int
gsl_linalg_complex_cholesky_solve (const gsl_matrix_complex * cholesky,
const gsl_vector_complex * b,
gsl_vector_complex * x)
{
if (cholesky->size1 != cholesky->size2)
{
GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
}
else if (cholesky->size1 != b->size)
{
GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
}
else if (cholesky->size2 != x->size)
{
GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
}
else
{
gsl_vector_complex_memcpy (x, b);
/* solve for y using forward-substitution, L y = b */
gsl_blas_ztrsv (CblasLower, CblasNoTrans, CblasNonUnit, cholesky, x);
/* perform back-substitution, L^H x = y */
gsl_blas_ztrsv (CblasLower, CblasConjTrans, CblasNonUnit, cholesky, x);
return GSL_SUCCESS;
}
} /* gsl_linalg_complex_cholesky_solve() */
int
gsl_linalg_complex_LU_solve (const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x)
{
if (LU->size1 != LU->size2)
{
GSL_ERROR ("LU matrix must be square", 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->size2 != x->size)
{
GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
}
else
{
/* Copy x <- b */
gsl_vector_complex_memcpy (x, b);
/* Solve for x */
gsl_linalg_complex_LU_svx (LU, p, x);
return GSL_SUCCESS;
}
}
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);
}
static VALUE rb_gsl_blas_zscal2(int argc, VALUE *argv, VALUE obj)
{
gsl_complex *a = NULL;
gsl_vector_complex *x = NULL, *xnew = NULL;
CHECK_COMPLEX(argv[0]);
switch (TYPE(obj)) {
case T_MODULE:
case T_CLASS:
case T_OBJECT:
if (argc != 2) rb_raise(rb_eArgError, "wrong number of arguments (%d for 2)",
argc);
CHECK_VECTOR_COMPLEX(argv[1]);
Data_Get_Struct(argv[0], gsl_complex, a);
Data_Get_Struct(argv[1], gsl_vector_complex, x);
break;
default:
if (argc != 1) rb_raise(rb_eArgError, "wrong number of arguments (%d for 1)",
argc);
Data_Get_Struct(obj, gsl_vector_complex, x);
Data_Get_Struct(argv[0], gsl_complex, a);
break;
}
xnew = gsl_vector_complex_alloc(x->size);
gsl_vector_complex_memcpy(xnew, x);
gsl_blas_zscal(*a, xnew);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, xnew);
}
static VALUE rb_fft_complex_trans(int argc, VALUE *argv, VALUE obj,
int (*transform)(gsl_complex_packed_array,
size_t, size_t,
const gsl_fft_complex_wavetable *,
gsl_fft_complex_workspace *),
int sss)
{
int flag = 0;
// local variable "status" was defined and set, but never used
//int status;
size_t stride, n;
gsl_complex_packed_array data;
gsl_vector_complex *vin, *vout;
gsl_fft_complex_wavetable *table = NULL;
gsl_fft_complex_workspace *space = NULL;
flag = gsl_fft_get_argv_complex(argc, argv, obj, &vin, &data, &stride, &n, &table, &space);
if (sss == RB_GSL_FFT_COPY) {
vout = gsl_vector_complex_alloc(n);
gsl_vector_complex_memcpy(vout, vin);
/*status =*/ (*transform)(vout->data, vout->stride /*1*/, vout->size /*n*/, table, space);
gsl_fft_free(flag, (GSL_FFT_Wavetable *) table, (GSL_FFT_Workspace *) space);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, vout);
} else { /* in-place */
/*status =*/ (*transform)(data, stride, n, table, space);
gsl_fft_free(flag, (GSL_FFT_Wavetable *) table, (GSL_FFT_Workspace *) space);
return obj;
}
}
//copy
complex_spinor::complex_spinor(const complex_spinor & another){
this->_numSites = another._numSites;
this->dimension = another.dimension;
this->priv_pVector = gsl_vector_complex_alloc(this->dimension);
gsl_vector_complex_memcpy(this->priv_pVector, another.priv_pVector);
}
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;
}
}
static CVECTOR *VECTOR_copy(CVECTOR *_object)
{
CVECTOR *copy = VECTOR_create(SIZE(THIS), COMPLEX(THIS), FALSE);
if (!COMPLEX(THIS))
gsl_vector_memcpy(VEC(copy), VEC(THIS));
else
gsl_vector_complex_memcpy(CVEC(copy), CVEC(THIS));
return copy;
}
/* module function */
static VALUE Vector_complex_memcpy(VALUE obj, VALUE dest, VALUE src) {
gsl_vector_complex * vdest, * vsrc;
Data_Get_Struct(dest, gsl_vector_complex, vdest);
Data_Get_Struct(src, gsl_vector_complex, vsrc);
gsl_vector_complex_memcpy(vdest, vsrc);
return obj;
}
int
lls_complex_solve(const double lambda, gsl_vector_complex *c, lls_complex_workspace *w)
{
if (c->size != w->p)
{
fprintf(stderr, "lls_complex_solve: coefficient vector has wrong size\n");
return GSL_EBADLEN;
}
else
{
int s = 0;
/* solve (AHA + lambda^2 I) c = AHb and estimate condition number */
s = lls_lapack_zposv(lambda, c, w);
/* compute residual || AHA c - AHb || */
gsl_vector_complex_memcpy(w->work_b, w->AHb);
gsl_blas_zhemv(CblasUpper, GSL_COMPLEX_ONE, w->AHA, c, GSL_COMPLEX_NEGONE, w->work_b);
w->residual = gsl_blas_dznrm2(w->work_b);
/* compute chi^2 = b^H b - 2 c^H A^H b + c^H A^H A c */
{
gsl_complex negtwo = gsl_complex_rect(-2.0, 0.0);
gsl_complex val;
/* compute: AHA c - 2 AHb */
gsl_vector_complex_memcpy(w->work_b, w->AHb);
gsl_blas_zhemv(CblasUpper, GSL_COMPLEX_ONE, w->AHA, c, negtwo, w->work_b);
/* compute: c^H ( AHA c - 2 AHb ) */
gsl_blas_zdotc(c, w->work_b, &val);
w->chisq = w->bHb + GSL_REAL(val);
}
/* save coefficient vector for future robust iterations */
gsl_vector_complex_memcpy(w->c, c);
++(w->niter);
return s;
}
} /* lls_complex_solve() */
static VALUE rb_gsl_heapsort_vector_complex2(VALUE obj)
{
gsl_vector_complex *v = NULL, *vnew = NULL;
if (!rb_block_given_p()) rb_raise(rb_eRuntimeError, "Proc is not given");
Data_Get_Struct(obj, gsl_vector_complex, v);
vnew = gsl_vector_complex_alloc(v->size);
gsl_vector_complex_memcpy(vnew, v);
gsl_heapsort(vnew->data, vnew->size, sizeof(gsl_complex), rb_gsl_comparison_complex);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, vnew);
}
static VALUE rb_gsl_fft_complex_radix2_dif_transform(VALUE obj, VALUE val_sign)
{
size_t stride, n;
gsl_complex_packed_array data;
gsl_vector_complex *vin, *vout;
gsl_fft_direction sign;
sign = NUM2INT(val_sign);
get_complex_stride_n(obj, &vin, &data, &stride, &n);
vout = gsl_vector_complex_alloc(n);
gsl_vector_complex_memcpy(vout, vin);
gsl_fft_complex_radix2_dif_transform(vout->data, vout->stride /*1*/, vout->size /*n*/, sign);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, vout);
}
static VALUE rb_fft_complex_radix2(VALUE obj,
int (*trans)(gsl_complex_packed_array,
size_t, size_t), int flag)
{
size_t stride, n;
gsl_complex_packed_array data;
gsl_vector_complex *vin, *vout;
VALUE ary;
ary = get_complex_stride_n(obj, &vin, &data, &stride, &n);
if (flag == RB_GSL_FFT_COPY) {
vout = gsl_vector_complex_alloc(n);
gsl_vector_complex_memcpy(vout, vin);
(*trans)(vout->data, vout->stride /*1*/, vout->size /*n*/);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, vout);
} else { /* in-place */
(*trans)(data, stride, n);
return ary;
}
}
static VALUE rb_gsl_fft_complex_transform(int argc, VALUE *argv, VALUE obj)
{
int flag = 0;
// local variable "status" was defined and set, but never used
//int status;
size_t stride, n;
gsl_vector_complex *vin, *vout;
gsl_fft_direction sign;
gsl_complex_packed_array data;
gsl_fft_complex_wavetable *table = NULL;
gsl_fft_complex_workspace *space = NULL;
CHECK_FIXNUM(argv[argc-1]);
sign = FIX2INT(argv[argc-1]);
flag = gsl_fft_get_argv_complex(argc-1, argv, obj, &vin, &data, &stride, &n, &table, &space);
vout = gsl_vector_complex_alloc(n);
gsl_vector_complex_memcpy(vout, vin);
/*status =*/ gsl_fft_complex_transform(vout->data, stride, n, table, space, sign);
gsl_fft_free(flag, (GSL_FFT_Wavetable *) table, (GSL_FFT_Workspace *) space);
return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, vout);
}
void
test_eigen_herm_results (const gsl_matrix_complex * A,
const gsl_vector * eval,
const gsl_matrix_complex * evec,
size_t count,
const char * desc,
const char * desc2)
{
const size_t N = A->size1;
size_t i, j;
gsl_vector_complex * x = gsl_vector_complex_alloc(N);
gsl_vector_complex * y = gsl_vector_complex_alloc(N);
/* check eigenvalues */
for (i = 0; i < N; i++)
{
double ei = gsl_vector_get (eval, i);
gsl_vector_complex_const_view vi =
gsl_matrix_complex_const_column(evec, i);
gsl_vector_complex_memcpy(x, &vi.vector);
/* compute y = m x (should = lambda v) */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, A, x,
GSL_COMPLEX_ZERO, y);
for (j = 0; j < N; j++)
{
gsl_complex xj = gsl_vector_complex_get (x, j);
gsl_complex yj = gsl_vector_complex_get (y, j);
gsl_test_rel(GSL_REAL(yj), ei * GSL_REAL(xj), 1e8*GSL_DBL_EPSILON,
"%s, eigenvalue(%d,%d), real, %s", desc, i, j, desc2);
gsl_test_rel(GSL_IMAG(yj), ei * GSL_IMAG(xj), 1e8*GSL_DBL_EPSILON,
"%s, eigenvalue(%d,%d), imag, %s", desc, i, j, desc2);
}
}
/* check eigenvectors are orthonormal */
for (i = 0; i < N; i++)
{
gsl_vector_complex_const_view vi = gsl_matrix_complex_const_column(evec, i);
double nrm_v = gsl_blas_dznrm2(&vi.vector);
gsl_test_rel (nrm_v, 1.0, N * GSL_DBL_EPSILON, "%s, normalized(%d), %s",
desc, i, desc2);
}
for (i = 0; i < N; i++)
{
gsl_vector_complex_const_view vi = gsl_matrix_complex_const_column(evec, i);
for (j = i + 1; j < N; j++)
{
gsl_vector_complex_const_view vj
= gsl_matrix_complex_const_column(evec, j);
gsl_complex vivj;
gsl_blas_zdotc (&vi.vector, &vj.vector, &vivj);
gsl_test_abs (gsl_complex_abs(vivj), 0.0, 10.0 * N * GSL_DBL_EPSILON,
"%s, orthogonal(%d,%d), %s", desc, i, j, desc2);
}
}
gsl_vector_complex_free(x);
gsl_vector_complex_free(y);
} /* test_eigen_herm_results() */
/** Assign */
vector<complex>& vector<complex>::operator=(const vector<complex>& v)
{
gsl_vector_complex_memcpy(_vector, v.as_gsl_type_ptr());
return *this;
}
int
lls_complex_fold(const gsl_matrix_complex *A, const gsl_vector_complex *b,
lls_complex_workspace *w)
{
const size_t n = A->size1;
if (A->size2 != w->p)
{
fprintf(stderr, "lls_complex_fold: A has wrong size2\n");
return GSL_EBADLEN;
}
else if (n != b->size)
{
fprintf(stderr, "lls_complex_fold: b has wrong size\n");
return GSL_EBADLEN;
}
else
{
int s = 0;
double bnorm;
#if 0
size_t i;
gsl_vector_view wv = gsl_vector_subvector(w->w_robust, 0, n);
if (w->niter > 0)
{
gsl_vector_complex_view rc = gsl_vector_complex_subvector(w->r_complex, 0, n);
gsl_vector_view rv = gsl_vector_subvector(w->r, 0, n);
/* calculate residuals with previously computed coefficients: r = b - A c */
gsl_vector_complex_memcpy(&rc.vector, b);
gsl_blas_zgemv(CblasNoTrans, GSL_COMPLEX_NEGONE, A, w->c, GSL_COMPLEX_ONE, &rc.vector);
/* compute Re(r) */
for (i = 0; i < n; ++i)
{
gsl_complex ri = gsl_vector_complex_get(&rc.vector, i);
gsl_vector_set(&rv.vector, i, GSL_REAL(ri));
}
/* calculate weights with robust weighting function */
gsl_multifit_robust_weights(&rv.vector, &wv.vector, w->robust_workspace_p);
}
else
gsl_vector_set_all(&wv.vector, 1.0);
/* compute final weights as product of input and robust weights */
gsl_vector_mul(wts, &wv.vector);
#endif
/* AHA += A^H A, using only the upper half of the matrix */
s = gsl_blas_zherk(CblasUpper, CblasConjTrans, 1.0, A, 1.0, w->AHA);
if (s)
return s;
/* AHb += A^H b */
s = gsl_blas_zgemv(CblasConjTrans, GSL_COMPLEX_ONE, A, b, GSL_COMPLEX_ONE, w->AHb);
if (s)
return s;
/* bHb += b^H b */
bnorm = gsl_blas_dznrm2(b);
w->bHb += bnorm * bnorm;
fprintf(stderr, "norm(AHb) = %.12e, bHb = %.12e\n",
gsl_blas_dznrm2(w->AHb), w->bHb);
if (!gsl_finite(w->bHb))
{
fprintf(stderr, "bHb is NAN\n");
exit(1);
}
return s;
}
} /* lls_complex_fold() */
vector<complex>::vector(const gsl_vector_complex& v)
{
_vector = gsl_vector_complex_alloc(v.size);
gsl_vector_complex_memcpy(_vector, &v);
}
vector<complex>::vector(const gsl_vector_complex* v)
{
_vector = gsl_vector_complex_alloc(v->size);
gsl_vector_complex_memcpy(_vector, v);
}
int
lls_complex_lcurve(gsl_vector *reg_param, gsl_vector *rho, gsl_vector *eta,
lls_complex_workspace *w)
{
const size_t N = rho->size; /* number of points on L-curve */
if (N != reg_param->size)
{
GSL_ERROR("size of reg_param and rho do not match", GSL_EBADLEN);
}
else if (N != eta->size)
{
GSL_ERROR("size of eta and rho do not match", GSL_EBADLEN);
}
else
{
int s;
const gsl_complex negtwo = gsl_complex_rect(-2.0, 0.0);
/* smallest regularization parameter */
const double smin_ratio = 16.0 * GSL_DBL_EPSILON;
double s1, sp, ratio, tmp;
size_t i;
/* compute eigenvalues of A^H A */
gsl_matrix_complex_transpose_memcpy(w->work_A, w->AHA);
s = gsl_eigen_herm(w->work_A, w->eval, w->eigen_p);
if (s)
return s;
/* find largest and smallest eigenvalues */
gsl_vector_minmax(w->eval, &sp, &s1);
/* singular values are square roots of eigenvalues */
s1 = sqrt(s1);
if (sp > GSL_DBL_EPSILON)
sp = sqrt(fabs(sp));
tmp = GSL_MAX(sp, s1*smin_ratio);
gsl_vector_set(reg_param, N - 1, tmp);
/* ratio so that reg_param(1) = s(1) */
ratio = pow(s1 / tmp, 1.0 / (N - 1.0));
/* calculate the regularization parameters */
for (i = N - 1; i > 0 && i--; )
{
double rp1 = gsl_vector_get(reg_param, i + 1);
gsl_vector_set(reg_param, i, ratio * rp1);
}
for (i = 0; i < N; ++i)
{
double r2;
double lambda = gsl_vector_get(reg_param, i);
gsl_complex val;
lls_complex_solve(lambda, w->c, w);
/* store ||c|| */
gsl_vector_set(eta, i, gsl_blas_dznrm2(w->c));
/* compute: A^H A c - 2 A^H b */
gsl_vector_complex_memcpy(w->work_b, w->AHb);
gsl_blas_zhemv(CblasUpper, GSL_COMPLEX_ONE, w->AHA, w->c, negtwo, w->work_b);
/* compute: c^T A^T A c - 2 c^T A^T b */
gsl_blas_zdotc(w->c, w->work_b, &val);
r2 = GSL_REAL(val) + w->bHb;
gsl_vector_set(rho, i, sqrt(r2));
}
return GSL_SUCCESS;
}
} /* lls_complex_lcurve() */
/** Copy constructor */
vector<complex>::vector(const vector<complex>& v)
{
_vector = gsl_vector_complex_alloc(v.size());
gsl_vector_complex_memcpy(_vector, v.as_gsl_type_ptr());
}
/// Copy constructor.
/// @param v :: The other vector
ComplexVector::ComplexVector(const ComplexVector &v) {
m_vector = gsl_vector_complex_alloc(v.size());
gsl_vector_complex_memcpy(m_vector, v.gsl());
}
/// Copy from a gsl vector
/// @param v :: A vector to copy from.
ComplexVector::ComplexVector(const gsl_vector_complex *v) {
m_vector = gsl_vector_complex_alloc(v->size);
gsl_vector_complex_memcpy(m_vector, v);
}
/** ----------------------------------------------------------------------------
* Sort eigenvectors
*/
int
gsl_ext_eigen_sort(gsl_matrix_complex *evec, gsl_vector_complex *eval, int sort_order)
{
gsl_complex z;
gsl_matrix_complex *evec_copy;
gsl_vector_complex *eval_copy;
int *idx_map, i, j, idx_temp;
double p1, p2;
if ((evec->size1 != evec->size2) || (evec->size1 != eval->size))
{
return -1;
}
evec_copy = gsl_matrix_complex_alloc(evec->size1, evec->size2);
eval_copy = gsl_vector_complex_alloc(eval->size);
idx_map = (int *)malloc(sizeof(int) * eval->size);
gsl_matrix_complex_memcpy(evec_copy, evec);
gsl_vector_complex_memcpy(eval_copy, eval);
// calculate new eigenvalue order
for (i = 0; i < eval->size; i++)
{
idx_map[i] = i;
}
for (i = 0; i < eval->size - 1; i++)
{
for (j = i+1; j < eval->size; j++)
{
idx_temp = -1;
if (sort_order == GSL_EXT_EIGEN_SORT_ABS)
{
p1 = gsl_complex_abs(gsl_vector_complex_get(eval, idx_map[i]));
p2 = gsl_complex_abs(gsl_vector_complex_get(eval, idx_map[j]));
if (p1 > p2)
{
idx_temp = idx_map[i];
}
}
if (sort_order == GSL_EXT_EIGEN_SORT_PHASE)
{
p1 = gsl_complex_arg(gsl_vector_complex_get(eval, idx_map[i]));
p2 = gsl_complex_arg(gsl_vector_complex_get(eval, idx_map[j]));
if (p1 > M_PI) p1 -= 2*M_PI;
if (p1 <= -M_PI) p1 += 2*M_PI;
if (p2 > M_PI) p2 -= 2*M_PI;
if (p2 <= -M_PI) p2 += 2*M_PI;
//if (((p2 < p1) && (p1 - p2 < M_PI)) || )
if (p2 < p1)
{
idx_temp = idx_map[i];
}
}
if (idx_temp != -1)
{
// swap
//idx_temp = idx_map[i];
idx_map[i] = idx_map[j];
idx_map[j] = idx_temp;
}
}
}
// reshuffle the eigenvectors and eigenvalues
for (i = 0; i < eval->size; i++)
{
for (j = 0; j < eval->size; j++)
{
z = gsl_matrix_complex_get(evec_copy, idx_map[i], j);
gsl_matrix_complex_set(evec, i, j, z);
//z = gsl_matrix_complex_get(evec_copy, i, idx_map[j]);
//gsl_matrix_complex_set(evec, i, j, z);
}
z = gsl_vector_complex_get(eval_copy, idx_map[i]);
gsl_vector_complex_set(eval, i, z);
}
gsl_matrix_complex_free(evec_copy);
gsl_vector_complex_free(eval_copy);
free(idx_map);
return 0;
}
void
test_eigen_nonsymm_results (const gsl_matrix * m,
const gsl_vector_complex * eval,
const gsl_matrix_complex * evec,
size_t count,
const char * desc,
const char * desc2)
{
size_t i,j;
size_t N = m->size1;
gsl_vector_complex * x = gsl_vector_complex_alloc(N);
gsl_vector_complex * y = gsl_vector_complex_alloc(N);
gsl_matrix_complex * A = gsl_matrix_complex_alloc(N, N);
/* we need a complex matrix for the blas routines, so copy m into A */
for (i = 0; i < N; ++i)
{
for (j = 0; j < N; ++j)
{
gsl_complex z;
GSL_SET_COMPLEX(&z, gsl_matrix_get(m, i, j), 0.0);
gsl_matrix_complex_set(A, i, j, z);
}
}
for (i = 0; i < N; i++)
{
gsl_complex ei = gsl_vector_complex_get (eval, i);
gsl_vector_complex_const_view vi = gsl_matrix_complex_const_column(evec, i);
double norm = gsl_blas_dznrm2(&vi.vector);
/* check that eigenvector is normalized */
gsl_test_rel(norm, 1.0, N * GSL_DBL_EPSILON,
"nonsymm(N=%u,cnt=%u), %s, normalized(%d), %s", N, count, desc, i, desc2);
gsl_vector_complex_memcpy(x, &vi.vector);
/* compute y = m x (should = lambda v) */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, A, x,
GSL_COMPLEX_ZERO, y);
/* compute x = lambda v */
gsl_blas_zscal(ei, x);
/* now test if y = x */
for (j = 0; j < N; j++)
{
gsl_complex xj = gsl_vector_complex_get (x, j);
gsl_complex yj = gsl_vector_complex_get (y, j);
/* use abs here in case the values are close to 0 */
gsl_test_abs(GSL_REAL(yj), GSL_REAL(xj), 1e8*GSL_DBL_EPSILON,
"nonsymm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), real, %s", N, count, desc, i, j, desc2);
gsl_test_abs(GSL_IMAG(yj), GSL_IMAG(xj), 1e8*GSL_DBL_EPSILON,
"nonsymm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), imag, %s", N, count, desc, i, j, desc2);
}
}
gsl_matrix_complex_free(A);
gsl_vector_complex_free(x);
gsl_vector_complex_free(y);
}
/// Copy assignment operator
/// @param v :: The other vector
ComplexVector &ComplexVector::operator=(const ComplexVector &v) {
gsl_vector_complex_free(m_vector);
m_vector = gsl_vector_complex_alloc(v.size());
gsl_vector_complex_memcpy(m_vector, v.gsl());
return *this;
}