix_geo_mean_hypo_cone with fullhyp=1 failed');
fprintf('OK\n');
fprintf('matrix_geo_mean_hypo_cone test OK\n');
end
function test_op_rel_entr_epi_cone()
fprintf('---- TESTING op_rel_entr_epi_cone ----\n');
nvec = [3 5 10];
for n=nvec
for cplx=[0 1]
A = randPSD(n,cplx); A = A/trace(A);
B = randPSD(n,cplx); B = B/trace(B);
for mk = [1 3]
for apx=[-1 0 1]
if mk == 1 && apx == 0
% When (m,k) = (1,1) we only check apx=\pm 1 and
% verify that the result is a valid upper/bound on
% the correct result. We do not check the quality
% of the result. For this setting we skip apx = 0
% (Pade) as this approximation is neither an upper
% nor a lower bound
continue;
end
cvx_quiet(true);
cvx_begin
if cplx
variable T(n,n) hermitian
else
variable T(n,n) symmetric
end
minimize trace(T)
{A,B,T} == op_rel_entr_epi_cone(n,cplx,mk,mk,eye(n),apx);
cvx_end
DopAB = A^(1/2)*logm(A^(1/2)*inv(B)*A^(1/2))*A^(1/2);
err = (T - DopAB)/norm(DopAB); % matrix
fprintf('n=%d, cplx=%d, (m,k)=(%d,%d), apx=%d, eig(err) in [%.4f,%.4f]: ',n,cplx,mk,mk,apx,min(eig(err)),max(eig(err)));
assert( min(eig(apx*err)) >= -1e-6,'Test failed (bound) op_rel_entr_epi_cone n=%d, cplx=%d, min(eig(apx*err))=%.4e',n,cplx,min(eig(apx*err)));
if mk >= 3
% Tolerance 1e-2 was set by inspection
assert(norm(err) <= 1e-2,'Test failed op_rel_entr_epi_cone n=%d, cplx=%d, error=%.4e',n,cplx,norm(err));
end
fprintf('OK\n');
end
end
end
end
fprintf('op_rel_entr_epi_cone test OK\n');
end
function test_trace_logm()
fprintf('---- TESTING trace_logm ----\n');
nvec = [3 5 10];
for n=nvec
for cplx=[0 1]
A = randPSD(n,cplx); A = A/trace(A);
C = randPSD(n,cplx);
for mk = [1 3]
for apx=[-1 0 1]
if mk == 1 && apx == 0
% When (m,k) = (1,1) we only check apx=\pm 1 and
% verify that the result is a valid upper/bound on
% the correct result. We do not check the quality
% of the result. For this setting we skip apx = 0
% (Pade) as this approximation is neither an upper
% nor a lower bound
continue;
end
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
else
variable X(n,n) symmetric
end
maximize (trace_logm(X,C,mk,mk,apx))
X == A;
cvx_end
trlog = trace_logm(A,C);
relerr = (cvx_optval - trlog)/abs(trlog);
fprintf('n=%d, cplx=%d, (m,k)=(%d,%d), apx=%d, err=%.4f: ',n,cplx,mk,mk,apx,relerr);
% Check it is a true bound depending on value of apx
assert(apx*relerr >= -1e-6,'Test failed (bound) trace_logm n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,relerr);
if mk >= 3
% Tolerance 1e-2 was set by inspection
assert(abs(relerr) <= 1e-2,'Test failed trace_logm n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,relerr);
end
fprintf('OK\n');
end
end
end
end
end
function test_quantum_entr()
fprintf('---- TESTING quantum_entr ----\n');
nvec = [3 5 10];
for n=nvec
for cplx=[0 1]
A = randPSD(n,cplx); A = A/trace(A);
for mk = [1 3]
for apx=[-1 0 1]
if mk == 1 && apx == 0
% When (m,k) = (1,1) we only check apx=\pm 1 and
% verify that the result is a valid upper/bound on
% the correct result. We do not check the quality
% of the result. For this setting we skip apx = 0
% (Pade) as this approximation is neither an upper
% nor a lower bound
continue;
end
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
else
variable X(n,n) symmetric
end
maximize (quantum_entr(X,mk,mk,apx))
X == A;
cvx_end
HA = quantum_entr(A);
relerr = (cvx_optval - HA)/abs(HA);
fprintf('n=%d, cplx=%d, (m,k)=(%d,%d), apx=%d, err=%.4f: ',n,cplx,mk,mk,apx,relerr);
% Check it is a true bound depending on value of apx
assert(apx*relerr >= -1e-6,'Test failed (bound) quantum_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,relerr);
if mk >= 3
% Tolerance 1e-2 was set by inspection
assert(abs(relerr) <= 1e-2,'Test failed quantum_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,relerr);
end
fprintf('OK\n');
end
end
end
end
end
function test_quantum_rel_entr()
fprintf('---- TESTING quantum_rel_entr ----\n');
for n=[2 3]
for cplx=[0 1]
A = randPSD(n,cplx); A = A/trace(A);
B = randPSD(n,cplx); B = B/trace(B);
for mk=[1 3]
for apx = [-1 0 +1]
if mk == 1 && apx == 0
% When (m,k) = (1,1) we only check apx=\pm 1 and
% verify that the result is a valid upper/bound on
% the correct result. We do not check the quality
% of the result. For this setting we skip apx = 0
% (Pade) as this approximation is neither an upper
% nor a lower bound
continue;
end
cvx_clear;
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
else
variable X(n,n) symmetric
end
minimize (quantum_rel_entr(X,B,mk,mk,apx))
X == A;
cvx_end
val1 = cvx_optval;
cvx_clear
cvx_quiet(true);
cvx_begin
if cplx
variable Y(n,n) hermitian
else
variable Y(n,n) symmetric
end
minimize (quantum_rel_entr(A,Y,mk,mk,apx))
Y == B;
cvx_end
val2 = cvx_optval;
cvx_clear
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
variable Y(n,n) hermitian
else
variable X(n,n) symmetric
variable Y(n,n) symmetric
end
minimize (quantum_rel_entr(X,Y,mk,mk,apx))
X == A;
Y == B;
cvx_end
val12 = cvx_optval;
DAB = quantum_rel_entr(A,B);
% relative errors
err1 = (val1-DAB)/abs(DAB);
err2 = (val2-DAB)/abs(DAB);
err12 = (val12-DAB)/abs(DAB);
fprintf('n=%d, cplx=%d, (m,k)=(%d,%d), apx=%d, errors=(%.4f,%.4f,%.4f) ',n,cplx,mk,mk,apx,err1,err2,err12);
% Tolerance of 1e-2 was set by inspection
if mk >= 3
assert(abs(err1) <= 1e-2,'Test failed quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,abs(err1));
assert(abs(err2) <= 1e-2,'Test failed quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,abs(err2));
assert(abs(err12) <= 1e-2,'Test failed quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,abs(err12));
end
if apx ~= 0
% sign(err) should be the same as apx:
assert(apx*err1 >= -1e-6, 'Test failed (bound) quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,err1);
assert(apx*err2 >= -1e-6, 'Test failed (bound) quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,err2);
assert(apx*err12 >= -1e-6, 'Test failed (bound) quantum_rel_entr n=%d, cplx=%d, apx=%d, error=%.4e',n,cplx,apx,err12);
end
fprintf('OK\n');
end
end
end
end
fprintf('quantum_rel_entr test OK\n');
end
function test_lieb_ando()
fprintf('---- TESTING lieb_ando ----\n');
nvec = [2 3];
tvec = [1/2 1/4 3/4 1/8 3/2 5/4];
for n=nvec
for t=tvec
for cplx=[0 1]
In = eye(n);
A = randPSD(n,cplx); A = A/trace(A);
B = randPSD(n,cplx); B = B/trace(B);
cvx_clear;
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
else
variable X(n,n) symmetric
end
if t >= 0 && t <= 1
maximize (lieb_ando(X,B,In,t))
else
minimize (lieb_ando(X,B,In,t))
end
X == A;
cvx_end
val1 = cvx_optval;
cvx_clear
cvx_quiet(true);
cvx_begin
if cplx
variable Y(n,n) hermitian
else
variable Y(n,n) symmetric
end
if t >= 0 && t <= 1
maximize (lieb_ando(A,Y,In,t))
else
minimize (lieb_ando(A,Y,In,t))
end
Y == B;
cvx_end
val2 = cvx_optval;
cvx_clear
cvx_quiet(true);
cvx_begin
if cplx
variable X(n,n) hermitian
variable Y(n,n) hermitian
else
variable X(n,n) symmetric
variable Y(n,n) symmetric
end
if t >= 0 && t <= 1
maximize (lieb_ando(X,Y,In,t))
else
minimize (lieb_ando(X,Y,In,t))
end
X == A;
Y == B;
cvx_end
val12 = cvx_optval;
QtAB = lieb_ando(A,B,In,t);
[p,q] = rat(t);
fprintf('n=%d, t=%d/%d, cplx=%d: ',n,p,q,cplx);
% Thresholds are generous here to account for inaccurate
% solving of SDPs (solver-dependent). In most cases,
% solving the SDP should return a value that's within
% 1e-8 or 1e-9 of true value (SDP representation in
% lieb_ando is exact, there is no approximation, the error
% can only come from solving the SDP)
assert(abs(QtAB-val1) <= 1e-4,'Test failed lieb_ando n=%d, cplx=%d',n,cplx);
assert(abs(QtAB-val2) <= 1e-4,'Test failed lieb_ando n=%d, cplx=%d',n,cplx);
assert(abs(QtAB-val12) <= 1e-4,'Test failed lieb_ando n=%d, cplx=%d',n,cplx);
fprintf('OK\n');
end
end
end
fprintf('lieb_ando test OK\n');
end
% Generate a random positive semidefinite matrix
function X = randPSD(n,iscplx)
A = randn(n);
if iscplx
A = A + 1i*randn(n);
end
X = A*A';
end