Foam::lduSolverPerformance Foam::gmresSolver::solve
(
scalarField& x,
const scalarField& b,
const direction cmpt
) const
{
// Prepare solver performance
lduSolverPerformance solverPerf(typeName, fieldName());
scalarField wA(x.size());
scalarField rA(x.size());
// Calculate initial residual
matrix_.Amul(wA, x, coupleBouCoeffs_, interfaces_, cmpt);
// Use rA as scratch space when calculating the normalisation factor
scalar normFactor = this->normFactor(x, b, wA, rA, cmpt);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// Calculate residual
forAll (rA, i)
{
rA[i] = b[i] - wA[i];
}
typename Foam::BlockSolverPerformance<Type>
Foam::BlockGaussSeidelSolver<Type>::solve
(
Field<Type>& x,
const Field<Type>& b
)
{
// Create local references to avoid the spread this-> ugliness
const BlockLduMatrix<Type>& matrix = this->matrix_;
// Prepare solver performance
BlockSolverPerformance<Type> solverPerf
(
typeName,
this->fieldName()
);
scalar norm = this->normFactor(x, b);
Field<Type> wA(x.size());
// Calculate residual. Note: sign of residual swapped for efficiency
matrix.Amul(wA, x);
wA -= b;
solverPerf.initialResidual() = gSum(cmptMag(wA))/norm;
solverPerf.finalResidual() = solverPerf.initialResidual();
// Check convergence, solve if not converged
if (!this->stop(solverPerf))
{
// Iteration loop
do
{
for (label i = 0; i < nSweeps_; i++)
{
gs_.precondition(x, b);
solverPerf.nIterations()++;
}
// Re-calculate residual. Note: sign of residual swapped
// for efficiency
matrix.Amul(wA, x);
wA -= b;
solverPerf.finalResidual() = gSum(cmptMag(wA))/norm;
solverPerf.nIterations()++;
} while (!this->stop(solverPerf));
}
return solverPerf;
}
typename Foam::BlockSolverPerformance<Type>
Foam::BlockGMRESSolver<Type>::solve
(
Field<Type>& x,
const Field<Type>& b
)
{
// Create local references to avoid the spread this-> ugliness
const BlockLduMatrix<Type>& matrix = this->matrix_;
// Prepare solver performance
BlockSolverPerformance<Type> solverPerf
(
typeName,
this->fieldName()
);
scalar norm = this->normFactor(x, b);
// Multiplication helper
typename BlockCoeff<Type>::multiply mult;
Field<Type> wA(x.size());
// Calculate initial residual
matrix.Amul(wA, x);
Field<Type> rA(b - wA);
solverPerf.initialResidual() = gSum(cmptMag(rA))/norm;
solverPerf.finalResidual() = solverPerf.initialResidual();
// Check convergence, solve if not converged
if (!solverPerf.checkConvergence(this->tolerance(), this->relTolerance()))
{
// Create the Hesenberg matrix
scalarSquareMatrix H(nDirs_, 0);
// Create y and b for Hessenberg matrix
scalarField yh(nDirs_, 0);
scalarField bh(nDirs_ + 1, 0);
// Givens rotation vectors
scalarField c(nDirs_, 0);
scalarField s(nDirs_, 0);
// Allocate Krylov space vectors
FieldField<Field, Type> V(nDirs_ + 1);
forAll (V, i)
{
V.set(i, new Field<Type>(x.size(), pTraits<Type>::zero));
}
Foam::scalar Foam::lduMatrix::solver::normFactor
(
const scalarField& x,
const scalarField& b,
const direction cmpt
) const
{
scalarField wA(x.size());
scalarField tmpField(x.size());
matrix_.Amul(wA, x, interfaceBouCoeffs_, interfaces_, cmpt);
return normFactor(x, b, wA, tmpField);
}
Foam::coupledSolverPerformance Foam::coupledBicgSolver::solve
(
FieldField<Field, scalar>& x,
const FieldField<Field, scalar>& b,
const direction cmpt
) const
{
// Prepare solver performance
coupledSolverPerformance solverPerf(typeName, fieldName());
FieldField<Field, scalar> wA(x.size());
FieldField<Field, scalar> rA(x.size());
forAll (x, rowI)
{
wA.set(rowI, new scalarField(x[rowI].size(), 0));
rA.set(rowI, new scalarField(x[rowI].size(), 0));
}
Foam::scalar Foam::BlockIterativeSolver<Type>::normFactor
(
Field<Type>& x,
const Field<Type>& b
) const
{
const BlockLduMatrix<Type>& matrix = this->matrix_;
// Calculate the normalisation factor
const label nRows = x.size();
Field<Type> pA(nRows);
Field<Type> wA(nRows);
// Calculate reference value of x
Type xRef = gAverage(x);
// Calculate A.x
matrix.Amul(wA, x);
// Calculate A.xRef, temporarily using pA for storage
matrix.Amul
(
pA,
Field<Type>(nRows, xRef)
);
scalar normFactor = gSum(mag(wA - pA) + mag(b - pA)) + this->small_;
if (BlockLduMatrix<Type>::debug >= 2)
{
Info<< "Iterative solver normalisation factor = "
<< normFactor << endl;
}
return normFactor;
}
/**
Purpose
-------
CUNMQL overwrites the general complex M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaConjTrans: Q**H * C C * Q**H
@endverbatim
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by CGEQLF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
dA COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQLF in the last k columns of its array argument A.
The diagonal and the lower part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft;
LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQLF.
@param[in,out]
dC COMPLEX array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) COMPLEX array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by CHETRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_cunmql2_gpu(magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *tau,
magmaFloatComplex *dC, magma_int_t lddc,
magmaFloatComplex *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Allocate work space on the GPU */
magmaFloatComplex *dwork;
magma_cmalloc( &dwork, 2*(m + 64)*64 );
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i, i__4;
magmaFloatComplex T[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, nb, mi, ni, nq, nw;
magma_int_t ldwork;
int left, notran;
wA -= 1 + ldwa;
dC -= 1 + lddc;
--tau;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = max(1,n);
} else {
nq = n;
nw = max(1,m);
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaConjTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0) {
return *info;
}
ldwork = nw;
/* Use hybrid CPU-GPU code */
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = (k - 1) / nb * nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
} else {
mi = m;
}
// set nb-1 sub-diagonals to 0, and diagonal to 1.
// This way we can copy V directly to the GPU,
// already with the lower triangle parts already set to identity.
magmablas_claset_band( MagmaLower, k, k, nb, c_zero, c_one, dA, ldda );
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
i__4 = nq - k + i + ib - 1;
lapackf77_clarft("Backward", "Columnwise", &i__4, &ib,
wA(1,i), &ldwa, &tau[i], T, &ib);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = m - k + i + ib - 1;
}
else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = n - k + i + ib - 1;
}
/* Apply H or H'; First copy T to the GPU */
magma_csetmatrix( ib, ib, T, ib, dwork+i__4*ib, ib );
magma_clarfb_gpu(side, trans, MagmaBackward, MagmaColumnwise,
mi, ni, ib,
dA(0,i-1), ldda, dwork+i__4*ib, ib, // dA using 0-based indices here
dC(1,1), lddc,
dwork+i__4*ib + ib*ib, ldwork);
}
magma_free( dwork );
return *info;
} /* magma_cunmql */
Foam::SolverPerformance<Type>
Foam::PBiCCCG<Type, DType, LUType>::solve
(
Field<Type>& psi
) const
{
word preconditionerName(this->controlDict_.lookup("preconditioner"));
// --- Setup class containing solver performance data
SolverPerformance<Type> solverPerf
(
preconditionerName + typeName,
this->fieldName_
);
label nCells = psi.size();
Type* __restrict__ psiPtr = psi.begin();
Field<Type> pA(nCells);
Type* __restrict__ pAPtr = pA.begin();
Field<Type> pT(nCells, Zero);
Type* __restrict__ pTPtr = pT.begin();
Field<Type> wA(nCells);
Type* __restrict__ wAPtr = wA.begin();
Field<Type> wT(nCells);
Type* __restrict__ wTPtr = wT.begin();
scalar wArT = 1e15; //this->matrix_.great_;
scalar wArTold = wArT;
// --- Calculate A.psi and T.psi
this->matrix_.Amul(wA, psi);
this->matrix_.Tmul(wT, psi);
// --- Calculate initial residual and transpose residual fields
Field<Type> rA(this->matrix_.source() - wA);
Field<Type> rT(this->matrix_.source() - wT);
Type* __restrict__ rAPtr = rA.begin();
Type* __restrict__ rTPtr = rT.begin();
// --- Calculate normalisation factor
Type normFactor = this->normFactor(psi, wA, pA);
if (LduMatrix<Type, DType, LUType>::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = cmptDivide(gSumCmptMag(rA), normFactor);
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
this->minIter_ > 0
|| !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<typename LduMatrix<Type, DType, LUType>::preconditioner>
preconPtr = LduMatrix<Type, DType, LUType>::preconditioner::New
(
*this,
this->controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA);
preconPtr->preconditionT(wT, rT);
// --- Update search directions:
wArT = gSumProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
scalar beta = wArT/wArTold;
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + (beta* pAPtr[cell]);
pTPtr[cell] = wTPtr[cell] + (beta* pTPtr[cell]);
}
}
// --- Update preconditioned residuals
this->matrix_.Amul(wA, pA);
this->matrix_.Tmul(wT, pT);
scalar wApT = gSumProd(wA, pT);
// --- Test for singularity
if
(
solverPerf.checkSingularity
(
cmptDivide(pTraits<Type>::one*mag(wApT), normFactor)
)
)
{
break;
}
// --- Update solution and residual:
scalar alpha = wArT/wApT;
for (label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += (alpha* pAPtr[cell]);
rAPtr[cell] -= (alpha* wAPtr[cell]);
rTPtr[cell] -= (alpha* wTPtr[cell]);
}
solverPerf.finalResidual() =
cmptDivide(gSumCmptMag(rA), normFactor);
} while
(
(
solverPerf.nIterations()++ < this->maxIter_
&& !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
|| solverPerf.nIterations() < this->minIter_
);
}
return solverPerf;
}
Foam::lduSolverPerformance Foam::PBiCG::solve
(
scalarField& x,
const scalarField& b,
const direction cmpt
) const
{
// --- Setup class containing solver performance data
lduSolverPerformance solverPerf
(
lduMatrix::preconditioner::getName(dict()) + typeName,
fieldName()
);
register label nCells = x.size();
scalar* __restrict__ xPtr = x.begin();
scalarField pA(nCells);
scalar* __restrict__ pAPtr = pA.begin();
scalarField pT(nCells, 0.0);
scalar* __restrict__ pTPtr = pT.begin();
scalarField wA(nCells);
scalar* __restrict__ wAPtr = wA.begin();
scalarField wT(nCells);
scalar* __restrict__ wTPtr = wT.begin();
scalar wArT = matrix_.great_;
scalar wArTold = wArT;
// Calculate A.x and T.x
matrix_.Amul(wA, x, coupleBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, x, coupleIntCoeffs_, interfaces_, cmpt);
// Calculate initial residual and transpose residual fields
scalarField rA(b - wA);
scalarField rT(b - wT);
scalar* __restrict__ rAPtr = rA.begin();
scalar* __restrict__ rTPtr = rT.begin();
// Calculate normalisation factor
scalar normFactor = this->normFactor(x, b, wA, pA, cmpt);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// Calculate normalised residual norm
solverPerf.initialResidual() = gSumMag(rA)/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// Check convergence, solve if not converged
if (!stop(solverPerf))
{
// Select and construct the preconditioner
autoPtr<lduPreconditioner> preconPtr;
preconPtr =
lduPreconditioner::New
(
matrix_,
coupleBouCoeffs_,
coupleIntCoeffs_,
interfaces_,
dict()
);
// Solver iteration
do
{
// Store previous wArT
wArTold = wArT;
// Precondition residuals
preconPtr->precondition(wA, rA, cmpt);
preconPtr->preconditionT(wT, rT, cmpt);
// Update search directions:
wArT = gSumProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
scalar beta = wArT/wArTold;
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + beta*pAPtr[cell];
pTPtr[cell] = wTPtr[cell] + beta*pTPtr[cell];
}
}
// Update preconditioned residuals
matrix_.Amul(wA, pA, coupleBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, pT, coupleIntCoeffs_, interfaces_, cmpt);
scalar wApT = gSumProd(wA, pT);
// Test for singularity
if (solverPerf.checkSingularity(mag(wApT)/normFactor)) break;
// Update solution and residual:
scalar alpha = wArT/wApT;
for (register label cell=0; cell<nCells; cell++)
{
xPtr[cell] += alpha*pAPtr[cell];
rAPtr[cell] -= alpha*wAPtr[cell];
rTPtr[cell] -= alpha*wTPtr[cell];
}
solverPerf.finalResidual() = gSumMag(rA)/normFactor;
solverPerf.nIterations()++;
} while (!stop(solverPerf));
}
return solverPerf;
}
/**
Purpose
-------
ZUNMQL overwrites the general complex M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = Magma_ConjTrans: Q**H * C C * Q**H
@endverbatim
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by ZGEQLF.
Q is of order M if SIDE = MagmaLeft
and of order N if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (LDDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQLF in the last k columns of its array argument dA.
The diagonal and the lower part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array dA.
If SIDE = MagmaLeft, LDDA >= max(1,M);
if SIDE = MagmaRight, LDDA >= max(1,N).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.
@param[in,out]
dC COMPLEX_16 array on the GPU, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
@param[in]
lddc INTEGER
The leading dimension of the array dC. LDDC >= max(1,M).
@param[in]
wA COMPLEX_16 array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by ZHETRD_GPU.
(A copy of the upper or lower part of dA, on the host.)
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
If SIDE = MagmaLeft, LDWA >= max(1,M);
if SIDE = MagmaRight, LDWA >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_zunmql2_gpu(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex *tau,
magmaDoubleComplex_ptr dC, magma_int_t lddc,
const magmaDoubleComplex *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Constants */
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magma_int_t nbmax = 64;
/* Local variables */
magmaDoubleComplex_ptr dwork = NULL, dT = NULL;
magmaDoubleComplex T[ nbmax*nbmax ];
magma_int_t i, i1, i2, step, ib, lddwork, nb, mi, ni, nq, nq_i, nw;
magma_queue_t queue = NULL;
// Parameter adjustments for Fortran indexing
wA -= 1 + ldwa;
dC -= 1 + lddc;
--tau;
*info = 0;
bool left = (side == MagmaLeft);
bool notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
/* Test the input arguments */
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != Magma_ConjTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
// size of the block
nb = nbmax;
lddwork = nw;
/* Use hybrid CPU-GPU code */
if ( ( left && notran) ||
(! left && ! notran) )
{
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = ((k - 1)/nb)*nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
} else {
mi = m;
}
// dwork is (n or m) x nb + nb x nb, for left or right respectively
if (MAGMA_SUCCESS != magma_zmalloc( &dwork, lddwork*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
dT = dwork + lddwork*nb;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// in bottom k x k portion of dA,
// set nb-1 sub-diagonals to 0, and diagonal to 1, in
// This way we can copy V directly to the GPU,
// with the lower triangle parts already set to identity.
// A is nq x k, either m x k (left) or n x k (right)
magmablas_zlaset_band( MagmaLower, k, k, nb, c_zero, c_one, dA(nq-k,0), ldda, queue );
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min( nb, k - i + 1 );
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
nq_i = nq - k + i + ib - 1;
lapackf77_zlarft( "Backward", "Columnwise", &nq_i, &ib,
wA(1,i), &ldwa, &tau[i], T, &ib );
if (left) {
/* H or H^H is applied to C(1:m-k+i+ib-1,1:n) */
mi = m - k + i + ib - 1;
}
else {
/* H or H^H is applied to C(1:m,1:n-k+i+ib-1) */
ni = n - k + i + ib - 1;
}
/* Apply H or H^H; First copy T to the GPU */
magma_zsetmatrix( ib, ib, T, ib, dT, ib, queue );
magma_zlarfb_gpu( side, trans, MagmaBackward, MagmaColumnwise,
mi, ni, ib,
dA(0,i-1), ldda, dT, ib, // dA using 0-based indices here
dC(1,1), lddc,
dwork, lddwork, queue );
}
cleanup:
magma_queue_destroy( queue );
magma_free( dwork );
return *info;
} /* magma_zunmql */
/**
Purpose
-------
DORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
dA DOUBLE_PRECISION array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument A.
The diagonal and the upper part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
@param[in,out]
dC DOUBLE_PRECISION array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
@param[in]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) DOUBLE_PRECISION array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by DSYTRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormqr2_gpu(magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau,
double *dC, magma_int_t lddc,
double *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Allocate work space on the GPU */
double *dwork;
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t i, i__4, lddwork;
double T[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, ic, jc, nb, mi, ni, nq, nw;
int left, notran;
wA -= 1 + ldwa;
dC -= 1 + lddc;
--tau;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
magma_dmalloc( &dwork, (n + 64)*64 ); // TODO after checking args, else memory leak!
} else {
nq = n;
nw = m;
magma_dmalloc( &dwork, (m + 64)*64 ); // TODO after checking args, else memory leak!
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
/* Use hybrid CPU-GPU code */
if ( ( left && (! notran) ) || ( (! left) && notran ) ) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = ((k - 1)/nb)*nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 1;
} else {
mi = m;
ic = 1;
}
// set nb-1 super-diagonals to 0, and diagonal to 1.
// This way we can copy V directly to the GPU,
// with the upper triangle parts already set to identity.
magmablas_dlaset_band( MagmaUpper, k, k, nb, c_zero, c_one, dA, ldda );
// for i=i1 to i2 by step
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i + 1;
lapackf77_dlarft("Forward", "Columnwise", &i__4, &ib,
wA(i,i), &ldwa, &tau[i], T, &ib);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = m - i + 1;
ic = i;
}
else {
/* H or H' is applied to C(1:m,i:n) */
ni = n - i + 1;
jc = i;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_dsetmatrix( ib, ib, T, ib, dwork, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i-1,i-1), ldda, dwork, ib, // dA using 0-based indices here
dC(ic,jc), lddc,
dwork + ib*ib, lddwork);
}
magma_free( dwork );
return *info;
} /* magma_dormqr */
Foam::solverPerformance Foam::paralution_AMG::solve
(
scalarField& psi,
const scalarField& source,
const direction cmpt
) const
{
word precond_name = lduMatrix::preconditioner::getName(controlDict_);
double div = controlDict_.lookupOrDefault<double>("div", 1e+08);
bool accel = controlDict_.lookupOrDefault<bool>("useAccelerator", true);
word mformat = controlDict_.lookupOrDefault<word>("MatrixFormat", "CSR");
word pformat = controlDict_.lookupOrDefault<word>("PrecondFormat", "CSR");
word sformat = controlDict_.lookupOrDefault<word>("SmootherFormat", "CSR");
word solver_name = controlDict_.lookupOrDefault<word>("CoarseGridSolver", "CG");
word smoother_name = controlDict_.lookupOrDefault<word>("smoother", "paralution_MultiColoredGS");
int MEp = controlDict_.lookupOrDefault<int>("MEp", 1);
word LBPre = controlDict_.lookupOrDefault<word>("LastBlockPrecond", "paralution_Jacobi");
int iterPreSmooth = controlDict_.lookupOrDefault<int>("nPreSweeps", 1);
int iterPostSmooth = controlDict_.lookupOrDefault<int>("nPostSweeps", 2);
double epsCoupling = controlDict_.lookupOrDefault<double>("couplingStrength", 0.01);
int coarsestCells = controlDict_.lookupOrDefault<int>("nCellsInCoarsestLevel", 300);
int ILUp = controlDict_.lookupOrDefault<int>("ILUp", 0);
int ILUq = controlDict_.lookupOrDefault<int>("ILUq", 1);
double relax = controlDict_.lookupOrDefault<double>("Relaxation", 1.0);
double aggrrelax = controlDict_.lookupOrDefault<double>("AggrRelax", 2./3.);
bool scaling = controlDict_.lookupOrDefault<bool>("scaleCorrection", true);
word interp_name = controlDict_.lookupOrDefault<word>("InterpolationType", "SmoothedAggregation");
solverPerformance solverPerf(typeName + '(' + precond_name + ')', fieldName_);
register label nCells = psi.size();
scalarField pA(nCells);
scalarField wA(nCells);
// --- Calculate A.psi
matrix_.Amul(wA, psi, interfaceBouCoeffs_, interfaces_, cmpt);
// --- Calculate initial residual field
scalarField rA(source - wA);
// --- Calculate normalisation factor
scalar normFactor = this->normFactor(psi, source, wA, pA);
// --- Calculate normalised residual norm
solverPerf.initialResidual() = gSumMag(rA)/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
if ( !solverPerf.checkConvergence(tolerance_, relTol_) ) {
paralution::_matrix_format mf = paralution::CSR;
if (mformat == "CSR") mf = paralution::CSR;
else if (mformat == "DIA") mf = paralution::DIA;
else if (mformat == "HYB") mf = paralution::HYB;
else if (mformat == "ELL") mf = paralution::ELL;
else if (mformat == "MCSR") mf = paralution::MCSR;
else if (mformat == "BCSR") mf = paralution::BCSR;
else if (mformat == "COO") mf = paralution::COO;
else if (mformat == "DENSE") mf = paralution::DENSE;
paralution::_interp ip = paralution::SmoothedAggregation;
if (interp_name == "SmoothedAggregation") ip = paralution::SmoothedAggregation;
else if (interp_name == "Aggregation") ip = paralution::Aggregation;
paralution::LocalVector<double> x;
paralution::LocalVector<double> rhs;
paralution::LocalMatrix<double> mat;
paralution::AMG<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double> ls;
paralution::import_openfoam_matrix(matrix(), &mat);
paralution::import_openfoam_vector(source, &rhs);
paralution::import_openfoam_vector(psi, &x);
ls.SetOperator(mat);
// coupling strength
ls.SetCouplingStrength(epsCoupling);
// number of unknowns on coarsest level
ls.SetCoarsestLevel(coarsestCells);
// interpolation type for grid transfer operators
ls.SetInterpolation(ip);
// Relaxation parameter for smoothed interpolation aggregation
ls.SetInterpRelax(aggrrelax);
// Manual smoothers
ls.SetManualSmoothers(true);
// Manual course grid solver
ls.SetManualSolver(true);
// grid transfer scaling
ls.SetScaling(scaling);
// operator format
ls.SetOperatorFormat(mf);
ls.SetSmootherPreIter(iterPreSmooth);
ls.SetSmootherPostIter(iterPostSmooth);
ls.BuildHierarchy();
int levels = ls.GetNumLevels();
// Smoother via preconditioned FixedPoint iteration
paralution::IterativeLinearSolver<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double > **fp = NULL;
fp = new paralution::IterativeLinearSolver<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double >*[levels-1];
paralution::Preconditioner<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double > **sm = NULL;
sm = new paralution::Preconditioner<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double >*[levels-1];
for (int i=0; i<levels-1; ++i) {
fp[i] = paralution::GetIterativeLinearSolver<double>("paralution_FixedPoint", relax);
sm[i] = paralution::GetPreconditioner<double>(smoother_name, LBPre, sformat, ILUp, ILUq, MEp);
fp[i]->SetPreconditioner(*sm[i]);
fp[i]->Verbose(0);
}
// Coarse Grid Solver and its Preconditioner
paralution::IterativeLinearSolver<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double > *cgs = NULL;
cgs = paralution::GetIterativeLinearSolver<double>(solver_name, relax);
cgs->Verbose(0);
paralution::Preconditioner<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double > *cgp = NULL;
cgp = paralution::GetPreconditioner<double>(precond_name, LBPre, pformat, ILUp, ILUq, MEp);
if (cgp != NULL) cgs->SetPreconditioner(*cgp);
ls.SetSmoother(fp);
ls.SetSolver(*cgs);
// Switch to L1 norm to be consistent with OpenFOAM solvers
ls.SetResidualNorm(1);
ls.Init(tolerance_*normFactor, // abs
relTol_, // rel
div, // div
maxIter_); // max iter
ls.Build();
if (accel) {
mat.MoveToAccelerator();
rhs.MoveToAccelerator();
x.MoveToAccelerator();
ls.MoveToAccelerator();
}
switch(mf) {
case paralution::DENSE:
mat.ConvertToDENSE();
break;
case paralution::CSR:
mat.ConvertToCSR();
break;
case paralution::MCSR:
mat.ConvertToMCSR();
break;
case paralution::BCSR:
mat.ConvertToBCSR();
break;
case paralution::COO:
mat.ConvertToCOO();
break;
case paralution::DIA:
mat.ConvertToDIA();
break;
case paralution::ELL:
mat.ConvertToELL();
break;
case paralution::HYB:
mat.ConvertToHYB();
break;
}
ls.Verbose(0);
// Solve linear system
ls.Solve(rhs, &x);
paralution::export_openfoam_vector(x, &psi);
solverPerf.finalResidual() = ls.GetCurrentResidual() / normFactor; // divide by normFactor, see lduMatrixSolver.C
solverPerf.nIterations() = ls.GetIterationCount();
solverPerf.checkConvergence(tolerance_, relTol_);
// Clear MultiGrid object
ls.Clear();
// Free all structures
for (int i=0; i<levels-1; ++i) {
delete fp[i];
delete sm[i];
}
cgs->Clear();
if (cgp != NULL)
delete cgp;
delete[] fp;
delete[] sm;
delete cgs;
}
return solverPerf;
}
/**
Purpose
-------
DORMTR overwrites the general real M-by-N matrix C with
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
where Q is a real unitary matrix of order nq, with nq = m if
SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of
nq-1 elementary reflectors, as returned by DSYTRD:
if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);
if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A contains elementary reflectors
from DSYTRD;
- = MagmaLower: Lower triangle of A contains elementary reflectors
from DSYTRD.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
dA DOUBLE_PRECISION array, dimension
(LDDA,M) if SIDE = MagmaLeft
(LDDA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by DSYTRD_GPU. On output the diagonal, the subdiagonal and the
upper part (UPLO=MagmaLower) or lower part (UPLO=MagmaUpper) are destroyed.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau DOUBLE_PRECISION array, dimension
(M-1) if SIDE = MagmaLeft
(N-1) if SIDE = MagmaRight
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DSYTRD.
@param[in,out]
dC DOUBLE_PRECISION array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
@param[in]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) DOUBLE_PRECISION array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by DSYTRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dsyev_comp
********************************************************************/
extern "C" magma_int_t
magma_dormtr_gpu(
magma_side_t side, magma_uplo_t uplo, magma_trans_t trans,
magma_int_t m, magma_int_t n,
magmaDouble_ptr dA, magma_int_t ldda,
double *tau,
magmaDouble_ptr dC, magma_int_t lddc,
double *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
magma_int_t i1, i2, mi, ni, nq;
int left, upper;
magma_int_t iinfo;
*info = 0;
left = (side == MagmaLeft);
upper = (uplo == MagmaUpper);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
//nw = n;
} else {
nq = n;
//nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! upper && uplo != MagmaLower) {
*info = -2;
} else if (trans != MagmaNoTrans &&
trans != MagmaTrans) {
*info = -3;
} else if (m < 0) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || nq == 1) {
return *info;
}
if (left) {
mi = m - 1;
ni = n;
} else {
mi = m;
ni = n - 1;
}
if (upper) {
magma_dormql2_gpu(side, trans, mi, ni, nq-1, dA(0,1), ldda, tau,
dC, lddc, wA(0,1), ldwa, &iinfo);
}
else {
/* Q was determined by a call to DSYTRD with UPLO = 'L' */
if (left) {
i1 = 1;
i2 = 0;
} else {
i1 = 0;
i2 = 1;
}
magma_dormqr2_gpu(side, trans, mi, ni, nq-1, dA(1,0), ldda, tau,
dC(i1,i2), lddc, wA(1,0), ldwa, &iinfo);
}
return *info;
} /* magma_dormtr */
Foam::lduMatrix::solverPerformance Foam::paralution_PFGMRES::solve
(
scalarField& psi,
const scalarField& source,
const direction cmpt
) const
{
word precond_name = lduMatrix::preconditioner::getName(controlDict_);
double div = controlDict_.lookupOrDefault<double>("div", 1e+08);
int basis = controlDict_.lookupOrDefault<int>("BasisSize", 30);
bool accel = controlDict_.lookupOrDefault<bool>("useAccelerator", true);
word mformat = controlDict_.lookupOrDefault<word>("MatrixFormat", "CSR");
word pformat = controlDict_.lookupOrDefault<word>("PrecondFormat", "CSR");
int ILUp = controlDict_.lookupOrDefault<int>("ILUp", 0);
int ILUq = controlDict_.lookupOrDefault<int>("ILUq", 1);
int MEp = controlDict_.lookupOrDefault<int>("MEp", 1);
word LBPre = controlDict_.lookupOrDefault<word>("LastBlockPrecond", "paralution_Jacobi");
lduMatrix::solverPerformance solverPerf(typeName + '(' + precond_name + ')', fieldName_);
register label nCells = psi.size();
scalarField pA(nCells);
scalarField wA(nCells);
// --- Calculate A.psi
matrix_.Amul(wA, psi, interfaceBouCoeffs_, interfaces_, cmpt);
// --- Calculate initial residual field
scalarField rA(source - wA);
// --- Calculate normalisation factor
scalar normFactor = this->normFactor(psi, source, wA, pA);
// --- Calculate normalised residual norm
solverPerf.initialResidual() = gSumMag(rA)/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// TODO check why we cannot skip 1 iteration when initial residual < relTol_ or why initial residual actually
// does not drop below relTol_
if (!solverPerf.checkConvergence(tolerance_, relTol_)) {
paralution::_matrix_format mf = paralution::CSR;
if (mformat == "CSR") mf = paralution::CSR;
else if (mformat == "DIA") mf = paralution::DIA;
else if (mformat == "HYB") mf = paralution::HYB;
else if (mformat == "ELL") mf = paralution::ELL;
else if (mformat == "MCSR") mf = paralution::MCSR;
else if (mformat == "BCSR") mf = paralution::BCSR;
else if (mformat == "COO") mf = paralution::COO;
else if (mformat == "DENSE") mf = paralution::DENSE;
paralution::init_paralution();
paralution::LocalVector<double> x;
paralution::LocalVector<double> rhs;
paralution::LocalMatrix<double> mat;
paralution::FGMRES<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double> ls;
import_openfoam_matrix(matrix(), &mat);
import_openfoam_vector(source, &rhs);
import_openfoam_vector(psi, &x);
ls.Clear();
if (accel) {
mat.MoveToAccelerator();
rhs.MoveToAccelerator();
x.MoveToAccelerator();
}
paralution::Preconditioner<paralution::LocalMatrix<double>,
paralution::LocalVector<double>,
double > *precond = NULL;
precond = GetPreconditioner<double>(precond_name, LBPre, pformat, ILUp, ILUq, MEp);
if (precond != NULL) ls.SetPreconditioner(*precond);
ls.SetOperator(mat);
ls.SetBasisSize(basis);
ls.Verbose(0);
ls.Init(tolerance_*normFactor, // abs
relTol_, // rel
div, // div
maxIter_); // max iter
ls.Build();
switch(mf) {
case paralution::DENSE:
mat.ConvertToDENSE();
break;
case paralution::CSR:
mat.ConvertToCSR();
break;
case paralution::MCSR:
mat.ConvertToMCSR();
break;
case paralution::BCSR:
mat.ConvertToBCSR();
break;
case paralution::COO:
mat.ConvertToCOO();
break;
case paralution::DIA:
mat.ConvertToDIA();
break;
case paralution::ELL:
mat.ConvertToELL();
break;
case paralution::HYB:
mat.ConvertToHYB();
break;
}
// mat.info();
ls.Solve(rhs, &x);
export_openfoam_vector(x, &psi);
solverPerf.finalResidual() = ls.GetCurrentResidual() / normFactor; // divide by normFactor, see lduMatrixSolver.C
solverPerf.nIterations() = ls.GetIterationCount();
solverPerf.checkConvergence(tolerance_, relTol_);
ls.Clear();
if (precond != NULL) {
precond->Clear();
delete precond;
}
paralution::stop_paralution();
}
return solverPerf;
}
/**
Purpose
-------
ZUNMQR overwrites the general complex M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = Magma_ConjTrans: Q**H * C C * Q**H
@endverbatim
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
dA COMPLEX_16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQRF in the first k columns of its array argument A.
The diagonal and the upper part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
@param[in,out]
dC COMPLEX_16 array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
@param[in]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) COMPLEX_16 array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by ZHETRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgeqrf_comp
********************************************************************/
template<typename Ty> magma_int_t
magma_unmqr2_gpu(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
cl_mem dA, size_t dA_offset, magma_int_t ldda,
Ty *tau,
cl_mem dC, size_t dC_offset, magma_int_t lddc,
Ty *wA, magma_int_t ldwa,
magma_queue_t queue,
magma_int_t *info)
{
#define dA(i_,j_) (dA) , ((i_) + (j_)*ldda) + dA_offset
#define dC(i_,j_) (dC) , ((i_) + (j_)*lddc) + dC_offset
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Allocate work space on the GPU */
cl_mem dwork;
static const Ty c_zero = magma_zero<Ty>();
static const Ty c_one = magma_one<Ty>();
magma_int_t i, i__4, lddwork;
Ty T[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, ic, jc, nb, mi, ni, nq;
int left, notran;
wA -= 1 + ldwa;
dC_offset -= 1 + lddc;
--tau;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
//nw = n;
magma_malloc<Ty>( &dwork, (n + 64)*64 ); // TODO after checking args, else memory leak!
} else {
nq = n;
//nw = m;
magma_malloc<Ty>( &dwork, (m + 64)*64 ); // TODO after checking args, else memory leak!
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != Magma_ConjTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < std::max(1,nq)) {
*info = -7;
} else if (lddc < std::max(1,m)) {
*info = -10;
} else if (ldwa < std::max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
//magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
/* Use hybrid CPU-GPU code */
if ( ( left && (! notran) ) || ( (! left) && notran ) ) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = ((k - 1)/nb)*nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 1;
} else {
mi = m;
ic = 1;
}
cpu_lapack_larft_func<Ty> cpu_lapack_larft;
// set nb-1 super-diagonals to 0, and diagonal to 1.
// This way we can copy V directly to the GPU,
// with the upper triangle parts already set to identity.
magmablas_laset_band<Ty>( MagmaUpper, k, k, nb, c_zero, c_one, dA, dA_offset, ldda, queue);
// for i=i1 to i2 by step
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = std::min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i + 1;
LAPACKE_CHECK(cpu_lapack_larft(
*MagmaForwardStr, *MagmaColumnwiseStr,
i__4, ib,
wA(i,i), ldwa, &tau[i], T, ib));
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = m - i + 1;
ic = i;
}
else {
/* H or H' is applied to C(1:m,i:n) */
ni = n - i + 1;
jc = i;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_setmatrix<Ty>( ib, ib, T, ib, dwork, 0, ib, queue);
magma_larfb_gpu<Ty>( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i-1,i-1), ldda,
dwork, 0, ib, // dA using 0-based indices here
dC(ic,jc), lddc,
dwork, ib*ib, lddwork, queue);
}
magma_free( dwork );
return *info;
} /* magma_zunmqr */
typename Foam::SolverPerformance<Type>
Foam::PCICG<Type, DType, LUType>::solve(Field<Type>& psi) const
{
word preconditionerName(this->controlDict_.lookup("preconditioner"));
// --- Setup class containing solver performance data
SolverPerformance<Type> solverPerf
(
preconditionerName + typeName,
this->fieldName_
);
label nCells = psi.size();
Type* __restrict__ psiPtr = psi.begin();
Field<Type> pA(nCells);
Type* __restrict__ pAPtr = pA.begin();
Field<Type> wA(nCells);
Type* __restrict__ wAPtr = wA.begin();
Type wArA = solverPerf.great_*pTraits<Type>::one;
Type wArAold = wArA;
// --- Calculate A.psi
this->matrix_.Amul(wA, psi);
// --- Calculate initial residual field
Field<Type> rA(this->matrix_.source() - wA);
Type* __restrict__ rAPtr = rA.begin();
// --- Calculate normalisation factor
Type normFactor = this->normFactor(psi, wA, pA);
if (LduMatrix<Type, DType, LUType>::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = cmptDivide(gSumCmptMag(rA), normFactor);
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
this->minIter_ > 0
|| !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<typename LduMatrix<Type, DType, LUType>::preconditioner>
preconPtr = LduMatrix<Type, DType, LUType>::preconditioner::New
(
*this,
this->controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArA
wArAold = wArA;
// --- Precondition residual
preconPtr->precondition(wA, rA);
// --- Update search directions:
wArA = gSumCmptProd(wA, rA);
if (solverPerf.nIterations() == 0)
{
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
}
}
else
{
Type beta = cmptDivide
(
wArA,
stabilise(wArAold, solverPerf.vsmall_)
);
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + cmptMultiply(beta, pAPtr[cell]);
}
}
// --- Update preconditioned residual
this->matrix_.Amul(wA, pA);
Type wApA = gSumCmptProd(wA, pA);
// --- Test for singularity
if
(
solverPerf.checkSingularity
(
cmptDivide(cmptMag(wApA), normFactor)
)
)
{
break;
}
// --- Update solution and residual:
Type alpha = cmptDivide
(
wArA,
stabilise(wApA, solverPerf.vsmall_)
);
for (label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += cmptMultiply(alpha, pAPtr[cell]);
rAPtr[cell] -= cmptMultiply(alpha, wAPtr[cell]);
}
solverPerf.finalResidual() =
cmptDivide(gSumCmptMag(rA), normFactor);
} while
(
(
solverPerf.nIterations()++ < this->maxIter_
&& !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
|| solverPerf.nIterations() < this->minIter_
);
}
return solverPerf;
}
Foam::solverPerformance Foam::PBiCG::solve
(
scalarField& psi,
const scalarField& source,
const direction cmpt
) const
{
// --- Setup class containing solver performance data
solverPerformance solverPerf
(
lduMatrix::preconditioner::getName(controlDict_) + typeName,
fieldName_
);
label nCells = psi.size();
scalar* __restrict__ psiPtr = psi.begin();
scalarField pA(nCells);
scalar* __restrict__ pAPtr = pA.begin();
scalarField pT(nCells, 0.0);
scalar* __restrict__ pTPtr = pT.begin();
scalarField wA(nCells);
scalar* __restrict__ wAPtr = wA.begin();
scalarField wT(nCells);
scalar* __restrict__ wTPtr = wT.begin();
scalar wArT = solverPerf.great_;
scalar wArTold = wArT;
// --- Calculate A.psi and T.psi
matrix_.Amul(wA, psi, interfaceBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, psi, interfaceIntCoeffs_, interfaces_, cmpt);
// --- Calculate initial residual and transpose residual fields
scalarField rA(source - wA);
scalarField rT(source - wT);
scalar* __restrict__ rAPtr = rA.begin();
scalar* __restrict__ rTPtr = rT.begin();
// --- Calculate normalisation factor
scalar normFactor = this->normFactor(psi, source, wA, pA);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() =
gSumMag(rA, matrix().mesh().comm())
/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
minIter_ > 0
|| !solverPerf.checkConvergence(tolerance_, relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<lduMatrix::preconditioner> preconPtr =
lduMatrix::preconditioner::New
(
*this,
controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA, cmpt);
preconPtr->preconditionT(wT, rT, cmpt);
// --- Update search directions:
wArT = gSumProd(wA, rT, matrix().mesh().comm());
if (solverPerf.nIterations() == 0)
{
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
scalar beta = wArT/wArTold;
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + beta*pAPtr[cell];
pTPtr[cell] = wTPtr[cell] + beta*pTPtr[cell];
}
}
// --- Update preconditioned residuals
matrix_.Amul(wA, pA, interfaceBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, pT, interfaceIntCoeffs_, interfaces_, cmpt);
scalar wApT = gSumProd(wA, pT, matrix().mesh().comm());
// --- Test for singularity
if (solverPerf.checkSingularity(mag(wApT)/normFactor))
{
break;
}
// --- Update solution and residual:
scalar alpha = wArT/wApT;
for (label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += alpha*pAPtr[cell];
rAPtr[cell] -= alpha*wAPtr[cell];
rTPtr[cell] -= alpha*wTPtr[cell];
}
solverPerf.finalResidual() =
gSumMag(rA, matrix().mesh().comm())
/normFactor;
} while
(
(
solverPerf.nIterations()++ < maxIter_
&& !solverPerf.checkConvergence(tolerance_, relTol_)
)
|| solverPerf.nIterations() < minIter_
);
}
return solverPerf;
}
Foam::lduMatrix::solverPerformance Foam::PCG::solve
(
scalarField& psi,
const scalarField& source,
const direction cmpt
) const
{
// --- Setup class containing solver performance data
lduMatrix::solverPerformance solverPerf
(
lduMatrix::preconditioner::getName(controlDict_) + typeName,
fieldName_
);
register label nCells = psi.size();
scalar* __restrict__ psiPtr = psi.begin();
scalarField pA(nCells);
scalar* __restrict__ pAPtr = pA.begin();
scalarField wA(nCells);
scalar* __restrict__ wAPtr = wA.begin();
scalar wArA = matrix_.great_;
scalar wArAold = wArA;
// --- Calculate A.psi
matrix_.Amul(wA, psi, interfaceBouCoeffs_, interfaces_, cmpt);
// --- Calculate initial residual field
scalarField rA(source - wA);
scalar* __restrict__ rAPtr = rA.begin();
// --- Calculate normalisation factor
scalar normFactor = this->normFactor(psi, source, wA, pA);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = gSumMag(rA)/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if (!solverPerf.checkConvergence(tolerance_, relTol_))
{
// --- Select and construct the preconditioner
autoPtr<lduMatrix::preconditioner> preconPtr =
lduMatrix::preconditioner::New
(
*this,
controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArA
wArAold = wArA;
// --- Precondition residual
preconPtr->precondition(wA, rA, cmpt);
// --- Update search directions:
wArA = gSumProd(wA, rA);
if (solverPerf.nIterations() == 0)
{
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
}
}
else
{
scalar beta = wArA/wArAold;
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + beta*pAPtr[cell];
}
}
// --- Update preconditioned residual
matrix_.Amul(wA, pA, interfaceBouCoeffs_, interfaces_, cmpt);
scalar wApA = gSumProd(wA, pA);
// --- Test for singularity
if (solverPerf.checkSingularity(mag(wApA)/normFactor)) break;
// --- Update solution and residual:
scalar alpha = wArA/wApA;
for (register label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += alpha*pAPtr[cell];
rAPtr[cell] -= alpha*wAPtr[cell];
}
solverPerf.finalResidual() = gSumMag(rA)/normFactor;
} while
(
solverPerf.nIterations()++ < maxIter_
&& !(solverPerf.checkConvergence(tolerance_, relTol_))
);
}
return solverPerf;
}
Foam::SolverPerformance<Type>
Foam::PBiCCCG<Type, DType, LUType>::solve
(
gpuField<Type>& psi
) const
{
word preconditionerName(this->controlDict_.lookup("preconditioner"));
// --- Setup class containing solver performance data
SolverPerformance<Type> solverPerf
(
preconditionerName + typeName,
this->fieldName_
);
register label nCells = psi.size();
gpuField<Type> pA(nCells);
gpuField<Type> pT(nCells, pTraits<Type>::zero);
gpuField<Type> wA(nCells);
gpuField<Type> wT(nCells);
scalar wArT = 1e15; //this->matrix_.great_;
scalar wArTold = wArT;
// --- Calculate A.psi and T.psi
this->matrix_.Amul(wA, psi);
this->matrix_.Tmul(wT, psi);
// --- Calculate initial residual and transpose residual fields
gpuField<Type> rA(this->matrix_.source() - wA);
gpuField<Type> rT(this->matrix_.source() - wT);
// --- Calculate normalisation factor
Type normFactor = this->normFactor(psi, wA, pA);
if (LduMatrix<Type, DType, LUType>::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = cmptDivide(gSumCmptMag(rA), normFactor);
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
this->minIter_ > 0
|| !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<typename LduMatrix<Type, DType, LUType>::preconditioner>
preconPtr = LduMatrix<Type, DType, LUType>::preconditioner::New
(
*this,
this->controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA);
preconPtr->preconditionT(wT, rT);
// --- Update search directions:
wArT = gSumProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
thrust::copy(wA.begin(),wA.end(),pA.begin());
thrust::copy(wT.begin(),wT.end(),pT.begin());
}
else
{
scalar beta = wArT/wArTold;
thrust::transform
(
wA.begin(),
wA.end(),
thrust::make_transform_iterator
(
pA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(beta)
),
pA.begin(),
addOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
wT.begin(),
wT.end(),
thrust::make_transform_iterator
(
pT.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(beta)
),
pT.begin(),
addOperatorFunctor<Type,Type,Type>()
);
}
// --- Update preconditioned residuals
this->matrix_.Amul(wA, pA);
this->matrix_.Tmul(wT, pT);
scalar wApT = gSumProd(wA, pT);
// --- Test for singularity
if
(
solverPerf.checkSingularity
(
cmptDivide(pTraits<Type>::one*mag(wApT), normFactor)
)
)
{
break;
}
// --- Update solution and residual:
scalar alpha = wArT/wApT;
thrust::transform
(
psi.begin(),
psi.end(),
thrust::make_transform_iterator
(
pA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
psi.begin(),
addOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
rA.begin(),
rA.end(),
thrust::make_transform_iterator
(
wA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
rA.begin(),
subtractOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
rT.begin(),
rT.end(),
thrust::make_transform_iterator
(
wT.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
rT.begin(),
subtractOperatorFunctor<Type,Type,Type>()
);
solverPerf.finalResidual() =
cmptDivide(gSumCmptMag(rA), normFactor);
} while
(
(
solverPerf.nIterations()++ < this->maxIter_
&& !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
|| solverPerf.nIterations() < this->minIter_
);
}
return solverPerf;
}
