static VALUE rb_gsl_blas_zaxpy2(int argc, VALUE *argv, VALUE obj)
{
gsl_complex *a = NULL;
gsl_vector_complex *x = NULL, *y = NULL, *y2 = NULL;
switch (TYPE(obj)) {
case T_MODULE:
case T_CLASS:
case T_OBJECT:
get_vector_complex2(argc-1, argv+1, obj, &x, &y);
CHECK_COMPLEX(argv[0]);
Data_Get_Struct(argv[0], gsl_complex, a);
break;
default:
Data_Get_Struct(obj, gsl_vector_complex, x);
if (argc != 2) rb_raise(rb_eArgError, "wrong number of arguments (%d for 2)",
argc);
CHECK_COMPLEX(argv[0]);
CHECK_VECTOR_COMPLEX(argv[1]);
Data_Get_Struct(argv[0], gsl_complex, a);
Data_Get_Struct(argv[1], gsl_vector_complex, y);
break;
}
y2 = gsl_vector_complex_alloc(y->size);
gsl_vector_complex_memcpy(y2, y);
gsl_blas_zaxpy(*a, x, y2);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, y2);
}
int
gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A, const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x, gsl_vector_complex * residual)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix a must be square", GSL_ENOTSQR);
}
if (LU->size1 != LU->size2)
{
GSL_ERROR ("LU matrix must be square", GSL_ENOTSQR);
}
else if (A->size1 != LU->size2)
{
GSL_ERROR ("LU matrix must be decomposition of a", GSL_ENOTSQR);
}
else if (LU->size1 != p->size)
{
GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN);
}
else if (LU->size1 != b->size)
{
GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
}
else if (LU->size1 != x->size)
{
GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
}
else if (singular (LU))
{
GSL_ERROR ("matrix is singular", GSL_EDOM);
}
else
{
int status;
/* Compute residual, residual = (A * x - b) */
gsl_vector_complex_memcpy (residual, b);
{
gsl_complex one = GSL_COMPLEX_ONE;
gsl_complex negone = GSL_COMPLEX_NEGONE;
gsl_blas_zgemv (CblasNoTrans, one, A, x, negone, residual);
}
/* Find correction, delta = - (A^-1) * residual, and apply it */
status = gsl_linalg_complex_LU_svx (LU, p, residual);
{
gsl_complex negone= GSL_COMPLEX_NEGONE;
gsl_blas_zaxpy (negone, residual, x);
}
return status;
}
}
/** Subtraction operator (vector) */
vector<complex> vector<complex>::operator-(const vector<complex>& v) const
{
vector<complex> v1(_vector);
gsl_complex z1;
GSL_SET_COMPLEX(&z1, -1., 0.);
if (gsl_blas_zaxpy(z1, v.as_gsl_type_ptr(), v1.as_gsl_type_ptr())) {
std::cout << "\n Error in vector<complex> -" << std::endl;
exit(EXIT_FAILURE);
}
return v1;
}
/** Subtraction assignment (complex) */
vector<complex> vector<complex>::operator-(const complex& z)
{
vector<complex> v1(_vector);
gsl_complex z1;
gsl_vector_complex *v2;
GSL_SET_COMPLEX(&z1, -1., 0.);
v2 = gsl_vector_complex_alloc(v1.size());
gsl_vector_complex_set_all(v2, z1);
if (gsl_blas_zaxpy(z, v2, v1.as_gsl_type_ptr())) {
std::cout << "\n Error in vector<complex> - (double)" << std::endl;
exit(EXIT_FAILURE);
}
gsl_vector_complex_free(v2);
return v1;
}
/**
* C++ version of gsl_blas_zaxpy().
* @param alpha A constant
* @param X A vector
* @param Y A vector
* @return Error code on failure
*/
int zaxpy( complex const& alpha, vector_complex const& X, vector_complex& Y ){
return gsl_blas_zaxpy( alpha.get(), X.get(), Y.get() ); }
int
gsl_linalg_hermtd_decomp (gsl_matrix_complex * A, gsl_vector_complex * tau)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("hermitian tridiagonal decomposition requires square matrix",
GSL_ENOTSQR);
}
else if (tau->size + 1 != A->size1)
{
GSL_ERROR ("size of tau must be (matrix size - 1)", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
size_t i;
const gsl_complex zero = gsl_complex_rect (0.0, 0.0);
const gsl_complex one = gsl_complex_rect (1.0, 0.0);
const gsl_complex neg_one = gsl_complex_rect (-1.0, 0.0);
for (i = 0 ; i < N - 1; i++)
{
gsl_vector_complex_view c = gsl_matrix_complex_column (A, i);
gsl_vector_complex_view v = gsl_vector_complex_subvector (&c.vector, i + 1, N - (i + 1));
gsl_complex tau_i = gsl_linalg_complex_householder_transform (&v.vector);
/* Apply the transformation H^T A H to the remaining columns */
if ((i + 1) < (N - 1)
&& !(GSL_REAL(tau_i) == 0.0 && GSL_IMAG(tau_i) == 0.0))
{
gsl_matrix_complex_view m =
gsl_matrix_complex_submatrix (A, i + 1, i + 1,
N - (i+1), N - (i+1));
gsl_complex ei = gsl_vector_complex_get(&v.vector, 0);
gsl_vector_complex_view x = gsl_vector_complex_subvector (tau, i, N-(i+1));
gsl_vector_complex_set (&v.vector, 0, one);
/* x = tau * A * v */
gsl_blas_zhemv (CblasLower, tau_i, &m.matrix, &v.vector, zero, &x.vector);
/* w = x - (1/2) tau * (x' * v) * v */
{
gsl_complex xv, txv, alpha;
gsl_blas_zdotc(&x.vector, &v.vector, &xv);
txv = gsl_complex_mul(tau_i, xv);
alpha = gsl_complex_mul_real(txv, -0.5);
gsl_blas_zaxpy(alpha, &v.vector, &x.vector);
}
/* apply the transformation A = A - v w' - w v' */
gsl_blas_zher2(CblasLower, neg_one, &v.vector, &x.vector, &m.matrix);
gsl_vector_complex_set (&v.vector, 0, ei);
}
gsl_vector_complex_set (tau, i, tau_i);
}
return GSL_SUCCESS;
}
}