/**
Purpose
-------
SLAEX3 finds the roots of the secular equation, as defined by the
values in D, W, and RHO, between 1 and K. It makes the
appropriate calls to SLAED4 and then updates the eigenvectors by
multiplying the matrix of eigenvectors of the pair of eigensystems
being combined by the matrix of eigenvectors of the K-by-K system
which is solved here.
It is used in the last step when only a part of the eigenvectors
is required.
It compute only the required part of the eigenvectors and the rest
is not used.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
k INTEGER
The number of terms in the rational function to be solved by
SLAED4. K >= 0.
@param[in]
n INTEGER
The number of rows and columns in the Q matrix.
N >= K (deflation may result in N > K).
@param[in]
n1 INTEGER
The location of the last eigenvalue in the leading submatrix.
min(1,N) <= N1 <= N/2.
@param[out]
d REAL array, dimension (N)
D(I) contains the updated eigenvalues for
1 <= I <= K.
@param[out]
Q REAL array, dimension (LDQ,N)
Initially the first K columns are used as workspace.
On output the columns ??? to ??? contain
the updated eigenvectors.
@param[in]
ldq INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
@param[in]
rho REAL
The value of the parameter in the rank one update equation.
RHO >= 0 required.
@param[in,out]
dlamda REAL array, dimension (K)
The first K elements of this array contain the old roots
of the deflated updating problem. These are the poles
of the secular equation. May be changed on output by
having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
Cray-2, or Cray C-90, as described above.
@param[in]
Q2 REAL array, dimension (LDQ2, N)
The first K columns of this matrix contain the non-deflated
eigenvectors for the split problem.
TODO what is LDQ2?
@param[in]
indx INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated
Q matrix into three groups (see SLAED2).
The rows of the eigenvectors found by SLAED4 must be likewise
permuted before the matrix multiply can take place.
@param[in]
ctot INTEGER array, dimension (4)
A count of the total number of the various types of columns
in Q, as described in INDX. The fourth column type is any
column which has been deflated.
@param[in,out]
w REAL array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector. Destroyed on
output.
@param
s (workspace) REAL array, dimension (N1 + 1)*K
Will contain the eigenvectors of the repaired matrix which
will be multiplied by the previously accumulated eigenvectors
to update the system.
@param[out]
indxq INTEGER array, dimension (N)
On exit, the permutation which will reintegrate the
subproblems back into sorted order,
i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
@param
dwork (workspace) REAL array, dimension (3*N*N/2+3*N)
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
TODO verify range, vl, vu, il, iu -- copied from slaex1.
@param[in]
vl REAL
@param[in]
vu REAL
if RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
if RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
info INTEGER
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = 1, an eigenvalue did not converge
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
@ingroup magma_ssyev_aux
********************************************************************/
extern "C" magma_int_t
magma_slaex3(magma_int_t k, magma_int_t n, magma_int_t n1, float* d,
float* Q, magma_int_t ldq, float rho,
float* dlamda, float* Q2, magma_int_t* indx,
magma_int_t* ctot, float* w, float* s, magma_int_t* indxq,
float* dwork,
magma_range_t range, float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t* info )
{
#define Q(i_,j_) (Q + (i_) + (j_)*ldq)
float d_one = 1.;
float d_zero = 0.;
magma_int_t ione = 1;
magma_int_t ineg_one = -1;
magma_int_t iil, iiu, rk;
float* dq2= dwork;
float* ds = dq2 + n*(n/2+1);
float* dq = ds + n*(n/2+1);
magma_int_t lddq = n/2 + 1;
magma_int_t i, iq2, j, n12, n2, n23, tmp, lq2;
float temp;
magma_int_t alleig, valeig, indeig;
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
*info = 0;
if (k < 0)
*info=-1;
else if (n < k)
*info=-2;
else if (ldq < max(1,n))
*info=-6;
else if (! (alleig || valeig || indeig))
*info = -15;
else {
if (valeig) {
if (n > 0 && vu <= vl)
*info = -17;
}
else if (indeig) {
if (il < 1 || il > max(1,n))
*info = -18;
else if (iu < min(n,il) || iu > n)
*info = -19;
}
}
if (*info != 0) {
magma_xerbla(__func__, -(*info));
return *info;
}
// Quick return if possible
if (k == 0)
return *info;
/*
Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
be computed with high relative accuracy (barring over/underflow).
This is a problem on machines without a guard digit in
add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
which on any of these machines zeros out the bottommost
bit of DLAMDA(I) if it is 1; this makes the subsequent
subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
occurs. On binary machines with a guard digit (almost all
machines) it does not change DLAMDA(I) at all. On hexadecimal
and decimal machines with a guard digit, it slightly
changes the bottommost bits of DLAMDA(I). It does not account
for hexadecimal or decimal machines without guard digits
(we know of none). We use a subroutine call to compute
2*DLAMBDA(I) to prevent optimizing compilers from eliminating
this code.*/
n2 = n - n1;
n12 = ctot[0] + ctot[1];
n23 = ctot[1] + ctot[2];
iq2 = n1 * n12;
lq2 = iq2 + n2 * n23;
magma_ssetvector_async( lq2, Q2, 1, dq2, 1, NULL );
#ifdef _OPENMP
/////////////////////////////////////////////////////////////////////////////////
//openmp implementation
/////////////////////////////////////////////////////////////////////////////////
magma_timer_t time=0;
timer_start( time );
#pragma omp parallel private(i, j, tmp, temp)
{
magma_int_t id = omp_get_thread_num();
magma_int_t tot = omp_get_num_threads();
magma_int_t ib = ( id * k) / tot; //start index of local loop
magma_int_t ie = ((id+1) * k) / tot; //end index of local loop
magma_int_t ik = ie - ib; //number of local indices
for (i = ib; i < ie; ++i)
dlamda[i]=lapackf77_slamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for (j = ib; j < ie; ++j) {
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_slaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if (iinfo != 0) {
#pragma omp critical (info)
*info=iinfo;
break;
}
}
#pragma omp barrier
if (*info == 0) {
#pragma omp single
{
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_slamrg( &k, &nk, d, &ione, &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_svrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_sirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
}
if (k == 2) {
#pragma omp single
{
for (j = 0; j < k; ++j) {
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
}
else if (k != 1) {
// Compute updated W.
blasf77_scopy( &ik, &w[ib], &ione, &s[ib], &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_scopy( &ik, Q(ib,ib), &tmp, &w[ib], &ione);
for (j = 0; j < k; ++j) {
magma_int_t i_tmp = min(j, ie);
for (i = ib; i < i_tmp; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
i_tmp = max(j+1, ib);
for (i = i_tmp; i < ie; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for (i = ib; i < ie; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
#pragma omp barrier
//reduce the number of used threads to have enough S workspace
tot = min(n1, omp_get_num_threads());
if (id < tot) {
ib = ( id * rk) / tot + iil - 1;
ie = ((id+1) * rk) / tot + iil - 1;
ik = ie - ib;
}
else {
ib = -1;
ie = -1;
ik = -1;
}
// Compute eigenvectors of the modified rank-1 modification.
for (j = ib; j < ie; ++j) {
for (i = 0; i < k; ++i)
s[id*k + i] = w[i] / *Q(i,j);
temp = magma_cblas_snrm2( k, s+id*k, 1 );
for (i = 0; i < k; ++i) {
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[id*k + iii] / temp;
}
}
}
}
}
if (*info != 0)
return *info;
timer_stop( time );
timer_printf( "eigenvalues/vector D+zzT = %6.2f\n", time );
#else
/////////////////////////////////////////////////////////////////////////////////
// Non openmp implementation
/////////////////////////////////////////////////////////////////////////////////
magma_timer_t time=0;
timer_start( time );
for (i = 0; i < k; ++i)
dlamda[i]=lapackf77_slamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for (j = 0; j < k; ++j) {
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_slaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if (iinfo != 0)
*info=iinfo;
}
if (*info != 0)
return *info;
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_slamrg( &k, &nk, d, &ione, &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_svrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_sirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
if (k == 2) {
for (j = 0; j < k; ++j) {
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
else if (k != 1) {
// Compute updated W.
blasf77_scopy( &k, w, &ione, s, &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_scopy( &k, Q, &tmp, w, &ione);
for (j = 0; j < k; ++j) {
for (i = 0; i < j; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
for (i = j+1; i < k; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for (i = 0; i < k; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
// Compute eigenvectors of the modified rank-1 modification.
for (j = iil-1; j < iiu; ++j) {
for (i = 0; i < k; ++i)
s[i] = w[i] / *Q(i,j);
temp = magma_cblas_snrm2( k, s, 1 );
for (i = 0; i < k; ++i) {
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[iii] / temp;
}
}
}
timer_stop( time );
timer_printf( "eigenvalues/vector D+zzT = %6.2f\n", time );
#endif //_OPENMP
// Compute the updated eigenvectors.
timer_start( time );
magma_queue_sync( NULL );
if (rk != 0) {
if ( n23 != 0 ) {
if (rk < magma_get_slaed3_k()) {
lapackf77_slacpy("A", &n23, &rk, Q(ctot[0],iil-1), &ldq, s, &n23);
blasf77_sgemm("N", "N", &n2, &rk, &n23, &d_one, &Q2[iq2], &n2,
s, &n23, &d_zero, Q(n1,iil-1), &ldq );
} else {
magma_ssetmatrix( n23, rk, Q(ctot[0],iil-1), ldq, ds, n23 );
magma_sgemm( MagmaNoTrans, MagmaNoTrans, n2, rk, n23, d_one, &dq2[iq2], n2, ds, n23, d_zero, dq, lddq);
magma_sgetmatrix( n2, rk, dq, lddq, Q(n1,iil-1), ldq );
}
} else
lapackf77_slaset("A", &n2, &rk, &d_zero, &d_zero, Q(n1,iil-1), &ldq);
if ( n12 != 0 ) {
if (rk < magma_get_slaed3_k()) {
lapackf77_slacpy("A", &n12, &rk, Q(0,iil-1), &ldq, s, &n12);
blasf77_sgemm("N", "N", &n1, &rk, &n12, &d_one, Q2, &n1,
s, &n12, &d_zero, Q(0,iil-1), &ldq);
} else {
magma_ssetmatrix( n12, rk, Q(0,iil-1), ldq, ds, n12 );
magma_sgemm( MagmaNoTrans, MagmaNoTrans, n1, rk, n12, d_one, dq2, n1, ds, n12, d_zero, dq, lddq);
magma_sgetmatrix( n1, rk, dq, lddq, Q(0,iil-1), ldq );
}
} else
lapackf77_slaset("A", &n1, &rk, &d_zero, &d_zero, Q(0,iil-1), &ldq);
}
timer_stop( time );
timer_printf( "gemms = %6.2f\n", time );
return *info;
} /* magma_slaex3 */
extern "C" magma_int_t
magma_slaex3(magma_int_t k, magma_int_t n, magma_int_t n1, float* d,
float* q, magma_int_t ldq, float rho,
float* dlamda, float* q2, magma_int_t* indx,
magma_int_t* ctot, float* w, float* s, magma_int_t* indxq,
float* dwork,
char range, float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t* info )
{
/*
Purpose
=======
SLAEX3 finds the roots of the secular equation, as defined by the
values in D, W, and RHO, between 1 and K. It makes the
appropriate calls to SLAED4 and then updates the eigenvectors by
multiplying the matrix of eigenvectors of the pair of eigensystems
being combined by the matrix of eigenvectors of the K-by-K system
which is solved here.
It is used in the last step when only a part of the eigenvectors
is required.
It compute only the required part of the eigenvectors and the rest
is not used.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
K (input) INTEGER
The number of terms in the rational function to be solved by
SLAED4. K >= 0.
N (input) INTEGER
The number of rows and columns in the Q matrix.
N >= K (deflation may result in N>K).
N1 (input) INTEGER
The location of the last eigenvalue in the leading submatrix.
min(1,N) <= N1 <= N/2.
D (output) REAL array, dimension (N)
D(I) contains the updated eigenvalues for
1 <= I <= K.
Q (output) REAL array, dimension (LDQ,N)
Initially the first K columns are used as workspace.
On output the columns ??? to ??? contain
the updated eigenvectors.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
RHO (input) REAL
The value of the parameter in the rank one update equation.
RHO >= 0 required.
DLAMDA (input/output) REAL array, dimension (K)
The first K elements of this array contain the old roots
of the deflated updating problem. These are the poles
of the secular equation. May be changed on output by
having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
Cray-2, or Cray C-90, as described above.
Q2 (input) REAL array, dimension (LDQ2, N)
The first K columns of this matrix contain the non-deflated
eigenvectors for the split problem.
INDX (input) INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated
Q matrix into three groups (see SLAED2).
The rows of the eigenvectors found by SLAED4 must be likewise
permuted before the matrix multiply can take place.
CTOT (input) INTEGER array, dimension (4)
A count of the total number of the various types of columns
in Q, as described in INDX. The fourth column type is any
column which has been deflated.
W (input/output) REAL array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector. Destroyed on
output.
S (workspace) REAL array, dimension (N1 + 1)*K
Will contain the eigenvectors of the repaired matrix which
will be multiplied by the previously accumulated eigenvectors
to update the system.
INDXQ (output) INTEGER array, dimension (N)
On exit, the permutation which will reintegrate the
subproblems back into sorted order,
i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
DWORK (device workspace) REAL array, dimension (3*N*N/2+3*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
===================================================================== */
float d_one = 1.;
float d_zero = 0.;
magma_int_t ione = 1;
magma_int_t ineg_one = -1;
char range_[] = {range, 0};
magma_int_t iil, iiu, rk;
float* dq2= dwork;
float* ds = dq2 + n*(n/2+1);
float* dq = ds + n*(n/2+1);
magma_int_t lddq = n/2 + 1;
magma_int_t i,iq2,j,n12,n2,n23,tmp,lq2;
float temp;
magma_int_t alleig, valeig, indeig;
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
*info = 0;
if(k < 0)
*info=-1;
else if(n < k)
*info=-2;
else if(ldq < max(1,n))
*info=-6;
else if (! (alleig || valeig || indeig))
*info = -15;
else {
if (valeig) {
if (n > 0 && vu <= vl)
*info = -17;
}
else if (indeig) {
if (il < 1 || il > max(1,n))
*info = -18;
else if (iu < min(n,il) || iu > n)
*info = -19;
}
}
if(*info != 0){
magma_xerbla(__func__, -(*info));
return MAGMA_ERR_ILLEGAL_VALUE;
}
// Quick return if possible
if(k == 0)
return MAGMA_SUCCESS;
/*
Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
be computed with high relative accuracy (barring over/underflow).
This is a problem on machines without a guard digit in
add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
which on any of these machines zeros out the bottommost
bit of DLAMDA(I) if it is 1; this makes the subsequent
subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
occurs. On binary machines with a guard digit (almost all
machines) it does not change DLAMDA(I) at all. On hexadecimal
and decimal machines with a guard digit, it slightly
changes the bottommost bits of DLAMDA(I). It does not account
for hexadecimal or decimal machines without guard digits
(we know of none). We use a subroutine call to compute
2*DLAMBDA(I) to prevent optimizing compilers from eliminating
this code.*/
n2 = n - n1;
n12 = ctot[0] + ctot[1];
n23 = ctot[1] + ctot[2];
iq2 = n1 * n12;
lq2 = iq2 + n2 * n23;
magma_ssetvector_async( lq2, q2, 1, dq2, 1, NULL );
#ifdef _OPENMP
/////////////////////////////////////////////////////////////////////////////////
//openmp implementation
/////////////////////////////////////////////////////////////////////////////////
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
magma_timestr_t start, end;
start = get_current_time();
#endif
#pragma omp parallel private(i, j, tmp, temp)
{
magma_int_t id = omp_get_thread_num();
magma_int_t tot = omp_get_num_threads();
magma_int_t ib = ( id * k) / tot; //start index of local loop
magma_int_t ie = ((id+1) * k) / tot; //end index of local loop
magma_int_t ik = ie - ib; //number of local indices
for(i = ib; i < ie; ++i)
dlamda[i]=lapackf77_slamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for(j = ib; j < ie; ++j){
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_slaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if(iinfo != 0){
#pragma omp critical (info)
*info=iinfo;
break;
}
}
#pragma omp barrier
if(*info == 0){
#pragma omp single
{
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_slamrg( &k, &nk, d, &ione , &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_svrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_sirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
}
if (k == 2){
#pragma omp single
{
for(j = 0; j < k; ++j){
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
}
else if(k != 1){
// Compute updated W.
blasf77_scopy( &ik, &w[ib], &ione, &s[ib], &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_scopy( &ik, Q(ib,ib), &tmp, &w[ib], &ione);
for(j = 0; j < k; ++j){
magma_int_t i_tmp = min(j, ie);
for(i = ib; i < i_tmp; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
i_tmp = max(j+1, ib);
for(i = i_tmp; i < ie; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for(i = ib; i < ie; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
#pragma omp barrier
//reduce the number of used threads to have enough S workspace
tot = min(n1, omp_get_num_threads());
if(id < tot){
ib = ( id * rk) / tot + iil - 1;
ie = ((id+1) * rk) / tot + iil - 1;
ik = ie - ib;
}
else{
ib = -1;
ie = -1;
ik = -1;
}
// Compute eigenvectors of the modified rank-1 modification.
for(j = ib; j < ie; ++j){
for(i = 0; i < k; ++i)
s[id*k + i] = w[i] / *Q(i,j);
temp = cblas_snrm2( k, s+id*k, 1);
for(i = 0; i < k; ++i){
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[id*k + iii] / temp;
}
}
}
}
}
if (*info != 0)
return MAGMA_SUCCESS; //??????
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
end = get_current_time();
printf("eigenvalues/vector D+zzT = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
#else
/////////////////////////////////////////////////////////////////////////////////
// Non openmp implementation
/////////////////////////////////////////////////////////////////////////////////
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
magma_timestr_t start, end;
start = get_current_time();
#endif
for(i = 0; i < k; ++i)
dlamda[i]=lapackf77_slamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for(j = 0; j < k; ++j){
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_slaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if(iinfo != 0)
*info=iinfo;
}
if(*info != 0)
return MAGMA_SUCCESS;
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_slamrg( &k, &nk, d, &ione , &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_svrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_sirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
if (k == 2){
for(j = 0; j < k; ++j){
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
else if(k != 1){
// Compute updated W.
blasf77_scopy( &k, w, &ione, s, &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_scopy( &k, q, &tmp, w, &ione);
for(j = 0; j < k; ++j){
for(i = 0; i < j; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
for(i = j+1; i < k; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for(i = 0; i < k; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
// Compute eigenvectors of the modified rank-1 modification.
for(j = iil-1; j < iiu; ++j){
for(i = 0; i < k; ++i)
s[i] = w[i] / *Q(i,j);
temp = cblas_snrm2( k, s, 1);
for(i = 0; i < k; ++i){
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[iii] / temp;
}
}
}
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
end = get_current_time();
printf("eigenvalues/vector D+zzT = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
#endif //_OPENMP
// Compute the updated eigenvectors.
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
start = get_current_time();
#endif
magma_queue_sync( NULL );
if (rk != 0){
if( n23 != 0 ){
if (rk < magma_get_slaed3_k()){
lapackf77_slacpy("A", &n23, &rk, Q(ctot[0],iil-1), &ldq, s, &n23);
blasf77_sgemm("N", "N", &n2, &rk, &n23, &d_one, &q2[iq2], &n2,
s, &n23, &d_zero, Q(n1,iil-1), &ldq );
} else {
magma_ssetmatrix( n23, rk, Q(ctot[0],iil-1), ldq, ds, n23 );
magma_sgemm('N', 'N', n2, rk, n23, d_one, &dq2[iq2], n2, ds, n23, d_zero, dq, lddq);
magma_sgetmatrix( n2, rk, dq, lddq, Q(n1,iil-1), ldq );
}
} else
lapackf77_slaset("A", &n2, &rk, &d_zero, &d_zero, Q(n1,iil-1), &ldq);
if( n12 != 0 ) {
if (rk < magma_get_slaed3_k()){
lapackf77_slacpy("A", &n12, &rk, Q(0,iil-1), &ldq, s, &n12);
blasf77_sgemm("N", "N", &n1, &rk, &n12, &d_one, q2, &n1,
s, &n12, &d_zero, Q(0,iil-1), &ldq);
} else {
magma_ssetmatrix( n12, rk, Q(0,iil-1), ldq, ds, n12 );
magma_sgemm('N', 'N', n1, rk, n12, d_one, dq2, n1, ds, n12, d_zero, dq, lddq);
magma_sgetmatrix( n1, rk, dq, lddq, Q(0,iil-1), ldq );
}
} else
lapackf77_slaset("A", &n1, &rk, &d_zero, &d_zero, Q(0,iil-1), &ldq);
}
#ifdef ENABLE_TIMER_DIVIDE_AND_CONQUER
end = get_current_time();
printf("gemms = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
return MAGMA_SUCCESS;
} /*magma_slaed3*/