/*************************************************************************
Problem testing
*************************************************************************/
static void testproblem(const ap::complex_2d_array& a, int n)
{
int i;
int j;
ap::complex_2d_array b;
ap::complex_2d_array c;
ap::integer_1d_array pivots;
ap::complex v1;
ap::complex v2;
ap::complex ve;
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);
}
}
ve = dettriangle(b, n);
v1 = cmatrixdet(a, n);
makeacopy(a, n, n, c);
cmatrixlu(c, n, n, pivots);
v2 = cmatrixludet(c, pivots, n);
if( ve!=0 )
{
deterrors = deterrors||ap::abscomplex((v1-ve)/ap::maxreal(ap::abscomplex(ve), double(1)))>1.0E-9;
deterrors = deterrors||ap::abscomplex((v1-ve)/ap::maxreal(ap::abscomplex(ve), double(1)))>1.0E-9;
}
else
{
deterrors = deterrors||v1!=ve;
deterrors = deterrors||v2!=ve;
}
}
/*************************************************************************
Inversion of a general complex matrix.
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
Output parameters:
A - inverse of matrix A.
Array whose indexes range within [0..N-1, 0..N-1].
Result:
True, if the matrix is not singular.
False, if the matrix is singular.
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
bool cmatrixinverse(ap::complex_2d_array& a, int n)
{
bool result;
ap::integer_1d_array pivots;
cmatrixlu(a, n, n, pivots);
result = cmatrixluinverse(a, pivots, n);
return result;
}
/*************************************************************************
Solving a system of linear equations.
The algorithm solves a system of linear equations by using the
LU decomposition. The algorithm solves systems with a square matrix only.
Input parameters:
A - system matrix.
Array whose indexes range within [0..N-1, 0..N-1].
B - right side of a system.
Array whose indexes range within [0..N-1].
N - size of matrix A.
Output parameters:
X - solution of a system.
Array whose index ranges within [0..N-1].
Result:
True, if the matrix is not singular.
False, if the matrix is singular. In this case, X doesn't contain a
solution.
-- ALGLIB --
Copyright 2005-2008 by Bochkanov Sergey
*************************************************************************/
bool cmatrixsolve(ap::complex_2d_array a,
ap::complex_1d_array b,
int n,
ap::complex_1d_array& x)
{
bool result;
ap::integer_1d_array pivots;
int i;
cmatrixlu(a, n, n, pivots);
result = cmatrixlusolve(a, pivots, b, n, x);
return result;
}
/*************************************************************************
Problem testing
*************************************************************************/
static void testproblem(const ap::complex_2d_array& a, int n)
{
ap::complex_2d_array b;
ap::complex_2d_array blu;
ap::complex_2d_array t1;
ap::integer_1d_array p;
int i;
int j;
ap::complex v;
//
// Decomposition
//
makeacopy(a, n, n, b);
cmatrixinverse(b, n);
makeacopy(a, n, n, blu);
cmatrixlu(blu, n, n, p);
cmatrixluinverse(blu, p, n);
//
// Test
//
t1.setbounds(0, n-1, 0, n-1);
internalmatrixmatrixmultiply(a, 0, n-1, 0, n-1, false, b, 0, n-1, 0, n-1, false, t1, 0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
v = t1(i,j);
if( i==j )
{
v = v-1;
}
inverrors = inverrors||ap::abscomplex(v)>threshold;
}
}
internalmatrixmatrixmultiply(a, 0, n-1, 0, n-1, false, blu, 0, n-1, 0, n-1, false, t1, 0, n-1, 0, n-1);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
v = t1(i,j);
if( i==j )
{
v = v-1;
}
inverrors = inverrors||ap::abscomplex(v)>threshold;
}
}
}
/*************************************************************************
Returns True for successful test, False - for failed test
*************************************************************************/
static bool testcmatrixrcond(int maxn, int passcount)
{
bool result;
ap::complex_2d_array a;
ap::complex_2d_array lua;
ap::integer_1d_array p;
int n;
int i;
int j;
int pass;
bool err50;
bool err90;
bool errless;
bool errspec;
double erc1;
double ercinf;
ap::real_1d_array q50;
ap::real_1d_array q90;
double v;
q50.setbounds(0, 3);
q90.setbounds(0, 3);
err50 = false;
err90 = false;
errless = false;
errspec = false;
//
// process
//
for(n = 1; n <= maxn; n++)
{
//
// special test for zero matrix
//
cmatrixgenzero(a, n);
cmatrixmakeacopy(a, n, n, lua);
cmatrixlu(lua, n, n, p);
errspec = errspec||ap::fp_neq(cmatrixrcond1(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixrcondinf(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcond1(lua, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcondinf(lua, n),0);
//
// general test
//
a.setbounds(0, n-1, 0, n-1);
for(i = 0; i <= 3; i++)
{
q50(i) = 0;
q90(i) = 0;
}
for(pass = 1; pass <= passcount; pass++)
{
cmatrixrndcond(n, exp(ap::randomreal()*log(double(1000))), a);
cmatrixmakeacopy(a, n, n, lua);
cmatrixlu(lua, n, n, p);
cmatrixrefrcond(a, n, erc1, ercinf);
//
// 1-norm, normal
//
v = 1/cmatrixrcond1(a, n);
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);
//
// 1-norm, LU
//
v = 1/cmatrixlurcond1(lua, n);
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);
//
// Inf-norm, normal
//
v = 1/cmatrixrcondinf(a, n);
if( ap::fp_greater_eq(v,threshold50*ercinf) )
{
q50(2) = q50(2)+double(1)/double(passcount);
}
if( ap::fp_greater_eq(v,threshold90*ercinf) )
{
q90(2) = q90(2)+double(1)/double(passcount);
}
errless = errless||ap::fp_greater(v,ercinf*1.001);
//
// Inf-norm, LU
//
v = 1/cmatrixlurcondinf(lua, n);
if( ap::fp_greater_eq(v,threshold50*ercinf) )
{
q50(3) = q50(3)+double(1)/double(passcount);
}
if( ap::fp_greater_eq(v,threshold90*ercinf) )
{
q90(3) = q90(3)+double(1)/double(passcount);
}
errless = errless||ap::fp_greater(v,ercinf*1.001);
}
for(i = 0; i <= 3; 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(cmatrixrcond1(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixrcondinf(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcond1(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcondinf(a, n),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(cmatrixrcond1(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixrcondinf(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcond1(a, n),0);
errspec = errspec||ap::fp_neq(cmatrixlurcondinf(a, n),0);
}
}
//
// report
//
result = !(err50||err90||errless||errspec);
return result;
}
