void
test_eigen_genherm_results (const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
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 A v = lambda B v */
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);
double norm = gsl_blas_dznrm2(&vi.vector);
/* check that eigenvector is normalized */
gsl_test_rel(norm, 1.0, N * GSL_DBL_EPSILON,
"genherm(N=%u,cnt=%u), %s, normalized(%d), %s", N, count,
desc, i, desc2);
/* compute y = A z */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, A, &vi.vector, GSL_COMPLEX_ZERO, y);
/* compute x = B z */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, B, &vi.vector, GSL_COMPLEX_ZERO, x);
/* compute x = lambda B z */
gsl_blas_zdscal(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);
gsl_test_rel(GSL_REAL(yj), GSL_REAL(xj), 1e9 * GSL_DBL_EPSILON,
"genherm(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), 1e9 * GSL_DBL_EPSILON,
"genherm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), imag, %s", N, count, desc, i, j, desc2);
}
}
gsl_vector_complex_free(x);
gsl_vector_complex_free(y);
}
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);
}
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() */
void
test_eigen_gen_results (const gsl_matrix * A, const gsl_matrix * B,
const gsl_vector_complex * alpha,
const gsl_vector * beta,
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_matrix_complex *ma, *mb;
gsl_vector_complex *x, *y;
gsl_complex z_one, z_zero;
ma = gsl_matrix_complex_alloc(N, N);
mb = gsl_matrix_complex_alloc(N, N);
y = gsl_vector_complex_alloc(N);
x = gsl_vector_complex_alloc(N);
/* ma <- A, mb <- B */
for (i = 0; i < N; ++i)
{
for (j = 0; j < N; ++j)
{
gsl_complex z;
GSL_SET_COMPLEX(&z, gsl_matrix_get(A, i, j), 0.0);
gsl_matrix_complex_set(ma, i, j, z);
GSL_SET_COMPLEX(&z, gsl_matrix_get(B, i, j), 0.0);
gsl_matrix_complex_set(mb, i, j, z);
}
}
GSL_SET_COMPLEX(&z_one, 1.0, 0.0);
GSL_SET_COMPLEX(&z_zero, 0.0, 0.0);
/* check eigenvalues */
for (i = 0; i < N; ++i)
{
gsl_vector_complex_const_view vi =
gsl_matrix_complex_const_column(evec, i);
gsl_complex ai = gsl_vector_complex_get(alpha, i);
double bi = gsl_vector_get(beta, i);
/* compute x = alpha * B * v */
gsl_blas_zgemv(CblasNoTrans, z_one, mb, &vi.vector, z_zero, x);
gsl_blas_zscal(ai, x);
/* compute y = beta * A v */
gsl_blas_zgemv(CblasNoTrans, z_one, ma, &vi.vector, z_zero, y);
gsl_blas_zdscal(bi, y);
/* 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);
gsl_test_abs(GSL_REAL(yj), GSL_REAL(xj), 1e8*GSL_DBL_EPSILON,
"gen(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,
"gen(N=%u,cnt=%u), %s, eigenvalue(%d,%d), real, %s",
N, count, desc, i, j, desc2);
}
}
gsl_matrix_complex_free(ma);
gsl_matrix_complex_free(mb);
gsl_vector_complex_free(y);
gsl_vector_complex_free(x);
} /* test_eigen_gen_results() */
void MAIAllocator::Run() {
// fetch channel matrix
gsl_matrix_complex hmm = min1.GetDataObj();
// hmm : channel coeffs matrix h(n) (M**2xN)
// ij
// ch matrix structure
//
// +- -+
// | h(0) . . . . h(n) | |
// | 11 11 | |
// | | | Rx1
// | h(0) . . . . h(n) | |
// | 12 12 | |
// | |
// | h(0) . . . . h(n) | |
// | 21 21 | |
// | | | Rx2
// | h(0) . . . . h(n) | |
// | 22 22 | |
// +- -+
//
// where h(n) represents the channel impulse response
// ij
//
// at time n, from tx_i to rx_j
// the matrix has MxM rows and N comumns.
// The (i,j) channel is locater at row i*M+j
// with i,j in the range [0,M-1] and rows counting from 0
//
//
// fetch error report
// e(u) = errors for user u in the last ERROR_REPORT_INTERVAL (ERI) frames
gsl_vector_uint temperr = vin2.GetDataObj();
// update error reports at receiver rx_m every ERI
if (ericount % ERROR_REPORT_INTERVAL == 0) { // once every ERU
if (temperr.size == M()) {
gsl_vector_uint_memcpy(errs,&temperr);
}
ericount = 0;
}
//
// every DECISION_INTERVAL frames we updates the CSI knowledge
//
if (framecount % DECISION_INTERVAL == 0) {
for (int u=0;u<M();u++) { // user loop
// extract time domain response from hmm corresponding to txn-->rxn channel
gsl_vector_complex_const_view hii = gsl_matrix_complex_const_row(&hmm,u*M()+u);
// copy the N-sized vector hii into u-th column of huu
gsl_matrix_complex_set_col(huu,u,&hii.vector);
} // user loop
//cout << "maiallocator:453 - CSI update received" << endl;
// huu matrix structure
//
// +- -+
// | h(0) . . . . h(n) |
// | 11 uu |
// | |
// | h(n) . . . . h(n) |
// | 11 uu |
// +- -+
//
// where h(n) represents the channel impulse response
// ii
//
// at time n, from tx_u to rx_u
// the matrix has N rows and M columns.
//
// ATTENTION! user_0 channel response is the first column
//
// Hmat(NxM) = Fourier( huu(NxM) )
//
gsl_blas_zgemm(CblasNoTrans,
CblasNoTrans,
gsl_complex_rect(1,0),
transform_mat,
huu,
gsl_complex_rect(0,0),
Hmat);
#ifdef SHOW_MATRIX
cout << "Hmat(freq,user) (frame:" << framecount << ") = " << endl;
gsl_matrix_complex_show(Hmat);
#endif
//
// ***********************************************************
// CARRIER ALLOCATION STRATEGIES
// ***********************************************************
//
switch (Mode()) {
case 0: // FIXED_ALLOCATION
break;
case 1: // GIVE_BEST_CARR
//
// SORT CARRIERS OF EACH USERS
//
// uses Hmat: the frequency responses of channel tx_n --> rx_n
//
// starting from user u ...
// find the best (in u ranking) unused carrier and assign it to u
// next user until no more available carriers
for(int u=0; u<M(); u++) { // cycle through users
gsl_vector_complex_const_view huser
= gsl_matrix_complex_const_column(Hmat,u);
gsl_vector_uint_view sortindu = gsl_matrix_uint_column(Hperm,u);
for (int j=0; j<N(); j++) {
double currpower
= gsl_complex_abs2(gsl_vector_complex_get(&huser.vector,j));
gsl_vector_set(huserabs,j,currpower);
}
// sort over c using abs(h(u,c))
gsl_sort_vector_index(p,huserabs);
for (int j=0; j<N(); j++) {
uint currindex = p->data[j];
gsl_vector_uint_set(&sortindu.vector,j,currindex);
}
}
//
// FIND INITIAL USER RANDOMLY
//
curruser = gsl_rng_uniform_int(ran,M());
//
// ASSIGN FREQUENCIES
//
gsl_vector_uint_set_all(nextcarr,0);
gsl_vector_uint_set_all(usedcarr,0);
for (int j=0; j<J(); j++) {
for (int uu=0; uu<M(); uu++) {
int u = (uu+curruser) % M();
int isassigned = 0;
while (! isassigned) {
int tag = gsl_vector_uint_get(nextcarr,u);
gsl_vector_uint_set(nextcarr,u,++tag);
int carrier = gsl_matrix_uint_get(Hperm,N()-tag,u);
if (! gsl_vector_uint_get(usedcarr,carrier)) {
isassigned = 1;
gsl_vector_uint_set(usedcarr,carrier,isassigned);
gsl_matrix_uint_set(signature_frequencies,u,j,carrier);
} else if (tag==N()) {
cerr << "Block: " << BlockName << " allocation problem." << endl;
exit(1);
}
}
}
}
//
// show channels and permutations
//
// gsl_matrix_complex_show(Hmat);
//gsl_matrix_uint_show(Hperm);
//gsl_matrix_uint_show(signature_frequencies);
break;
case 2: // SWAP_BAD_GOOD
//
// SWAP_BAD_GOOD
//
// sort carriers for each user
// choose randomly a starting user u
// for each user starting with u
// swap worst carrier used by u with best carrier if used by others
// sort carriers
for(int u=0; u<M(); u++) {
gsl_vector_complex_const_view huser
= gsl_matrix_complex_const_column(Hmat,u);
gsl_vector_uint_view sortindu = gsl_matrix_uint_column(Hperm,u);
gsl_vector_view huserabs = gsl_matrix_column(habs,u);
for (int j=0; j<N(); j++) {
double currpower
= gsl_complex_abs2(gsl_vector_complex_get(&huser.vector,j));
gsl_vector_set(&huserabs.vector,j,currpower);
}
//
// sort channels for user <u>
//
gsl_sort_vector_index(p,&huserabs.vector);
for (int j=0; j<N(); j++) {
uint currindex = p->data[j];
gsl_vector_uint_set(&sortindu.vector,j,currindex);
}
}
//
// Hperm(N,USERS) contains sorted channels index for each users
// habs(N,USERS) contains channel energy per each user
//
//
// FIND INITIAL USER RANDOMLY for fairness
//
curruser = gsl_rng_uniform_int(ran,M());
//
// ASSIGN FREQUENCIES
//
//
// for each user ...
//
for (int uu=0; uu<M(); uu++) {
int u = (uu+curruser) % M();
//
// worst allocated channel for user u
//
double worstvalue=GSL_POSINF;
unsigned int worstjindex;
for (int j=0; j<J(); j++) {
unsigned int chind = gsl_matrix_uint_get(signature_frequencies,u,j);
double currh = gsl_matrix_get(habs,chind,u);
if (currh < worstvalue) {
worstvalue = currh;
worstjindex = j;
}
}
//
// find best channel allocated by other users
//
//
double bestvalue=0;
unsigned int bestuser, bestjindex;
for (int uuu=0; uuu<M()-1; uuu++) {
unsigned int otheru = (uuu+u) % M();
for (int j=0; j<J(); j++) {
unsigned int chind
= gsl_matrix_uint_get(signature_frequencies,otheru,j);
double currh = gsl_matrix_get(habs,chind,otheru);
if (currh > bestvalue) {
bestvalue = currh;
bestjindex = j;
bestuser = otheru;
}
}
}
//
// finally the swap !
//
unsigned int chind
= gsl_matrix_uint_get(signature_frequencies,u,worstjindex);
gsl_matrix_uint_set(signature_frequencies,u,worstjindex,
gsl_matrix_uint_get(signature_frequencies,
bestuser,bestjindex));
gsl_matrix_uint_set(signature_frequencies,bestuser,bestjindex,chind);
// cout << "\n\nProcessing user " << u << endl
// << "\tSwapped " << u << "." << worstjindex
// << " <-> " << bestuser << "." << bestjindex << endl;
}
break;
case 3: // BEST_OVERLAP
//
// SORT CARRIERS OF EACH USERS
//
gsl_matrix_uint_memcpy(signature_frequencies,
signature_frequencies_init);
for(int u=0; u<M(); u++) {
gsl_vector_complex_const_view huser
= gsl_matrix_complex_const_column(Hmat,u);
gsl_vector_uint_view sortindu = gsl_matrix_uint_column(Hperm,u);
for (int j=0; j<N(); j++) {
double currpower = gsl_complex_abs2(gsl_vector_complex_get(&huser.vector,
j));
gsl_vector_set(huserabs,j,currpower);
}
gsl_sort_vector_index(p,huserabs);
for (int j=0; j<N(); j++) {
uint currindex = p->data[j];
gsl_vector_uint_set(&sortindu.vector,j,currindex);
}
}
//
// each user take his best carriers allowing carrier overlap
//
for (int u=0; u<M(); u++) {
for (int j=0; j<J(); j++) {
int carrier = gsl_matrix_uint_get(Hperm,N()-j-1,u);
gsl_matrix_uint_set(signature_frequencies,u,j,carrier);
}
}
//
// show channels and permutations
//
//gsl_matrix_complex_show(Hmat);
//gsl_matrix_uint_show(Hperm);
//gsl_matrix_uint_show(signature_frequencies);
break;
case 4: // SOAR_AI
//
// SOAR
//
// agent crai5
// bases the decisions on the frequency response tx_m --> rx_m in Hmat(N,M)
// for each user it proposes a swap between carriers if the instantaneous impulse channel response
// is better
//
// agent crai6
// for each user it proposes a swap of allocated carriers with one other users
// error report is the metric for correct decisions (RL)
#ifdef PAUSED
// keypress
cout << "pause maillocator: before decision loop ... (press ENTER key)" << endl;
cin.ignore();
#endif
// Every DECISION_INTERVAL we increase the input-time and allow decisions
if (framecount % DECISION_INTERVAL == 0) {
pAgent->Update(inputTime,++input_time);
pAgent->Commit();
}
// run agent till output
noDecisions = 0;
numberCommands=0;
while (! (noDecisions) ) { // main decisional loop
//
// INPUT LINK Update
//
UpdateInputLink();
//pAgent->RunSelf(1);
pAgent->RunSelfTilOutput();
numberCommands = pAgent->GetNumberCommands() ;
#ifdef PAUSED
// keypress
cout << "pause maillocator: after RunSelfTilOutput() ... (press ENTER key)" << endl;
cin.ignore();
#endif
// loop through received commands
for (int cmd = 0 ; cmd < numberCommands ; cmd++) {
Identifier* pCommand = pAgent->GetCommand(cmd) ;
string name = pCommand->GetCommandName() ;
if (name == "assign-free") {
std::string sUid = pCommand->GetParameterValue("uid");
std::string sDeassign = pCommand->GetParameterValue("deassign");
std::string sAssign = pCommand->GetParameterValue("assign");
#ifdef SHOW_SOAR
cout << "assign-free command received [ u:"
<< sUid << " , -"
<< sDeassign << " , +"
<< sAssign << " ]"
<< endl;
#endif
AssignFree(sUid,sDeassign,sAssign);
pCommand->AddStatusComplete();
} else if (name == "swap-carriers") {
std::string sU1 = pCommand->GetParameterValue("u1");
std::string sC1 = pCommand->GetParameterValue("c1");
std::string sU2 = pCommand->GetParameterValue("u2");
std::string sC2 = pCommand->GetParameterValue("c2");
#ifdef SHOW_SOAR
cout << "swap-carriers command received [ u1:"
<< sU1 << " , c1:"
<< sC1 << " , u2:"
<< sU2 << " , c2:"
<< sC2 << " ]" << endl;
#endif
SwapCarriers(sU1,sC1,sU2,sC2);
pCommand->AddStatusComplete();
} else if (name == "increase-power") {
std::string sUid = pCommand->GetParameterValue("uid");
std::string sCid = pCommand->GetParameterValue("cid");
#ifdef SHOW_SOAR
cout << "increase-power command received [ u:"
<< sUid << " , c:"
<< sCid << " ]" << endl;
#endif
IncreasePower(sUid,sCid);
pCommand->AddStatusComplete();
break;
} else if (name == "no-choices") {
#ifdef SHOW_SOAR
cout << "no-choices command received" << endl;
#endif
noDecisions = 1;
pCommand->AddStatusComplete();
break;
} else {
#ifdef SHOW_SOAR
cout << "ignoring unknown output command from SOAR" << endl;
#endif
break;
}
// cout << "framecount = " << framecount << endl;
} // end command loop
} // while (! (noDecisions) )
break;
} // switch (Mode())
} // if DECISION_INTERVAL % 0
//
// every 10s dump frame count
//
time(&nowtime);
if (difftime(nowtime,reporttime) > TIMEDELTA) {
reporttime = nowtime;
cout << "frame:" << framecount << "\r";
cout.flush();
}
//////// production of data
framecount++;
ericount++;
mout1.DeliverDataObj( *signature_frequencies );
mout2.DeliverDataObj( *signature_powers );
#ifdef SHOW_MATRIX
cout << "signature frequencies (frame:" << framecount-1 << ") = " << endl;
gsl_matrix_uint_show(signature_frequencies);
#endif
}
int
gsl_linalg_hermtd_unpack (const gsl_matrix_complex * A,
const gsl_vector_complex * tau,
gsl_matrix_complex * U,
gsl_vector * diag,
gsl_vector * sdiag)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix A must be sqaure", GSL_ENOTSQR);
}
else if (tau->size + 1 != A->size1)
{
GSL_ERROR ("size of tau must be (matrix size - 1)", GSL_EBADLEN);
}
else if (U->size1 != A->size1 || U->size2 != A->size1)
{
GSL_ERROR ("size of U must match size of A", GSL_EBADLEN);
}
else if (diag->size != A->size1)
{
GSL_ERROR ("size of diagonal must match size of A", GSL_EBADLEN);
}
else if (sdiag->size + 1 != A->size1)
{
GSL_ERROR ("size of subdiagonal must be (matrix size - 1)", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
size_t i;
/* Initialize U to the identity */
gsl_matrix_complex_set_identity (U);
for (i = N - 1; i-- > 0;)
{
gsl_complex ti = gsl_vector_complex_get (tau, i);
gsl_vector_complex_const_view c = gsl_matrix_complex_const_column (A, i);
gsl_vector_complex_const_view h =
gsl_vector_complex_const_subvector (&c.vector, i + 1, N - (i+1));
gsl_matrix_complex_view m =
gsl_matrix_complex_submatrix (U, i + 1, i + 1, N-(i+1), N-(i+1));
gsl_linalg_complex_householder_hm (ti, &h.vector, &m.matrix);
}
/* Copy diagonal into diag */
for (i = 0; i < N; i++)
{
gsl_complex Aii = gsl_matrix_complex_get (A, i, i);
gsl_vector_set (diag, i, GSL_REAL(Aii));
}
/* Copy subdiagonal into sdiag */
for (i = 0; i < N - 1; i++)
{
gsl_complex Aji = gsl_matrix_complex_get (A, i+1, i);
gsl_vector_set (sdiag, i, GSL_REAL(Aji));
}
return GSL_SUCCESS;
}
}
