bool testmatgen(bool silent)
{
bool result;
ap::real_2d_array a;
ap::real_2d_array b;
ap::real_2d_array u;
ap::real_2d_array v;
ap::complex_2d_array ca;
ap::complex_2d_array cb;
ap::real_2d_array r1;
ap::real_2d_array r2;
ap::complex_2d_array c1;
ap::complex_2d_array c2;
ap::real_1d_array w;
int n;
int maxn;
int i;
int j;
int pass;
int passcount;
bool waserrors;
double cond;
double threshold;
double vt;
ap::complex ct;
double minw;
double maxw;
bool serr;
bool herr;
bool spderr;
bool hpderr;
bool rerr;
bool cerr;
int i_;
rerr = false;
cerr = false;
serr = false;
herr = false;
spderr = false;
hpderr = false;
waserrors = false;
maxn = 20;
passcount = 15;
threshold = 1000*ap::machineepsilon;
//
// Testing orthogonal
//
for(n = 1; n <= maxn; n++)
{
for(pass = 1; pass <= passcount; pass++)
{
r1.setbounds(0, n-1, 0, 2*n-1);
r2.setbounds(0, 2*n-1, 0, n-1);
c1.setbounds(0, n-1, 0, 2*n-1);
c2.setbounds(0, 2*n-1, 0, n-1);
//
// Random orthogonal, real
//
unset2d(a);
unset2d(b);
rmatrixrndorthogonal(n, a);
rmatrixrndorthogonal(n, b);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
vt = ap::vdotproduct(&a(i, 0), &a(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
vt = ap::vdotproduct(&b(i, 0), &b(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
//
// test for difference in A and B
//
if( n>=2 )
{
rerr = rerr||ap::fp_eq(a(i,j),b(i,j));
}
}
}
//
// Random orthogonal, complex
//
unset2dc(ca);
unset2dc(cb);
cmatrixrndorthogonal(n, ca);
cmatrixrndorthogonal(n, cb);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += ca(i,i_)*ap::conj(ca(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += cb(i,i_)*ap::conj(cb(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
//
// test for difference in A and B
//
if( n>=2 )
{
cerr = cerr||ca(i,j)==cb(i,j);
}
}
}
//
// From the right real tests:
// 1. E*Q is orthogonal
// 2. Q1<>Q2 (routine result is changing)
// 3. (E E)'*Q = (Q' Q')' (correct handling of non-square matrices)
//
unset2d(a);
unset2d(b);
a.setbounds(0, n-1, 0, n-1);
b.setbounds(0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
a(i,j) = 0;
b(i,j) = 0;
}
a(i,i) = 1;
b(i,i) = 1;
}
rmatrixrndorthogonalfromtheright(a, n, n);
rmatrixrndorthogonalfromtheright(b, n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
vt = ap::vdotproduct(&a(i, 0), &a(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
vt = ap::vdotproduct(&b(i, 0), &b(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
//
// test for difference in A and B
//
if( n>=2 )
{
rerr = rerr||ap::fp_eq(a(i,j),b(i,j));
}
}
}
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
r2(i,j) = 2*ap::randomreal()-1;
r2(i+n,j) = r2(i,j);
}
}
rmatrixrndorthogonalfromtheright(r2, 2*n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
rerr = rerr||ap::fp_greater(fabs(r2(i+n,j)-r2(i,j)),threshold);
}
}
//
// From the left real tests:
// 1. Q*E is orthogonal
// 2. Q1<>Q2 (routine result is changing)
// 3. Q*(E E) = (Q Q) (correct handling of non-square matrices)
//
unset2d(a);
unset2d(b);
a.setbounds(0, n-1, 0, n-1);
b.setbounds(0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
a(i,j) = 0;
b(i,j) = 0;
}
a(i,i) = 1;
b(i,i) = 1;
}
rmatrixrndorthogonalfromtheleft(a, n, n);
rmatrixrndorthogonalfromtheleft(b, n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
vt = ap::vdotproduct(&a(i, 0), &a(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
vt = ap::vdotproduct(&b(i, 0), &b(j, 0), ap::vlen(0,n-1));
if( i==j )
{
rerr = rerr||ap::fp_greater(fabs(vt-1),threshold);
}
else
{
rerr = rerr||ap::fp_greater(fabs(vt),threshold);
}
//
// test for difference in A and B
//
if( n>=2 )
{
rerr = rerr||ap::fp_eq(a(i,j),b(i,j));
}
}
}
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
r1(i,j) = 2*ap::randomreal()-1;
r1(i,j+n) = r1(i,j);
}
}
rmatrixrndorthogonalfromtheleft(r1, n, 2*n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
rerr = rerr||ap::fp_greater(fabs(r1(i,j)-r1(i,j+n)),threshold);
}
}
//
// From the right complex tests:
// 1. E*Q is orthogonal
// 2. Q1<>Q2 (routine result is changing)
// 3. (E E)'*Q = (Q' Q')' (correct handling of non-square matrices)
//
unset2dc(ca);
unset2dc(cb);
ca.setbounds(0, n-1, 0, n-1);
cb.setbounds(0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
ca(i,j) = 0;
cb(i,j) = 0;
}
ca(i,i) = 1;
cb(i,i) = 1;
}
cmatrixrndorthogonalfromtheright(ca, n, n);
cmatrixrndorthogonalfromtheright(cb, n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += ca(i,i_)*ap::conj(ca(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += cb(i,i_)*ap::conj(cb(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
//
// test for difference in A and B
//
cerr = cerr||ca(i,j)==cb(i,j);
}
}
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
c2(i,j) = 2*ap::randomreal()-1;
c2(i+n,j) = c2(i,j);
}
}
cmatrixrndorthogonalfromtheright(c2, 2*n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
cerr = cerr||ap::fp_greater(ap::abscomplex(c2(i+n,j)-c2(i,j)),threshold);
}
}
//
// From the left complex tests:
// 1. Q*E is orthogonal
// 2. Q1<>Q2 (routine result is changing)
// 3. Q*(E E) = (Q Q) (correct handling of non-square matrices)
//
unset2dc(ca);
unset2dc(cb);
ca.setbounds(0, n-1, 0, n-1);
cb.setbounds(0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
ca(i,j) = 0;
cb(i,j) = 0;
}
ca(i,i) = 1;
cb(i,i) = 1;
}
cmatrixrndorthogonalfromtheleft(ca, n, n);
cmatrixrndorthogonalfromtheleft(cb, n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
//
// orthogonality test
//
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += ca(i,i_)*ap::conj(ca(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
ct = 0.0;
for(i_=0; i_<=n-1;i_++)
{
ct += cb(i,i_)*ap::conj(cb(j,i_));
}
if( i==j )
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct-1),threshold);
}
else
{
cerr = cerr||ap::fp_greater(ap::abscomplex(ct),threshold);
}
//
// test for difference in A and B
//
cerr = cerr||ca(i,j)==cb(i,j);
}
}
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
c1(i,j) = 2*ap::randomreal()-1;
c1(i,j+n) = c1(i,j);
}
}
cmatrixrndorthogonalfromtheleft(c1, n, 2*n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
cerr = cerr||ap::fp_greater(ap::abscomplex(c1(i,j)-c1(i,j+n)),threshold);
}
}
}
}
//
// Testing GCond
//
for(n = 2; n <= maxn; n++)
{
for(pass = 1; pass <= passcount; pass++)
{
//
// real test
//
unset2d(a);
cond = exp(log(double(1000))*ap::randomreal());
rmatrixrndcond(n, cond, a);
b.setbounds(1, n, 1, n);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
b(i,j) = a(i-1,j-1);
}
}
if( obsoletesvddecomposition(b, n, n, w, v) )
{
maxw = w(1);
minw = w(1);
for(i = 2; i <= n; i++)
{
if( ap::fp_greater(w(i),maxw) )
{
maxw = w(i);
}
if( ap::fp_less(w(i),minw) )
{
minw = w(i);
}
}
vt = maxw/minw/cond;
if( ap::fp_greater(fabs(log(vt)),log(1+threshold)) )
{
rerr = true;
}
}
}
}
//
// Symmetric/SPD
// N = 2 .. 30
//
for(n = 2; n <= maxn; n++)
{
//
// SPD matrices
//
for(pass = 1; pass <= passcount; pass++)
{
//
// Generate A
//
unset2d(a);
cond = exp(log(double(1000))*ap::randomreal());
spdmatrixrndcond(n, cond, a);
//
// test condition number
//
spderr = spderr||ap::fp_greater(svdcond(a, n)/cond-1,threshold);
//
// test SPD
//
spderr = spderr||!isspd(a, n, true);
//
// test that A is symmetic
//
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
spderr = spderr||ap::fp_greater(fabs(a(i,j)-a(j,i)),threshold);
}
}
//
// test for difference between A and B (subsequent matrix)
//
unset2d(b);
spdmatrixrndcond(n, cond, b);
if( n>=2 )
{
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
spderr = spderr||ap::fp_eq(a(i,j),b(i,j));
}
}
}
}
//
// HPD matrices
//
for(pass = 1; pass <= passcount; pass++)
{
//
// Generate A
//
unset2dc(ca);
cond = exp(log(double(1000))*ap::randomreal());
hpdmatrixrndcond(n, cond, ca);
//
// test HPD
//
hpderr = hpderr||!ishpd(ca, n);
//
// test that A is Hermitian
//
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
hpderr = hpderr||ap::fp_greater(ap::abscomplex(ca(i,j)-ap::conj(ca(j,i))),threshold);
}
}
//
// test for difference between A and B (subsequent matrix)
//
unset2dc(cb);
hpdmatrixrndcond(n, cond, cb);
if( n>=2 )
{
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
hpderr = hpderr||ca(i,j)==cb(i,j);
}
}
}
}
//
// Symmetric matrices
//
for(pass = 1; pass <= passcount; pass++)
{
//
// test condition number
//
unset2d(a);
cond = exp(log(double(1000))*ap::randomreal());
smatrixrndcond(n, cond, a);
serr = serr||ap::fp_greater(svdcond(a, n)/cond-1,threshold);
//
// test for difference between A and B
//
unset2d(b);
smatrixrndcond(n, cond, b);
if( n>=2 )
{
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
serr = serr||ap::fp_eq(a(i,j),b(i,j));
}
}
}
}
//
// Hermitian matrices
//
for(pass = 1; pass <= passcount; pass++)
{
//
// Generate A
//
unset2dc(ca);
cond = exp(log(double(1000))*ap::randomreal());
hmatrixrndcond(n, cond, ca);
//
// test that A is Hermitian
//
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
herr = herr||ap::fp_greater(ap::abscomplex(ca(i,j)-ap::conj(ca(j,i))),threshold);
}
}
//
// test for difference between A and B (subsequent matrix)
//
unset2dc(cb);
hmatrixrndcond(n, cond, cb);
if( n>=2 )
{
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
herr = herr||ca(i,j)==cb(i,j);
}
}
}
}
}
//
// report
//
waserrors = rerr||cerr||serr||spderr||herr||hpderr;
if( !silent )
{
printf("TESTING MATRIX GENERATOR\n");
printf("REAL TEST: ");
if( !rerr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
printf("COMPLEX TEST: ");
if( !cerr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
printf("SYMMETRIC TEST: ");
if( !serr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
printf("HERMITIAN TEST: ");
if( !herr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
printf("SPD TEST: ");
if( !spderr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
printf("HPD TEST: ");
if( !hpderr )
{
printf("OK\n");
}
else
{
printf("FAILED\n");
}
if( waserrors )
{
printf("TEST FAILED\n");
}
else
{
printf("TEST PASSED\n");
}
printf("\n\n");
}
result = !waserrors;
return result;
}
/*************************************************************************
Returns True for successful test, False - for failed test
*************************************************************************/
static bool testspdmatrixrcond(int maxn, int passcount)
{
bool result;
ap::real_2d_array a;
ap::real_2d_array cha;
ap::integer_1d_array p;
int n;
int i;
int j;
int pass;
bool err50;
bool err90;
bool errspec;
bool errless;
bool isupper;
double erc1;
double ercinf;
ap::real_1d_array q50;
ap::real_1d_array q90;
double v;
err50 = false;
err90 = false;
errless = false;
errspec = false;
q50.setlength(2);
q90.setlength(2);
for(n = 1; n <= maxn; n++)
{
isupper = ap::fp_greater(ap::randomreal(),0.5);
//
// general test
//
a.setlength(n, n);
for(i = 0; i <= 1; i++)
{
q50(i) = 0;
q90(i) = 0;
}
for(pass = 1; pass <= passcount; pass++)
{
spdmatrixrndcond(n, exp(ap::randomreal()*log(double(1000))), a);
rmatrixrefrcond(a, n, erc1, ercinf);
rmatrixdrophalf(a, n, isupper);
rmatrixmakeacopy(a, n, n, cha);
spdmatrixcholesky(cha, n, isupper);
//
// normal
//
v = 1/spdmatrixrcond(a, n, isupper);
if( ap::fp_greater_eq(v,threshold50*erc1) )
{
q50(0) = q50(0)+double(1)/double(passcount);
}
if( ap::fp_greater_eq(v,threshold90*erc1) )
{
q90(0) = q90(0)+double(1)/double(passcount);
}
errless = errless||ap::fp_greater(v,erc1*1.001);
//
// Cholesky
//
v = 1/spdmatrixcholeskyrcond(cha, n, isupper);
if( ap::fp_greater_eq(v,threshold50*erc1) )
{
q50(1) = q50(1)+double(1)/double(passcount);
}
if( ap::fp_greater_eq(v,threshold90*erc1) )
{
q90(1) = q90(1)+double(1)/double(passcount);
}
errless = errless||ap::fp_greater(v,erc1*1.001);
}
for(i = 0; i <= 1; i++)
{
err50 = err50||ap::fp_less(q50(i),0.50);
err90 = err90||ap::fp_less(q90(i),0.90);
}
//
// degenerate matrix test
//
if( n>=3 )
{
a.setlength(n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
a(i,j) = 0.0;
}
}
a(0,0) = 1;
a(n-1,n-1) = 1;
errspec = errspec||ap::fp_neq(spdmatrixrcond(a, n, isupper),-1);
errspec = errspec||ap::fp_neq(spdmatrixcholeskyrcond(a, n, isupper),0);
}
//
// near-degenerate matrix test
//
if( n>=2 )
{
a.setlength(n, n);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
a(i,j) = 0.0;
}
}
for(i = 0; i <= n-1; i++)
{
a(i,i) = 1;
}
i = ap::randominteger(n);
a(i,i) = 0.1*ap::maxrealnumber;
errspec = errspec||ap::fp_neq(spdmatrixrcond(a, n, isupper),0);
errspec = errspec||ap::fp_neq(spdmatrixcholeskyrcond(a, n, isupper),0);
}
}
//
// report
//
result = !(err50||err90||errless||errspec);
return result;
}
