double spectral_game(int n)
{
double *A;
double u[n] __attribute__ ((aligned (16)));
double v[n] __attribute__ ((aligned (16)));
int i, j;
/* Aligned allocation. */
/* A = (double *)malloc(n*n*sizeof(double)); */
if ( posix_memalign( (void **)&A , 4*sizeof(double) , sizeof(double) * n * n ) != 0 ) {
printf( "spectral_game:%i: call to posix_memalign failed.\n" , __LINE__ );
abort();
}
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
A[i*n+j] = Ac(i, j);
}
}
for (i = 0; i < n; i++) {
u[i] = 1.0;
}
for (i = 0; i < 10; i++) {
AvA(n, A, u, v);
AvA(n, A, v, u);
}
free(A);
return sqrt(dot_product2(n, u, v) / dot_product2(n, v, v));
}
Vector<value_type> lin_solve(Matrix<value_type> const & A, Vector<value_type> const & bin) {
//Create A=QR
if(A.dimension().first > A.dimension().second)
return lin_solve(A.trans()*A,A.trans()*bin);
Matrix<value_type> Ac(std::max(A.dimension().first,A.dimension().second),A.dimension().second);
Ac = A;
QR_Givens<value_type> qr(Ac);
/*std::cout << "A:\n " << A << " b: " << bin << "\n\n" ;
std::cout << "Q: " << qr.get_q() << " R: " << qr.get_r() << "\n";
std::cout << "a=QR: " << qr.get_q() * qr.get_r() << "\n";*/
// calc b=QT*bin
Vector<value_type> b = qr.get_q().trans()*bin;
//std::cout << "Qb: \n" << b << "\n\n";
// backtrack Rx=b
Vector<value_type> x(A.dimension().second);
// If check if zerolines for overdefined
size_type dim1 = A.dimension().first, dim2 = A.dimension().second;
for(size_type i=dim1-1;i!=0;--i)
if(qr.get_r().is_zero(i))
{
x[i] = 1.0;
//std::cout << "found zeroline\n";
}
else
{
dim1 = i+1;
break;
}
if(dim1 < dim2)
{
//=> extend R to nxn and set k xs to 1 and beging at n-k line in backtracking
for(size_type i = dim1; i<dim2;++i)
{
x[i] = 1.0;
}
}
// real backtracking:
for(size_type i = dim1-1;;--i)
{
x[i] = b[i];
for(size_type j = i+1;j<dim2;++j)
{
x[i] -= qr.get_r()[i][j]*x[j];
}
x[i]/= qr.get_r()[i][i];
if(i==0)
break;
}
//std::cout << "x: \n" << x << "\n";
return x;
}
long sprGetCol()
{
long j, i;
sparse_int_t *ir = new sparse_int_t[10];
sparse_int_t *jc = new sparse_int_t[4];
real_t *val = new real_t[10];
real_t *col = new real_t[4];
/* Test matrix:
*
* [ 0 3 6 ]
* [ 1 0 7 ]
* [ 2 0 8 ]
* [ 0 4 9 ]
* [ 0 5 10 ]
*/
jc[0] = 0; jc[1] = 2; jc[2] = 5; jc[3] = 10;
ir[0] = 1; ir[1] = 2;
ir[2] = 0; ir[3] = 3; ir[4] = 4;
ir[5] = 0; ir[6] = 1; ir[7] = 2; ir[8] = 3; ir[9] = 4;
for (i = 0; i < 10; i++) val[i] = 1.0+i;
SparseMatrix Ac(5, 3, ir, jc, val);
real_t *Acv = Ac.full(); // row major format
SparseMatrixRow A(5, 3, 3, Acv);
delete[] Acv;
Ac.free (); // or delete[] val,jc,ir;
Indexlist rows(4);
rows.addNumber(2);
rows.addNumber(4);
rows.addNumber(3);
rows.addNumber(0);
/* Indexed matrix:
*
* [ 2 0 8 ]
* [ 0 5 10 ]
* [ 0 4 9 ]
* [ 0 3 6 ]
*/
for (j = 0; j < 3; j++)
{
fprintf(stdFile, "Column %ld:\n", j);
A.getCol(j, &rows, 1.0, col);
for (i = 0; i < 4; i++)
fprintf(stdFile, " %3.0f\n", col[i]);
}
delete[] col;
A.free (); // or delete[] val,jc,ir;
return 0;
}
long sprTimes()
{
long i;
sparse_int_t *ir = new sparse_int_t[10];
sparse_int_t *jc = new sparse_int_t[6];
real_t *val = new real_t[10];
real_t *x = new real_t[5*2];
real_t *y = new real_t[3*2];
real_t Ax[] = {-23, -11, -26, 42, 74, 99};
real_t ATy[] = {-63, -69, -222, -423, -359, 272, 126, 663, 1562, 1656};
real_t err = 0.0;
for (i = 0; i < 10; i++) x[i] = -4.0+i;
/* Test matrix:
*
* [ 0 3 4 6 0 ]
* [ 1 0 0 7 9 ]
* [ 2 0 5 8 10 ]
*/
jc[0] = 0; jc[1] = 2; jc[2] = 3; jc[3] = 5; jc[4] = 8; jc[5] = 10;
ir[0] = 1; ir[1] = 2;
ir[2] = 0;
ir[3] = 0; ir[4] = 2;
ir[5] = 0; ir[6] = 1; ir[7] = 2;
ir[8] = 1; ir[9] = 2;
for (i = 0; i < 10; i++) val[i] = 1.0+i;
SparseMatrix Ac(3, 5, ir, jc, val); // reference to ir, jc, val
real_t *Acv = Ac.full(); // row major format
SparseMatrixRow A(3, 5, 5, Acv);
delete[] Acv;
Ac.free (); // or delete[] val,jc,ir;
A.times(2, 1.0, x, 5, 0.0, y, 3);
for (i = 0; i < 6; i++)
if (fabs(y[i] - Ax[i]) > err) err = fabs(y[i] - Ax[i]);
fprintf(stdFile, "Error in sparse A*x: %9.2e\n", err);
A.transTimes(2, 1.0, y, 3, 0.0, x, 5);
err = 0.0;
for (i = 0; i < 10; i++)
if (fabs(x[i] - ATy[i]) > err) err = fabs(x[i] - ATy[i]);
fprintf(stdFile, "Error in sparse A'*x: %9.2e\n", err);
A.free (); // or delete[] val,ir,jc
delete[] y;
delete[] x;
return 0;
}
long sprGetRow()
{
long j, i;
sparse_int_t *ir = new sparse_int_t[10];
sparse_int_t *jc = new sparse_int_t[6];
real_t *val = new real_t[10];
real_t *row = new real_t[4];
/* Test matrix:
*
* [ 0 3 4 6 0 ]
* [ 1 0 0 7 9 ]
* [ 2 0 5 8 10 ]
*/
jc[0] = 0; jc[1] = 2; jc[2] = 3; jc[3] = 5; jc[4] = 8; jc[5] = 10;
ir[0] = 1; ir[1] = 2;
ir[2] = 0;
ir[3] = 0; ir[4] = 2;
ir[5] = 0; ir[6] = 1; ir[7] = 2;
ir[8] = 1; ir[9] = 2;
for (i = 0; i < 10; i++) val[i] = 1.0+i;
SparseMatrix Ac(3, 5, ir, jc, val);
real_t *Acv = Ac.full(); // row major format
SparseMatrixRow A(3, 5, 5, Acv);
delete[] Acv;
Ac.free (); // or delete[] val,jc,ir;
Indexlist cols(4);
cols.addNumber(2);
cols.addNumber(4);
cols.addNumber(3);
cols.addNumber(1);
/* Indexed matrix:
*
* [ 4 0 6 3 ]
* [ 0 9 7 0 ]
* [ 5 10 8 0 ]
*/
for (j = 0; j < 3; j++)
{
A.getRow(j, &cols, 1.0, row);
for (i = 0; i < 4; i++)
fprintf(stdFile, " %3.0f", row[i]);
fprintf(stdFile, "\n");
}
delete[] row;
A.free ();
return 0;
}
int main()
{
const int sz=7;
CArray A(sz);
A(0) = complex<float>(1,2);
A(1) = complex<float>(3,4);
Array<float,1> Ar = real(A);
BZTEST(int(Ar(0)) == 1 && int(Ar(1)) == 3);
Array<float,1> Ai = imag(A);
BZTEST(int(Ai(0)) == 2 && int(Ai(1)) == 4);
CArray Ac(sz);
Ac = conj(A);
BZTEST(Ac(0) == complex<float>(1,-2));
BZTEST(Ac(1) == complex<float>(3,-4));
Array<float,1> Ab(sz);
Ab = abs(A);
BZTEST(fabs(Ab(0) - 2.236068) < eps);
BZTEST(fabs(Ab(1) - 5.0) < eps);
Ab = arg(A);
BZTEST(fabs(Ab(0) - atan(2.0)) < eps);
BZTEST(fabs(Ab(1) - atan(4.0/3.0)) < eps);
Array<float,1> r(sz), theta(sz);
r(0) = 4.0f;
r(1) = 15.0f;
theta(0) = float(3.141592/3.0);
theta(1) = float(3.0*3.141592/2.0);
Ac = blitz::polar(r,theta);
BZTEST(fabs(real(Ac(0)) - 2) < eps);
BZTEST(fabs(imag(Ac(0)) - 3.4641012) < eps);
BZTEST(fabs(real(Ac(1)) - 0.0) < eps);
BZTEST(fabs(imag(Ac(1)) + 15.0) < eps);
Array<complex<long double>,1> A11(5),B11(5),C11(5);
A11=1,2,3,4,5;
B11=1,2,3,4,5;
C11=A11+B11;
BZTEST(fabs(real(C11(0)) - 2.) < eps);
C11=A11/B11;
BZTEST(fabs(real(C11(1)) - 1.) < eps);
C11=1.0l/A11;
BZTEST(fabs(real(C11(2)) - 1/3.) < eps);
C11=A11/1.0l;
BZTEST(fabs(real(C11(3)) - 4.) < eps);
C11=complex<long double>(0,1)/A11;
BZTEST(fabs(imag(C11(4)) - 1/5.) < eps);
C11=A11/complex<long double>(0,1);
BZTEST(fabs(imag(C11(0)) - -1.) < eps);
return 0;
}
long sprIndTimes()
{
const long N = 4;
long i, j;
long nRows = 2 * N + 1;
long nCols = N;
long nnz = 3 * N;
sparse_int_t *ir = new sparse_int_t[nnz];
sparse_int_t *jc = new sparse_int_t[nCols+1];
real_t *val = new real_t[nnz];
real_t *xc = new real_t[3*2];
real_t *yc = new real_t[4*2];
real_t Ax[] = {0.31, 0.05, 0.06, 0.30, 0.76, 0.20, 0.24, 0.60};
real_t ATy[] = {0.278, 0.000, 0.548, 0.776, 0.000, 1.208};
Indexlist rows(4), cols(3), allcols(nCols);
rows.addNumber(2);
rows.addNumber(4);
rows.addNumber(3);
rows.addNumber(0);
cols.addNumber(1);
cols.addNumber(3);
cols.addNumber(0);
for (i = 0; i < nCols; i++)
allcols.addNumber(i);
// build test matrix
for (i = 0; i <= N; i++) jc[i] = 3*i;
for (j = 0; j < N; j++)
for (i = 0; i < 3; i++)
{
ir[j*3+i] = 2*j + i;
val[j*3+i] = 1.0 - 0.1 * (j*3+i);
}
SparseMatrix Ac(nRows, nCols, ir, jc, val);
real_t *Acv = Ac.full(); // row major format
SparseMatrixRow A(nRows, nCols, nCols, Acv);
delete[] Acv;
Ac.free (); // or delete[] val,jc,ir;
fprintf(stdFile, "Test matrix A =\n");
for (j = 0; j < nRows; j++)
{
A.getRow(j, &allcols, 1.0, xc);
for (i = 0; i < nCols; i++)
fprintf(stdFile, "%6.2f", xc[i]);
fprintf(stdFile, "\n");
}
for (i = 0; i < 6; i++)
xc[i] = (1.0 + i) * 0.1;
A.times(&rows, &cols, 2, 1.0, xc, 3, 0.0, yc, 4, BT_TRUE);
real_t err = 0.0;
for (i = 0; i < 8; i++)
if (fabs(yc[i] - Ax[i]) > err)
err = fabs(yc[i] - Ax[i]);
fprintf(stdFile, "Error in sparse indexed A*x: %9.2e\n", err);
A.transTimes(&rows, &cols, 2, 1.0, yc, 4, 0.0, xc, 3);
for (i = 0; i < 3; i++)
{
for (j = 0; j < 2; j++)
fprintf(stdFile, "%6.2f", ATy[i + j*3]);
fprintf(stdFile, "\n");
}
for (i = 0; i < 3; i++)
{
for (j = 0; j < 2; j++)
fprintf(stdFile, "%6.2f", xc[i + j*3]);
fprintf(stdFile, "\n");
}
err = 0.0;
for (i = 0; i < 6; i++)
if (fabs(xc[i] - ATy[i]) > err)
err = fabs(xc[i] - ATy[i]);
fprintf(stdFile, "Error in sparse indexed A'*y: %9.2e\n", err);
delete[] xc;
delete[] yc;
A.free ();
return 0;
}
