void PushPairInto
( Matrix<Real>& s,
Matrix<Real>& z,
const Matrix<Real>& w,
const Matrix<Int>& orders,
const Matrix<Int>& firstInds,
Real wMaxNormLimit )
{
DEBUG_ONLY(CSE cse("soc::PushPairInto"))
Matrix<Real> sLower, zLower;
soc::LowerNorms( s, sLower, orders, firstInds );
soc::LowerNorms( z, zLower, orders, firstInds );
const Int height = s.Height();
for( Int i=0; i<height; ++i )
{
const Real w0 = w.Get(i,0);
const Int firstInd = firstInds.Get(i,0);
if( i == firstInd && w0 > wMaxNormLimit )
{
// TODO: Switch to a non-adhoc modification
s.Update( i, 0, Real(1)/wMaxNormLimit );
z.Update( i, 0, Real(1)/wMaxNormLimit );
}
}
}
double gen_adjsrc
( const Matrix<Complex<double>>& S,
const Matrix<Complex<double>>& O,
Matrix<Complex<double>>& A )
{
// TODO: Compute local misfits and then sum the result with an
// MPI_Allreduce summation
// NOTE: This routine should already work but may not be as fast
// as possible.
double l2MisfitSquared=0.0;
const int nsrc = S.Height();
const int nrec = S.Width();
A.Resize( nsrc, nrec );
for (int isrc=0;isrc<nsrc;isrc++ ) {
for (int irec=0;irec<nrec;irec++ ) {
Complex<double> obs = O.Get(irec,isrc);
Complex<double> syn = S.Get(irec,isrc);
A.Set( irec, isrc, obs-syn );
l2MisfitSquared += Abs(A.Get(irec,isrc));
}
}
return l2MisfitSquared;
}
void SOCSquareRoot
( const Matrix<Real>& x,
Matrix<Real>& xRoot,
const Matrix<Int>& orders,
const Matrix<Int>& firstInds )
{
DEBUG_ONLY(CSE cse("SOCSquareRoot"))
Matrix<Real> d;
SOCDets( x, d, orders, firstInds );
ConeBroadcast( d, orders, firstInds );
const Int height = x.Height();
Zeros( xRoot, height, 1 );
for( Int i=0; i<height; )
{
const Int order = orders.Get(i,0);
const Int firstInd = firstInds.Get(i,0);
if( i != firstInd )
LogicError("Inconsistency in orders and firstInds");
const Real eta0 = Sqrt(x.Get(i,0)+Sqrt(d.Get(i,0)))/Sqrt(Real(2));
xRoot.Set( i, 0, eta0 );
for( Int k=1; k<order; ++k )
xRoot.Set( i+k, 0, x.Get(i+k,0)/(2*eta0) );
i += order;
}
}
Matrix operator-(Matrix a,Matrix b){
Matrix result(a.Rows(),a.Cols());
for(int i = 0 ; i < a.Rows() ; i++)
for( int j = 0 ; j < a.Cols() ; j++)
result.Set(j,i,a.Get(j,i) - b.Get(j,i));
return result;
}
void
QuasiDiagonalSolve
( LeftOrRight side, UpperOrLower uplo,
const Matrix<FMain>& d,
const Matrix<F>& dSub,
Matrix<F>& X,
bool conjugated )
{
DEBUG_CSE
const Int m = X.Height();
const Int n = X.Width();
Matrix<F> D( 2, 2 );
if( side == LEFT && uplo == LOWER )
{
if( m == 0 )
return;
DEBUG_ONLY(
if( d.Height() != m )
LogicError
("d was the wrong size: m=",m,",n=",n,", d ~ ",
d.Height()," x ",d.Width());
if( dSub.Height() != m-1 )
LogicError
("dSub was the wrong size: m=",m,",n=",n,", dSub ~ ",
dSub.Height()," x ",dSub.Width());
)
Int i=0;
while( i < m )
{
Int nb;
if( i < m-1 && Abs(dSub.Get(i,0)) > 0 )
nb = 2;
else
nb = 1;
auto XRow = X( IR(i,i+nb), IR(0,n) );
if( nb == 1 )
{
Scale( F(1)/d.Get(i,0), XRow );
}
else
{
D.Set(0,0,d.Get(i,0));
D.Set(1,1,d.Get(i+1,0));
D.Set(1,0,dSub.Get(i,0));
Symmetric2x2Inv( LOWER, D, conjugated );
MakeSymmetric( LOWER, D, conjugated );
Transform2x2Rows( D, X, i, i+1 );
}
i += nb;
}
}
inline Complex<R>
Reflector( Matrix<Complex<R> >& chi, Matrix<Complex<R> >& x )
{
#ifndef RELEASE
CallStackEntry entry("Reflector");
#endif
typedef Complex<R> C;
R norm = Nrm2( x );
C alpha = chi.Get(0,0);
if( norm == 0 && alpha.imag == R(0) )
{
chi.Set(0,0,-chi.Get(0,0));
return C(2);
}
R beta;
if( alpha.real <= 0 )
beta = lapack::SafeNorm( alpha.real, alpha.imag, norm );
else
beta = -lapack::SafeNorm( alpha.real, alpha.imag, norm );
const R one = 1;
const R safeMin = lapack::MachineSafeMin<R>();
const R epsilon = lapack::MachineEpsilon<R>();
const R safeInv = safeMin/epsilon;
Int count = 0;
if( Abs(beta) < safeInv )
{
R invOfSafeInv = one/safeInv;
do
{
++count;
Scale( invOfSafeInv, x );
alpha *= invOfSafeInv;
beta *= invOfSafeInv;
} while( Abs(beta) < safeInv );
norm = Nrm2( x );
if( alpha.real <= 0 )
beta = lapack::SafeNorm( alpha.real, alpha.imag, norm );
else
beta = -lapack::SafeNorm( alpha.real, alpha.imag, norm );
}
C tau = C( (beta-alpha.real)/beta, -alpha.imag/beta );
Scale( one/(alpha-beta), x );
for( Int j=0; j<count; ++j )
beta *= safeInv;
chi.Set(0,0,beta);
return tau;
}
void SOCMaxEig
( const Matrix<Real>& x,
Matrix<Real>& maxEigs,
const Matrix<Int>& orders,
const Matrix<Int>& firstInds )
{
DEBUG_ONLY(CSE cse("SOCMaxEig"))
SOCLowerNorms( x, maxEigs, orders, firstInds );
const Int height = x.Height();
for( Int i=0; i<height; ++i )
if( i == firstInds.Get(i,0) )
maxEigs.Set( i, 0, x.Get(i,0)+maxEigs.Get(i,0) );
}
inline R
Reflector( Matrix<R>& chi, Matrix<R>& x )
{
#ifndef RELEASE
CallStackEntry entry("Reflector");
#endif
R norm = Nrm2( x );
if( norm == 0 )
{
chi.Set(0,0,-chi.Get(0,0));
return R(2);
}
R beta;
R alpha = chi.Get(0,0);
if( alpha <= 0 )
beta = lapack::SafeNorm( alpha, norm );
else
beta = -lapack::SafeNorm( alpha, norm );
const R one = 1;
const R safeMin = lapack::MachineSafeMin<R>();
const R epsilon = lapack::MachineEpsilon<R>();
const R safeInv = safeMin/epsilon;
Int count = 0;
if( Abs(beta) < safeInv )
{
R invOfSafeInv = one/safeInv;
do
{
++count;
Scale( invOfSafeInv, x );
alpha *= invOfSafeInv;
beta *= invOfSafeInv;
} while( Abs(beta) < safeInv );
norm = Nrm2( x );
if( alpha <= 0 )
beta = lapack::SafeNorm( alpha, norm );
else
beta = -lapack::SafeNorm( alpha, norm );
}
R tau = (beta-alpha) / beta;
Scale( one/(alpha-beta), x );
for( Int j=0; j<count; ++j )
beta *= safeInv;
chi.Set(0,0,beta);
return tau;
}
Matrix operator^(Matrix a,Matrix b){
Matrix result(3,1);
result.Set(0,0,( a.Get(1,0) * b.Get(2,0) ) - ( a.Get(2,0) * b.Get(1,0) ));
result.Set(1,0,( a.Get(2,0) * b.Get(0,0) ) - ( a.Get(0,0) * b.Get(2,0) ));
result.Set(2,0,( a.Get(0,0) * b.Get(1,0) ) - ( a.Get(1,0) * b.Get(0,0) ));
return result;
}
inline void
SortEig( Matrix<R>& w, Matrix<R>& Z )
{
#ifndef RELEASE
PushCallStack("SortEig");
#endif
const int n = Z.Height();
const int k = Z.Width();
// Initialize the pairs of indices and eigenvalues
std::vector<internal::IndexValuePair<R> > pairs( k );
for( int i=0; i<k; ++i )
{
pairs[i].index = i;
pairs[i].value = w.Get(i,0);
}
// Sort the eigenvalues and simultaneously form the permutation
std::sort
( pairs.begin(), pairs.end(), internal::IndexValuePair<R>::Compare );
// Reorder the eigenvectors and eigenvalues using the new ordering
Matrix<R> ZPerm( n, k );
for( int j=0; j<k; ++j )
{
const int source = pairs[j].index;
MemCopy( ZPerm.Buffer(0,j), Z.LockedBuffer(0,source), n );
w.Set(j,0,pairs[j].value);
}
Z = ZPerm;
#ifndef RELEASE
PopCallStack();
#endif
}
inline SafeProduct<F>
AfterLUPartialPiv( const Matrix<F>& A, const Matrix<Int>& p )
{
#ifndef RELEASE
CallStackEntry entry("determinant::AfterLUPartialPiv");
#endif
if( A.Height() != A.Width() )
LogicError("Cannot compute determinant of nonsquare matrix");
if( A.Height() != p.Height() )
LogicError("Pivot vector is incorrect length");
typedef BASE(F) R;
const Int n = A.Height();
Matrix<F> d;
A.GetDiagonal( d );
const R scale(n);
SafeProduct<F> det( n );
for( Int i=0; i<n; ++i )
{
const F delta = d.Get(i,0);
R alpha = Abs(delta);
det.rho *= delta/alpha;
det.kappa += Log(alpha)/scale;
}
const bool isOdd = PivotParity( p );
if( isOdd )
det.rho = -det.rho;
return det;
}
FrobeniusNorm( const Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("FrobeniusNorm");
#endif
typedef BASE(F) R;
R scale = 0;
R scaledSquare = 1;
const Int width = A.Width();
const Int height = A.Height();
for( Int j=0; j<width; ++j )
{
for( Int i=0; i<height; ++i )
{
const R alphaAbs = Abs(A.Get(i,j));
if( alphaAbs != 0 )
{
if( alphaAbs <= scale )
{
const R relScale = alphaAbs/scale;
scaledSquare += relScale*relScale;
}
else
{
const R relScale = scale/alphaAbs;
scaledSquare = scaledSquare*relScale*relScale + 1;
scale = alphaAbs;
}
}
}
}
return scale*Sqrt(scaledSquare);
}
double Matrix::dot(Matrix other) {
double dot = 0;
for(int i = 0 ; i < 3 ; i ++ ){
dot = dot + (Get(i,0) * other.Get(i,0));
}
return dot;
}
void Transform2x2( const Matrix<T>& G, Matrix<T>& a1, Matrix<T>& a2 )
{
DEBUG_CSE
T* a1Buf = a1.Buffer();
T* a2Buf = a2.Buffer();
const Int inc1 = ( a1.Height() == 1 ? a1.LDim() : 1 );
const Int inc2 = ( a2.Height() == 1 ? a2.LDim() : 1 );
const Int n = ( a1.Height() == 1 ? a1.Width() : a1.Height() );
const T gamma11 = G.Get(0,0);
const T gamma12 = G.Get(0,1);
const T gamma21 = G.Get(1,0);
const T gamma22 = G.Get(1,1);
Transform2x2
( n, gamma11, gamma12, gamma21, gamma22, a1Buf, inc1, a2Buf, inc2 );
}
Matrix::Matrix(Matrix& x) {
int i,j;
AllocMxMem(x.GetZSize(),x.GetSSize());
for (i=1;i<=zSize;i++)
for(j=1;j<=sSize;j++)
Set(i,j,x.Get(i,j));
}
void LLN( const Matrix<F>& L, Matrix<F>& X, bool checkIfSingular )
{
DEBUG_CSE
const Int m = X.Height();
const Int bsize = Blocksize();
for( Int k=0; k<m; k+=bsize )
{
const Int nbProp = Min(bsize,m-k);
const bool in2x2 = ( k+nbProp<m && L.Get(k+nbProp-1,k+nbProp) != F(0) );
const Int nb = ( in2x2 ? nbProp+1 : nbProp );
const Range<Int> ind1( k, k+nb ),
ind2( k+nb, m );
auto L11 = L( ind1, ind1 );
auto L21 = L( ind2, ind1 );
auto X1 = X( ind1, ALL );
auto X2 = X( ind2, ALL );
LLNUnb( L11, X1, checkIfSingular );
Gemm( NORMAL, NORMAL, F(-1), L21, X1, F(1), X2 );
}
}
// ==================================================================================================================
int mainloop() {
this->render.BeginScene();
{
Matrix worldMatrix;
worldMatrix.Identity();
worldMatrix.RotateRPY(t, .3455*t, .7346*t);
struct {
matrix worldMatrix;
matrix viewMatrix;
matrix projectionMatrix;
} viewMatrices;
m_camera->Calculate(render);
viewMatrices.worldMatrix = XMMatrixTranspose(worldMatrix.Get());
viewMatrices.viewMatrix = XMMatrixTranspose(m_camera->GetViewMatrix().Get());
viewMatrices.projectionMatrix = XMMatrixTranspose(m_camera->GetProjectionMatrix().Get());
m_vertexShader->GetParam("MatrixBuffer").SetP(&viewMatrices);
m_fragmentShader->GetBRes("diffuse").Set(m_texture->GetTextureResource());
m_fragmentShader->GetBRes("SampleType").Set(m_textureSampler->GetSamplerState());
m_vertexShader->Render(this->render);
m_fragmentShader->Render(this->render);
m_model->RenderMesh(this->render);
this->t += 0.01;
}
this->render.EndScene();
return 0;
};
inline void
HermitianSign( UpperOrLower uplo, Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("HermitianSign");
#endif
typedef BASE(F) R;
// Get the EVD of A
Matrix<R> w;
Matrix<F> Z;
HermitianEig( uplo, A, w, Z );
// Compute the two-norm of A as the maximum absolute value of its eigvals
const R twoNorm = MaxNorm( w );
// Set the tolerance equal to n ||A||_2 eps, and invert values above it
const int n = A.Height();
const R eps = lapack::MachineEpsilon<R>();
const R tolerance = n*twoNorm*eps;
for( int i=0; i<n; ++i )
{
const R omega = w.Get(i,0);
if( Abs(omega) < tolerance )
w.Set(i,0,0);
else if( omega > 0 )
w.Set(i,0,R(1));
else
w.Set(i,0,R(-1));
}
// Reform the Hermitian matrix with the modified eigenvalues
hermitian_function::ReformHermitianMatrix( uplo, A, w, Z );
}
pair<Base<F>,Base<F>>
HermitianHelper( const DistSparseMatrix<F>& A, Int basisSize )
{
typedef Base<F> Real;
Grid grid( A.Comm() );
DistMatrix<Real,STAR,STAR> T(grid);
Lanczos( A, T, basisSize );
const Int k = T.Height();
if( k == 0 )
return pair<Real,Real>(0,0);
auto d = GetDiagonal( T.Matrix() );
auto dSub = GetDiagonal( T.Matrix(), -1 );
Matrix<Real> w;
HermitianTridiagEig( d, dSub, w );
pair<Real,Real> extremal;
extremal.second = MaxNorm(w);
extremal.first = extremal.second;
for( Int i=0; i<k; ++i )
extremal.first = Min(extremal.first,Abs(w.Get(i,0)));
return extremal;
}
Matrix CCSCMatrix<T,U>::operator*(const Matrix& array) const {
if(this->NRows()!=array.NRows())
throw runtime_error("CSCMatrix::operator*: Dimension mismatch.");
// zero matrix
Matrix result(this->NCols(),array.NCols());
// columns of the input matrix
for(size_t k=0; k<array.NCols(); k++) {
for(size_t i=0; i<m_ncols; i++) {
for(size_t j=m_colptr->at(i); j<m_colptr->at(i+1); j++) {
result(i,k) += m_vals->at(j)*array.Get(m_rows->at(j),k);
}
}
}
return result;
}
void TestMatrix( int m, int n, int ldim )
{
if( m > ldim || ldim == 0 )
throw std::logic_error("Leading dimension must be >= m and nonzero");
std::vector<T> buffer(ldim*n);
for( int j=0; j<n; ++j )
for( int i=0; i<m; ++i )
buffer[i+j*ldim] = i+j*m;
Matrix<T> A( m, n, &buffer[0], ldim );
for( int j=0; j<n; ++j )
for( int i=0; i<m; ++i )
if( A.Get(i,j) != buffer[i+j*ldim] )
throw std::logic_error
("Matrix class was not properly filled with buffer");
const Matrix<T> B( m, n, (const T*)&buffer[0], ldim );
for( int j=0; j<n; ++j )
for( int i=0; i<m; ++i )
if( B.Get(i,j) != buffer[i+j*ldim] )
throw std::logic_error
("Matrix class was not properly filled with const buffer");
const int commRank = mpi::CommRank( mpi::COMM_WORLD );
if( commRank == 0 )
std::cout << "passed" << std::endl;
}
void TestMatrix( Int m, Int n, Int ldim )
{
if( m > ldim || ldim == 0 )
LogicError("Leading dimension must be >= m and nonzero");
vector<T> buffer(ldim*n);
for( Int j=0; j<n; ++j )
for( Int i=0; i<m; ++i )
buffer[i+j*ldim] = i+j*m;
Matrix<T> A( m, n, buffer.data(), ldim );
for( Int j=0; j<n; ++j )
for( Int i=0; i<m; ++i )
if( A.Get(i,j) != buffer[i+j*ldim] )
LogicError
("Matrix class was not properly filled with buffer");
const Matrix<T> B( m, n, (const T*)buffer.data(), ldim );
for( Int j=0; j<n; ++j )
for( Int i=0; i<m; ++i )
if( B.Get(i,j) != buffer[i+j*ldim] )
LogicError
("Matrix class was not properly filled with const buffer");
const Int commRank = mpi::Rank( mpi::COMM_WORLD );
if( commRank == 0 )
cout << "passed" << endl;
}
void
Matrix<T>::UpdateDiagonal( const Matrix<T>& d, Int offset )
{
#ifndef RELEASE
CallStackEntry entry("Matrix::UpdateDiagonal");
if( d.Height() != DiagonalLength(offset) || d.Width() != 1 )
LogicError("d is not a column-vector of the right length");
#endif
const Int diagLength = DiagonalLength(offset);
if( offset >= 0 )
for( Int j=0; j<diagLength; ++j )
Set_( j, j+offset ) += d.Get(j,0);
else
for( Int j=0; j<diagLength; ++j )
Set_( j-offset, j ) += d.Get(j,0);
}
void LUN( const Matrix<F>& U, Matrix<F>& X, bool checkIfSingular )
{
DEBUG_CSE
const Int m = X.Height();
const Int bsize = Blocksize();
const Int kLast = LastOffset( m, bsize );
Int k=kLast, kOld=m;
while( true )
{
const bool in2x2 = ( k>0 && U.Get(k,k-1) != F(0) );
if( in2x2 )
--k;
const Int nb = kOld-k;
const Range<Int> ind0( 0, k ),
ind1( k, k+nb );
auto U01 = U( ind0, ind1 );
auto U11 = U( ind1, ind1 );
auto X0 = X( ind0, ALL );
auto X1 = X( ind1, ALL );
LUNUnb( U11, X1, checkIfSingular );
Gemm( NORMAL, NORMAL, F(-1), U01, X1, F(1), X0 );
if( k == 0 )
break;
kOld = k;
k -= Min(bsize,k);
}
}
ConditionNumber( const Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("ConditionNumber");
#endif
typedef BASE(F) R;
Matrix<F> B( A );
Matrix<R> s;
SVD( B, s );
R cond = 1;
const int numVals = s.Height();
if( numVals > 0 )
cond = s.Get(0,0) / s.Get(numVals-1,0);
return cond;
}
inline typename Base<F>::type
HermitianEntrywiseOneNorm( UpperOrLower uplo, const Matrix<F>& A )
{
#ifndef RELEASE
PushCallStack("HermitianEntrywiseOneNorm");
#endif
if( A.Height() != A.Width() )
throw std::logic_error("Hermitian matrices must be square.");
typedef typename Base<F>::type R;
R norm = 0;
const int height = A.Height();
const int width = A.Width();
if( uplo == UPPER )
{
for( int j=0; j<width; ++j )
{
for( int i=0; i<j; ++i )
{
const R alpha = Abs(A.Get(i,j));
if( i ==j )
norm += alpha;
else
norm += 2*alpha;
}
}
}
else
{
for( int j=0; j<width; ++j )
{
for( int i=j+1; i<height; ++i )
{
const R alpha = Abs(A.Get(i,j));
if( i ==j )
norm += alpha;
else
norm += 2*alpha;
}
}
}
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
Matrix operator*(Matrix a,Matrix b){
int i,j,k;
Matrix result(a.Rows(),b.Cols());
if(a.Cols() != b.Rows())
cerr << "WARNING : matrix inner dimen. not equal\n";
for(i=0;i<a.Rows();i++){
for(k=0;k<b.Cols();k++){
result.Set(i,k,0);
for(j=0;j<a.Cols();j++){
result.Set(i,k,(a.Get(i,j) * b.Get(j,k)) + result.Get(i,k));
}
}
}
return result;
}
Matrix operator*(Matrix a,double b){
Matrix result(a.Rows(),a.Cols());
for( int i = 0 ; i < a.Rows() ; i++ ){
for( int j = 0 ; j < a.Cols() ; j++ ){
result.Set(j,i,a.Get(j,i) * b);
}
}
return result;
}
vector<double> project(basis b, vector<basis> B) {
// first we need to create the matrix
// Getting the support
vector<chain> SupportVec;
for(vector<basis>::iterator iter = B.begin(); iter != B.end(); ++iter) {
list<chain> TempSup = (*iter).Support();
for(list<chain>::const_iterator iter2 = TempSup.begin(); iter2 != TempSup.end(); ++iter2) {
bool found = false;
for(vector<chain>::iterator iter3 = SupportVec.begin(); iter3 != SupportVec.end(); ++iter3) {
if (*iter3 == *iter2) {
found = true;
break;
}
}
if (!found) {
SupportVec.push_back(*iter2);
}
}
}
// Now that we have the basis we can begin to make the matrix
Matrix M;
int n = SupportVec.size();
int m = B.size();
// we use column insert
for(int i = 0; i < m; i++) {
// we need to make the column
vector<double> TempCol(n);
for (int j = 0; j < n; j++) {
basis TempBasis(SupportVec[j]);
TempCol[j] = Prod(B[i], TempBasis);
}
// Now we insert the column
M.ColumnSet(i+1, TempCol);
}
// Now we add the last column
vector<double> TempCol(n);
for (int j = 0; j < n; j++) {
basis TempBasis(SupportVec[j]);
TempCol[j] = Prod(b, TempBasis);
}
M.ColumnSet(m+1, TempCol);
// Now we rowreduce
Matrix R = RowReduce(M);
//Now we have b in terms of elements of B
//Now we read off the last column for coefficients
vector<double> Answer(m);
for (i = 0; i < m; i++) {
Answer[i] = R.Get(i, m);
}
return(Answer);
}
inline void
DiagonalScale
( LeftOrRight side, Orientation orientation,
const Matrix<T>& d, Matrix<T>& X )
{
#ifndef RELEASE
PushCallStack("DiagonalScale");
#endif
const int m = X.Height();
const int n = X.Width();
const int ldim = X.LDim();
if( side == LEFT )
{
for( int i=0; i<m; ++i )
{
const T delta = d.Get(i,0);
T* XBuffer = X.Buffer(i,0);
if( orientation == ADJOINT )
for( int j=0; j<n; ++j )
XBuffer[j*ldim] *= Conj(delta);
else
for( int j=0; j<n; ++j )
XBuffer[j*ldim] *= delta;
}
}
else
{
for( int j=0; j<n; ++j )
{
const T delta = d.Get(j,0);
T* XBuffer = X.Buffer(0,j);
if( orientation == ADJOINT )
for( int i=0; i<m; ++i )
XBuffer[i] *= Conj(delta);
else
for( int i=0; i<m; ++i )
XBuffer[i] *= delta;
}
}
#ifndef RELEASE
PopCallStack();
#endif
}