/** @brief Copies 'bytes_to_copy' bytes from address 'src_buffer + src_offset' to memory starting at address 'dst_buffer + dst_offset'.
*
* @param src_buffer A smart pointer to the begin of an allocated buffer
* @param dst_buffer A smart pointer to the end of an allocated buffer
* @param src_offset Offset of the first byte to be written from the address given by 'src_buffer' (in bytes)
* @param dst_offset Offset of the first byte to be written to the address given by 'dst_buffer' (in bytes)
* @param bytes_to_copy Number of bytes to be copied
*/
inline void memory_copy(handle_type const & src_buffer,
handle_type & dst_buffer,
vcl_size_t src_offset,
vcl_size_t dst_offset,
vcl_size_t bytes_to_copy)
{
assert( (dst_buffer.get() != NULL) && bool("Memory not initialized!"));
assert( (src_buffer.get() != NULL) && bool("Memory not initialized!"));
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for
#endif
for (long i=0; i<long(bytes_to_copy); ++i)
dst_buffer.get()[vcl_size_t(i)+dst_offset] = src_buffer.get()[vcl_size_t(i) + src_offset];
}
vcl_size_t size(vector_expression<LHS, const int, op_matrix_diag> const & proxy)
{
int k = proxy.rhs();
int A_size1 = static_cast<int>(size1(proxy.lhs()));
int A_size2 = static_cast<int>(size2(proxy.lhs()));
int row_depth = std::min(A_size1, A_size1 + k);
int col_depth = std::min(A_size2, A_size2 - k);
return vcl_size_t(std::min(row_depth, col_depth));
}
void copy_to_complex_array(std::complex<NumericT> * input_complex,
viennacl::vector<NumericT, AlignmentV> const & in, vcl_size_t size)
{
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for if (size > VIENNACL_OPENMP_VECTOR_MIN_SIZE)
#endif
for (long i2 = 0; i2 < long(size * 2); i2 += 2)
{ //change array to complex array
vcl_size_t i = vcl_size_t(i2);
input_complex[i / 2] = std::complex<NumericT>(in[i], in[i + 1]);
}
}
void zero2(NumericT *input1, NumericT *input2, vcl_size_t size)
{
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for if (size > VIENNACL_OPENMP_VECTOR_MIN_SIZE)
#endif
for (long i2 = 0; i2 < long(size); i2++)
{
vcl_size_t i = vcl_size_t(i2);
input1[i] = 0;
input2[i] = 0;
}
}
void copy_to_vector(std::complex<NumericT> * input_complex, NumericT * in, vcl_size_t size)
{
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for if (size > VIENNACL_OPENMP_VECTOR_MIN_SIZE)
#endif
for (long i2 = 0; i2 < long(size); i2++)
{
vcl_size_t i = vcl_size_t(i2);
in[i * 2] = static_cast<NumericT>(std::real(input_complex[i]));
in[i * 2 + 1] = static_cast<NumericT>(std::imag(input_complex[i]));
}
}
/** @brief Reads data from a buffer back to main RAM.
*
* @param src_buffer A smart pointer to the beginning of an allocated source buffer
* @param src_offset Offset of the first byte to be read from the beginning of src_buffer (in bytes_
* @param bytes_to_copy Number of bytes to be read
* @param ptr Location in main RAM where to read data should be written to
*/
inline void memory_read(handle_type const & src_buffer,
vcl_size_t src_offset,
vcl_size_t bytes_to_copy,
void * ptr,
bool /*async*/)
{
assert( (src_buffer.get() != NULL) && bool("Memory not initialized!"));
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for
#endif
for (long i=0; i<long(bytes_to_copy); ++i)
static_cast<char *>(ptr)[i] = src_buffer.get()[vcl_size_t(i)+src_offset];
}
/** @brief Writes data from main RAM identified by 'ptr' to the buffer identified by 'dst_buffer'
*
* @param dst_buffer A smart pointer to the beginning of an allocated buffer
* @param dst_offset Offset of the first written byte from the beginning of 'dst_buffer' (in bytes)
* @param bytes_to_copy Number of bytes to be copied
* @param ptr Pointer to the first byte to be written
*/
inline void memory_write(handle_type & dst_buffer,
vcl_size_t dst_offset,
vcl_size_t bytes_to_copy,
const void * ptr,
bool /*async*/)
{
assert( (dst_buffer.get() != NULL) && bool("Memory not initialized!"));
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for
#endif
for (long i=0; i<long(bytes_to_copy); ++i)
dst_buffer.get()[vcl_size_t(i)+dst_offset] = static_cast<const char *>(ptr)[i];
}
void copy_to_vector(std::complex<NumericT> * input_complex,
viennacl::vector_base<NumericT> & in, vcl_size_t size)
{
std::vector<NumericT> temp(2 * size);
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for if (size > VIENNACL_OPENMP_VECTOR_MIN_SIZE)
#endif
for (long i2 = 0; i2 < long(size); i2++)
{
vcl_size_t i = vcl_size_t(i2);
temp[i * 2] = static_cast<NumericT>(std::real(input_complex[i]));
temp[i * 2 + 1] = static_cast<NumericT>(std::imag(input_complex[i]));
}
viennacl::copy(temp, in);
}
void svd_qr_shift(MatrixType & vcl_u,
MatrixType & vcl_v,
CPU_VectorType & q,
CPU_VectorType & e)
{
typedef typename MatrixType::value_type ScalarType;
typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type CPU_ScalarType;
vcl_size_t n = q.size();
int m = static_cast<int>(vcl_u.size1());
detail::transpose(vcl_u);
detail::transpose(vcl_v);
std::vector<CPU_ScalarType> signs_v(n, 1);
std::vector<CPU_ScalarType> cs1(n), ss1(n), cs2(n), ss2(n);
viennacl::vector<CPU_ScalarType> tmp1(n, viennacl::traits::context(vcl_u)), tmp2(n, viennacl::traits::context(vcl_u));
bool goto_test_conv = false;
for (int k = static_cast<int>(n) - 1; k >= 0; k--)
{
// std::cout << "K = " << k << std::endl;
vcl_size_t iter = 0;
for (iter = 0; iter < detail::ITER_MAX; iter++)
{
// test for split
int l;
for (l = k; l >= 0; l--)
{
goto_test_conv = false;
if (std::fabs(e[vcl_size_t(l)]) <= detail::EPS)
{
// set it
goto_test_conv = true;
break;
}
if (std::fabs(q[vcl_size_t(l) - 1]) <= detail::EPS)
{
// goto
break;
}
}
if (!goto_test_conv)
{
CPU_ScalarType c = 0.0;
CPU_ScalarType s = 1.0;
//int l1 = l - 1;
//int l2 = k;
for (int i = l; i <= k; i++)
{
CPU_ScalarType f = s * e[vcl_size_t(i)];
e[vcl_size_t(i)] = c * e[vcl_size_t(i)];
if (std::fabs(f) <= detail::EPS)
{
//l2 = i - 1;
break;
}
CPU_ScalarType g = q[vcl_size_t(i)];
CPU_ScalarType h = detail::pythag(f, g);
q[vcl_size_t(i)] = h;
c = g / h;
s = -f / h;
cs1[vcl_size_t(i)] = c;
ss1[vcl_size_t(i)] = s;
}
// std::cout << "Hitted!" << l1 << " " << l2 << "\n";
// for (int i = l; i <= l2; i++)
// {
// for (int j = 0; j < m; j++)
// {
// CPU_ScalarType y = u(j, l1);
// CPU_ScalarType z = u(j, i);
// u(j, l1) = y * cs1[i] + z * ss1[i];
// u(j, i) = -y * ss1[i] + z * cs1[i];
// }
// }
}
CPU_ScalarType z = q[vcl_size_t(k)];
if (l == k)
{
if (z < 0)
{
q[vcl_size_t(k)] = -z;
signs_v[vcl_size_t(k)] *= -1;
}
break;
}
if (iter >= detail::ITER_MAX - 1)
break;
CPU_ScalarType x = q[vcl_size_t(l)];
CPU_ScalarType y = q[vcl_size_t(k) - 1];
CPU_ScalarType g = e[vcl_size_t(k) - 1];
CPU_ScalarType h = e[vcl_size_t(k)];
CPU_ScalarType f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2 * h * y);
g = detail::pythag<CPU_ScalarType>(f, 1);
if (f < 0) {
f = ((x - z) * (x + z) + h * (y / (f - g) - h)) / x;
} else {
f = ((x - z) * (x + z) + h * (y / (f + g) - h)) / x;
}
CPU_ScalarType c = 1;
CPU_ScalarType s = 1;
for (vcl_size_t i = static_cast<vcl_size_t>(l) + 1; i <= static_cast<vcl_size_t>(k); i++)
{
g = e[i];
y = q[i];
h = s * g;
g = c * g;
CPU_ScalarType z2 = detail::pythag(f, h);
e[i - 1] = z2;
c = f / z2;
s = h / z2;
f = x * c + g * s;
g = -x * s + g * c;
h = y * s;
y = y * c;
cs1[i] = c;
ss1[i] = s;
z2 = detail::pythag(f, h);
q[i - 1] = z2;
c = f / z2;
s = h / z2;
f = c * g + s * y;
x = -s * g + c * y;
cs2[i] = c;
ss2[i] = s;
}
{
viennacl::copy(cs1, tmp1);
viennacl::copy(ss1, tmp2);
givens_prev(vcl_v, tmp1, tmp2, static_cast<int>(n), l, k);
}
{
viennacl::copy(cs2, tmp1);
viennacl::copy(ss2, tmp2);
givens_prev(vcl_u, tmp1, tmp2, m, l, k);
}
e[vcl_size_t(l)] = 0.0;
e[vcl_size_t(k)] = f;
q[vcl_size_t(k)] = x;
}
}
viennacl::copy(signs_v, tmp1);
change_signs(vcl_v, tmp1, static_cast<int>(n));
// transpose singular matrices again
detail::transpose(vcl_u);
detail::transpose(vcl_v);
}
void tql1(vcl_size_t n,
VectorType & d,
VectorType & e)
{
for (vcl_size_t i = 1; i < n; i++)
e[i - 1] = e[i];
e[n - 1] = 0;
SCALARTYPE f = 0.;
SCALARTYPE tst1 = 0.;
SCALARTYPE eps = static_cast<SCALARTYPE>(1e-6);
for (vcl_size_t l = 0; l < n; l++)
{
// Find small subdiagonal element.
tst1 = std::max<SCALARTYPE>(tst1, std::fabs(d[l]) + std::fabs(e[l]));
vcl_size_t m = l;
while (m < n)
{
if (std::fabs(e[m]) <= eps * tst1)
break;
m++;
}
// If m == l, d[l) is an eigenvalue, otherwise, iterate.
if (m > l)
{
vcl_size_t iter = 0;
do
{
iter = iter + 1; // (Could check iteration count here.)
// Compute implicit shift
SCALARTYPE g = d[l];
SCALARTYPE p = (d[l + 1] - g) / (2 * e[l]);
SCALARTYPE r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, 1);
if (p < 0)
{
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
SCALARTYPE h = g - d[l];
for (vcl_size_t i = l + 2; i < n; i++)
{
d[i] -= h;
}
f = f + h;
// Implicit QL transformation.
p = d[m];
SCALARTYPE c = 1;
SCALARTYPE s = 0;
for (int i = int(m - 1); i >= int(l); i--)
{
g = c * e[vcl_size_t(i)];
h = c * p;
r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, e[vcl_size_t(i)]);
e[vcl_size_t(i) + 1] = s * r;
s = e[vcl_size_t(i)] / r;
c = p / r;
p = c * d[vcl_size_t(i)] - s * g;
d[vcl_size_t(i) + 1] = h + s * (c * g + s * d[vcl_size_t(i)]);
}
e[l] = s * p;
d[l] = c * p;
// Check for convergence.
}
while (std::fabs(e[l]) > eps * tst1);
}
d[l] = d[l] + f;
e[l] = 0;
}
}
void tql2(matrix_base<SCALARTYPE, F> & Q,
VectorType & d,
VectorType & e)
{
vcl_size_t n = static_cast<vcl_size_t>(viennacl::traits::size1(Q));
//boost::numeric::ublas::vector<SCALARTYPE> cs(n), ss(n);
std::vector<SCALARTYPE> cs(n), ss(n);
viennacl::vector<SCALARTYPE> tmp1(n), tmp2(n);
for (vcl_size_t i = 1; i < n; i++)
e[i - 1] = e[i];
e[n - 1] = 0;
SCALARTYPE f = 0;
SCALARTYPE tst1 = 0;
SCALARTYPE eps = static_cast<SCALARTYPE>(viennacl::linalg::detail::EPS);
for (vcl_size_t l = 0; l < n; l++)
{
// Find small subdiagonal element.
tst1 = std::max<SCALARTYPE>(tst1, std::fabs(d[l]) + std::fabs(e[l]));
vcl_size_t m = l;
while (m < n)
{
if (std::fabs(e[m]) <= eps * tst1)
break;
m++;
}
// If m == l, d[l) is an eigenvalue, otherwise, iterate.
if (m > l)
{
vcl_size_t iter = 0;
do
{
iter = iter + 1; // (Could check iteration count here.)
// Compute implicit shift
SCALARTYPE g = d[l];
SCALARTYPE p = (d[l + 1] - g) / (2 * e[l]);
SCALARTYPE r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, 1);
if (p < 0)
{
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
SCALARTYPE dl1 = d[l + 1];
SCALARTYPE h = g - d[l];
for (vcl_size_t i = l + 2; i < n; i++)
{
d[i] -= h;
}
f = f + h;
// Implicit QL transformation.
p = d[m];
SCALARTYPE c = 1;
SCALARTYPE c2 = c;
SCALARTYPE c3 = c;
SCALARTYPE el1 = e[l + 1];
SCALARTYPE s = 0;
SCALARTYPE s2 = 0;
for (int i = int(m - 1); i >= int(l); i--)
{
c3 = c2;
c2 = c;
s2 = s;
g = c * e[vcl_size_t(i)];
h = c * p;
r = viennacl::linalg::detail::pythag(p, e[vcl_size_t(i)]);
e[vcl_size_t(i) + 1] = s * r;
s = e[vcl_size_t(i)] / r;
c = p / r;
p = c * d[vcl_size_t(i)] - s * g;
d[vcl_size_t(i) + 1] = h + s * (c * g + s * d[vcl_size_t(i)]);
cs[vcl_size_t(i)] = c;
ss[vcl_size_t(i)] = s;
}
p = -s * s2 * c3 * el1 * e[l] / dl1;
e[l] = s * p;
d[l] = c * p;
viennacl::copy(cs, tmp1);
viennacl::copy(ss, tmp2);
viennacl::linalg::givens_next(Q, tmp1, tmp2, int(l), int(m));
// Check for convergence.
}
while (std::fabs(e[l]) > eps * tst1);
}
d[l] = d[l] + f;
e[l] = 0;
}
// Sort eigenvalues and corresponding vectors.
/*
for (int i = 0; i < n-1; i++) {
int k = i;
SCALARTYPE p = d[i];
for (int j = i+1; j < n; j++) {
if (d[j] > p) {
k = j;
p = d[j);
}
}
if (k != i) {
d[k] = d[i];
d[i] = p;
for (int j = 0; j < n; j++) {
p = Q(j, i);
Q(j, i) = Q(j, k);
Q(j, k) = p;
}
}
}
*/
}
std::vector<
typename viennacl::result_of::cpu_value_type<typename VectorT::value_type>::type
>
bisect(VectorT const & alphas, VectorT const & betas)
{
typedef typename viennacl::result_of::value_type<VectorT>::type NumericType;
typedef typename viennacl::result_of::cpu_value_type<NumericType>::type CPU_NumericType;
vcl_size_t size = betas.size();
std::vector<CPU_NumericType> x_temp(size);
std::vector<CPU_NumericType> beta_bisect;
std::vector<CPU_NumericType> wu;
double rel_error = std::numeric_limits<CPU_NumericType>::epsilon();
beta_bisect.push_back(0);
for (vcl_size_t i = 1; i < size; i++)
beta_bisect.push_back(betas[i] * betas[i]);
double xmin = alphas[size - 1] - std::fabs(betas[size - 1]);
double xmax = alphas[size - 1] + std::fabs(betas[size - 1]);
for (vcl_size_t i = 0; i < size - 1; i++)
{
double h = std::fabs(betas[i]) + std::fabs(betas[i + 1]);
if (alphas[i] + h > xmax)
xmax = alphas[i] + h;
if (alphas[i] - h < xmin)
xmin = alphas[i] - h;
}
double eps1 = 1e-6;
/*double eps2 = (xmin + xmax > 0) ? (rel_error * xmax) : (-rel_error * xmin);
if (eps1 <= 0)
eps1 = eps2;
else
eps2 = 0.5 * eps1 + 7.0 * eps2; */
double x0 = xmax;
for (vcl_size_t i = 0; i < size; i++)
{
x_temp[i] = xmax;
wu.push_back(xmin);
}
for (long k = static_cast<long>(size) - 1; k >= 0; --k)
{
double xu = xmin;
for (long i = k; i >= 0; --i)
{
if (xu < wu[vcl_size_t(k-i)])
{
xu = wu[vcl_size_t(i)];
break;
}
}
if (x0 > x_temp[vcl_size_t(k)])
x0 = x_temp[vcl_size_t(k)];
double x1 = (xu + x0) / 2.0;
while (x0 - xu > 2.0 * rel_error * (std::fabs(xu) + std::fabs(x0)) + eps1)
{
vcl_size_t a = 0;
double q = 1;
for (vcl_size_t i = 0; i < size; i++)
{
if (q > 0 || q < 0)
q = alphas[i] - x1 - beta_bisect[i] / q;
else
q = alphas[i] - x1 - std::fabs(betas[i] / rel_error);
if (q < 0)
a++;
}
if (a <= static_cast<vcl_size_t>(k))
{
xu = x1;
if (a < 1)
wu[0] = x1;
else
{
wu[a] = x1;
if (x_temp[a - 1] > x1)
x_temp[a - 1] = x1;
}
}
else
x0 = x1;
x1 = (xu + x0) / 2.0;
}
x_temp[vcl_size_t(k)] = x1;
}
return x_temp;
}