// @(#)root/matrix:$Name: $:$Id: TMatrixDSym.cxx,v 1.23 2005/03/28 20:38:35 brun Exp $
// Authors: Fons Rademakers, Eddy Offermann Nov 2003
/*************************************************************************
* Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
* All rights reserved. *
* *
* For the licensing terms see $ROOTSYS/LICENSE. *
* For the list of contributors see $ROOTSYS/README/CREDITS. *
*************************************************************************/
//////////////////////////////////////////////////////////////////////////
// //
// TMatrixDSym //
// //
// Implementation of a symmetric matrix in the linear algebra package //
// //
// Note that in this implementation both matrix element m[i][j] and //
// m[j][i] are updated and stored in memory . However, when making the //
// object persistent only the upper right triangle is stored . //
// //
//////////////////////////////////////////////////////////////////////////
#include "TMatrixDSym.h"
#include "TMatrixFSym.h"
#include "TMatrixDLazy.h"
#include "TMatrixDSymCramerInv.h"
#include "TDecompLU.h"
#include "TDecompBK.h"
#include "TMatrixDSymEigen.h"
ClassImp(TMatrixDSym)
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(Int_t no_rows)
{
Allocate(no_rows,no_rows,0,0,1);
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(Int_t row_lwb,Int_t row_upb)
{
const Int_t no_rows = row_upb-row_lwb+1;
Allocate(no_rows,no_rows,row_lwb,row_lwb,1);
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(Int_t no_rows,const Double_t *elements,Option_t *option)
{
// option="F": array elements contains the matrix stored column-wise
// like in Fortran, so a[i,j] = elements[i+no_rows*j],
// else it is supposed that array elements are stored row-wise
// a[i,j] = elements[i*no_cols+j]
//
// array elements are copied
Allocate(no_rows,no_rows);
SetMatrixArray(elements,option);
if (!IsSymmetric()) {
Error("TMatrixDSym(Int_t,Double_t*,Option_t*)","matrix not symmetric");
Invalidate();
}
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(Int_t row_lwb,Int_t row_upb,const Double_t *elements,Option_t *option)
{
// array elements are copied
const Int_t no_rows = row_upb-row_lwb+1;
Allocate(no_rows,no_rows,row_lwb,row_lwb);
SetMatrixArray(elements,option);
if (!IsSymmetric()) {
Error("TMatrixDSym(Int_t,Int_t,Double_t*,Option_t*)","matrix not symmetric");
Invalidate();
}
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(const TMatrixDSym &another) : TMatrixDBase()
{
Assert(another.IsValid());
Allocate(another.GetNrows(),another.GetNcols(),another.GetRowLwb(),another.GetColLwb());
*this = another;
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(const TMatrixFSym &another) : TMatrixDBase()
{
Assert(another.IsValid());
Allocate(another.GetNrows(),another.GetNcols(),another.GetRowLwb(),another.GetColLwb());
*this = another;
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(EMatrixCreatorsOp1 op,const TMatrixDSym &prototype)
{
// Create a matrix applying a specific operation to the prototype.
// Example: TMatrixDSym a(10,12); ...; TMatrixDSym b(TMatrixDBase::kTransposed, a);
// Supported operations are: kZero, kUnit, kTransposed, kInverted and kAtA.
Assert(this != &prototype);
Invalidate();
Assert(prototype.IsValid());
switch(op) {
case kZero:
Allocate(prototype.GetNrows(),prototype.GetNcols(),
prototype.GetRowLwb(),prototype.GetColLwb(),1);
break;
case kUnit:
Allocate(prototype.GetNrows(),prototype.GetNcols(),
prototype.GetRowLwb(),prototype.GetColLwb(),1);
UnitMatrix();
break;
case kTransposed:
Allocate(prototype.GetNcols(), prototype.GetNrows(),
prototype.GetColLwb(),prototype.GetRowLwb());
Transpose(prototype);
break;
case kInverted:
{
Allocate(prototype.GetNrows(),prototype.GetNcols(),
prototype.GetRowLwb(),prototype.GetColLwb(),1);
*this = prototype;
// Since the user can not control the tolerance of this newly created matrix
// we put it to the smallest possible number
const Double_t oldTol = this->SetTol(DBL_MIN);
this->Invert();
this->SetTol(oldTol);
break;
}
case kAtA:
AtMultA(prototype);
break;
default:
Error("TMatrixDSym(EMatrixCreatorOp1,const TMatrixDSym)",
"operation %d not yet implemented", op);
}
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(EMatrixCreatorsOp1 op,const TMatrixD &prototype)
{
Assert(dynamic_cast<TMatrixD *>(this) != &prototype);
Invalidate();
Assert(prototype.IsValid());
switch(op) {
case kAtA:
AtMultA(prototype);
break;
default:
Error("TMatrixDSym(EMatrixCreatorOp1,const TMatrixD)",
"operation %d not yet implemented", op);
}
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(const TMatrixDSym &a,EMatrixCreatorsOp2 op,const TMatrixDSym &b)
{
Invalidate();
Assert(a.IsValid());
Assert(b.IsValid());
switch(op) {
case kPlus:
{
Allocate(a.GetNrows(),a.GetRowLwb(),1);
*this = a;
*this += b;
break;
}
case kMinus:
{
Allocate(a.GetNrows(),a.GetRowLwb(),1);
*this = a;
*this -= b;
break;
}
default:
Error("TMatrixDSym(EMatrixCreatorOp2)", "operation %d not yet implemented", op);
}
}
//______________________________________________________________________________
TMatrixDSym::TMatrixDSym(const TMatrixDSymLazy &lazy_constructor)
{
Allocate(lazy_constructor.GetRowUpb()-lazy_constructor.GetRowLwb()+1,
lazy_constructor.GetRowUpb()-lazy_constructor.GetRowLwb()+1,
lazy_constructor.GetRowLwb(),lazy_constructor.GetRowLwb(),1);
lazy_constructor.FillIn(*this);
if (!IsSymmetric()) {
Error("TMatrixDSym(TMatrixDSymLazy)","matrix not symmetric");
Invalidate();
}
}
//______________________________________________________________________________
void TMatrixDSym::Delete_m(Int_t size,Double_t *&m)
{
// delete data pointer m, if it was assigned on the heap
if (m) {
if (size > kSizeMax)
delete [] m;
m = 0;
}
}
//______________________________________________________________________________
Double_t* TMatrixDSym::New_m(Int_t size)
{
// return data pointer . if requested size <= kSizeMax, assign pointer
// to the stack space
if (size == 0) return 0;
else {
if ( size <= kSizeMax )
return fDataStack;
else {
Double_t *heap = new Double_t[size];
return heap;
}
}
}
//______________________________________________________________________________
Int_t TMatrixDSym::Memcpy_m(Double_t *newp,const Double_t *oldp,Int_t copySize,
Int_t newSize,Int_t oldSize)
{
// copy copySize doubles from *oldp to *newp . However take care of the
// situation where both pointers are assigned to the same stack space
if (copySize == 0 || oldp == newp)
return 0;
else {
if ( newSize <= kSizeMax && oldSize <= kSizeMax ) {
// both pointers are inside fDataStack, be careful with copy direction !
if (newp > oldp) {
for (Int_t i = copySize-1; i >= 0; i--)
newp[i] = oldp[i];
} else {
for (Int_t i = 0; i < copySize; i++)
newp[i] = oldp[i];
}
}
else
memcpy(newp,oldp,copySize*sizeof(Double_t));
}
return 0;
}
//______________________________________________________________________________
void TMatrixDSym::Allocate(Int_t no_rows,Int_t no_cols,Int_t row_lwb,Int_t col_lwb,
Int_t init,Int_t /*nr_nonzeros*/)
{
// Allocate new matrix. Arguments are number of rows, columns, row
// lowerbound (0 default) and column lowerbound (0 default).
if (no_rows < 0 || no_cols < 0)
{
Error("Allocate","no_rows=%d no_cols=%d",no_rows,no_cols);
Invalidate();
return;
}
MakeValid();
fNrows = no_rows;
fNcols = no_cols;
fRowLwb = row_lwb;
fColLwb = col_lwb;
fNelems = fNrows*fNcols;
fIsOwner = kTRUE;
fTol = DBL_EPSILON;
if (fNelems > 0) {
fElements = New_m(fNelems);
if (init)
memset(fElements,0,fNelems*sizeof(Double_t));
} else
fElements = 0;
}
//______________________________________________________________________________
void TMatrixDSym::AtMultA(const TMatrixD &a,Int_t constr)
{
// Create a matrix C such that C = A' * A. In other words,
// c[i,j] = SUM{ a[k,i] * a[k,j] }. Note, matrix C is allocated for constr=1.
Assert(a.IsValid());
if (constr)
Allocate(a.GetNcols(),a.GetNcols(),a.GetColLwb(),a.GetColLwb(),1);
#ifdef CBLAS
const Double_t *ap = a.GetMatrixArray();
Double_t *cp = this->GetMatrixArray();
cblas_dgemm (CblasRowMajor,CblasTrans,CblasNoTrans,fNrows,fNcols,a.GetNrows(),
1.0,ap,a.GetNcols(),ap,a.GetNcols(),1.0,cp,fNcols);
#else
const Int_t nb = a.GetNoElements();
const Int_t ncolsa = a.GetNcols();
const Int_t ncolsb = ncolsa;
const Double_t * const ap = a.GetMatrixArray();
const Double_t * const bp = ap;
Double_t * cp = this->GetMatrixArray();
const Double_t *acp0 = ap; // Pointer to A[i,0];
while (acp0 < ap+a.GetNcols()) {
for (const Double_t *bcp = bp; bcp < bp+ncolsb; ) { // Pointer to the j-th column of A, Start bcp = A[0,0]
const Double_t *acp = acp0; // Pointer to the i-th column of A, reset to A[0,i]
Double_t cij = 0;
while (bcp < bp+nb) { // Scan the i-th column of A and
cij += *acp * *bcp; // the j-th col of A
acp += ncolsa;
bcp += ncolsb;
}
*cp++ = cij;
bcp -= nb-1; // Set bcp to the (j+1)-th col
}
acp0++; // Set acp0 to the (i+1)-th col
}
Assert(cp == this->GetMatrixArray()+fNelems && acp0 == ap+ncolsa);
#endif
}
//______________________________________________________________________________
void TMatrixDSym::AtMultA(const TMatrixDSym &a,Int_t constr)
{
// Matrix multiplication, with A symmetric
// Create a matrix C such that C = A' * A = A * A = A * A'
// Note, matrix C is allocated for constr=1.
Assert(a.IsValid());
if (constr)
Allocate(a.GetNcols(),a.GetNcols(),a.GetColLwb(),a.GetColLwb(),1);
const Double_t *ap1 = a.GetMatrixArray();
const Double_t *bp1 = ap1;
Double_t *cp1 = this->GetMatrixArray();
#ifdef CBLAS
cblas_dsymm (CblasRowMajor,CblasLeft,CblasUpper,fNrows,fNcols,1.0,
ap1,a.GetNcols(),bp1,a.GetNcols(),0.0,cp1,fNcols);
#else
const Double_t *ap2 = a.GetMatrixArray();
const Double_t *bp2 = ap2;
Double_t *cp2 = this->GetMatrixArray();
for (Int_t i = 0; i < fNrows; i++) {
for (Int_t j = 0; j < fNcols; j++) {
const Double_t b_ij = *bp1++;
*cp1 += b_ij*(*ap1);
Double_t tmp = 0.0;
ap2 = ap1+1;
for (Int_t k = i+1; k < fNrows; k++) {
const Int_t index_kj = k*fNcols+j;
const Double_t a_ik = *ap2++;
const Double_t b_kj = bp2[index_kj];
cp2[index_kj] += a_ik*b_ij;
tmp += a_ik*b_kj;
}
*cp1++ += tmp;
}
ap1 += fNrows+1;
}
#endif
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Use(Int_t row_lwb,Int_t row_upb,Double_t *data)
{
if (row_upb < row_lwb)
{
Error("Use","row_upb=%d < row_lwb=%d",row_upb,row_lwb);
Invalidate();
return *this;
}
Clear();
fNrows = row_upb-row_lwb+1;
fNcols = fNrows;
fRowLwb = row_lwb;
fColLwb = row_lwb;
fNelems = fNrows*fNcols;
fElements = data;
fIsOwner = kFALSE;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::GetSub(Int_t row_lwb,Int_t row_upb,TMatrixDSym &target,Option_t *option) const
{
// Get submatrix [row_lwb..row_upb][row_lwb..row_upb]; The indexing range of the
// returned matrix depends on the argument option:
//
// option == "S" : return [0..row_upb-row_lwb+1][0..row_upb-row_lwb+1] (default)
// else : return [row_lwb..row_upb][row_lwb..row_upb]
Assert(IsValid());
if (row_lwb < fRowLwb || row_lwb > fRowLwb+fNrows-1) {
Error("GetSub","row_lwb out of bounds");
target.Invalidate();
return target;
}
if (row_upb < fRowLwb || row_upb > fRowLwb+fNrows-1) {
Error("GetSub","row_upb out of bounds");
target.Invalidate();
return target;
}
if (row_upb < row_lwb) {
Error("GetSub","row_upb < row_lwb");
target.Invalidate();
return target;
}
TString opt(option);
opt.ToUpper();
const Int_t shift = (opt.Contains("S")) ? 1 : 0;
Int_t row_lwb_sub;
Int_t row_upb_sub;
if (shift) {
row_lwb_sub = 0;
row_upb_sub = row_upb-row_lwb;
} else {
row_lwb_sub = row_lwb;
row_upb_sub = row_upb;
}
target.ResizeTo(row_lwb_sub,row_upb_sub,row_lwb_sub,row_upb_sub);
const Int_t nrows_sub = row_upb_sub-row_lwb_sub+1;
if (target.GetRowIndexArray() && target.GetColIndexArray()) {
for (Int_t irow = 0; irow < nrows_sub; irow++) {
for (Int_t icol = 0; icol < nrows_sub; icol++) {
target(irow+row_lwb_sub,icol+row_lwb_sub) = (*this)(row_lwb+irow,row_lwb+icol);
}
}
} else {
const Double_t *ap = this->GetMatrixArray()+(row_lwb-fRowLwb)*fNrows+(row_lwb-fRowLwb);
Double_t *bp = target.GetMatrixArray();
for (Int_t irow = 0; irow < nrows_sub; irow++) {
const Double_t *ap_sub = ap;
for (Int_t icol = 0; icol < nrows_sub; icol++) {
*bp++ = *ap_sub++;
}
ap += fNrows;
}
}
return target;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::GetSub(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
TMatrixDBase &target,Option_t *option) const
{
// Get submatrix [row_lwb..row_upb][col_lwb..col_upb]; The indexing range of the
// returned matrix depends on the argument option:
//
// option == "S" : return [0..row_upb-row_lwb+1][0..col_upb-col_lwb+1] (default)
// else : return [row_lwb..row_upb][col_lwb..col_upb]
Assert(IsValid());
if (row_lwb < fRowLwb || row_lwb > fRowLwb+fNrows-1) {
Error("GetSub","row_lwb out of bounds");
target.Invalidate();
return target;
}
if (col_lwb < fColLwb || col_lwb > fColLwb+fNcols-1) {
Error("GetSub","col_lwb out of bounds");
target.Invalidate();
return target;
}
if (row_upb < fRowLwb || row_upb > fRowLwb+fNrows-1) {
Error("GetSub","row_upb out of bounds");
target.Invalidate();
return target;
}
if (col_upb < fColLwb || col_upb > fColLwb+fNcols-1) {
Error("GetSub","col_upb out of bounds");
target.Invalidate();
return target;
}
if (row_upb < row_lwb || col_upb < col_lwb) {
Error("GetSub","row_upb < row_lwb || col_upb < col_lwb");
target.Invalidate();
return target;
}
TString opt(option);
opt.ToUpper();
const Int_t shift = (opt.Contains("S")) ? 1 : 0;
const Int_t row_lwb_sub = (shift) ? 0 : row_lwb;
const Int_t row_upb_sub = (shift) ? row_upb-row_lwb : row_upb;
const Int_t col_lwb_sub = (shift) ? 0 : col_lwb;
const Int_t col_upb_sub = (shift) ? col_upb-col_lwb : col_upb;
target.ResizeTo(row_lwb_sub,row_upb_sub,col_lwb_sub,col_upb_sub);
const Int_t nrows_sub = row_upb_sub-row_lwb_sub+1;
const Int_t ncols_sub = col_upb_sub-col_lwb_sub+1;
if (target.GetRowIndexArray() && target.GetColIndexArray()) {
for (Int_t irow = 0; irow < nrows_sub; irow++) {
for (Int_t icol = 0; icol < ncols_sub; icol++) {
target(irow+row_lwb_sub,icol+col_lwb_sub) = (*this)(row_lwb+irow,col_lwb+icol);
}
}
} else {
const Double_t *ap = this->GetMatrixArray()+(row_lwb-fRowLwb)*fNcols+(col_lwb-fColLwb);
Double_t *bp = target.GetMatrixArray();
for (Int_t irow = 0; irow < nrows_sub; irow++) {
const Double_t *ap_sub = ap;
for (Int_t icol = 0; icol < ncols_sub; icol++) {
*bp++ = *ap_sub++;
}
ap += fNcols;
}
}
return target;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::SetSub(Int_t row_lwb,const TMatrixDBase &source)
{
// Insert matrix source starting at [row_lwb][row_lwb], thereby overwriting the part
// [row_lwb..row_lwb+nrows_source][row_lwb..row_lwb+nrows_source];
Assert(IsValid());
Assert(source.IsValid());
if (!source.IsSymmetric()) {
Error("SetSub","source matrix is not symmetric");
Invalidate();
return *this;
}
if (row_lwb < fRowLwb || row_lwb > fRowLwb+fNrows-1) {
Error("SetSub","row_lwb outof bounds");
Invalidate();
return *this;
}
const Int_t nRows_source = source.GetNrows();
if (row_lwb+nRows_source > fRowLwb+fNrows) {
Error("SetSub","source matrix too large");
Invalidate();
return *this;
}
if (source.GetRowIndexArray() && source.GetColIndexArray()) {
const Int_t rowlwb_s = source.GetRowLwb();
for (Int_t irow = 0; irow < nRows_source; irow++) {
for (Int_t icol = 0; icol < nRows_source; icol++) {
(*this)(row_lwb+irow,row_lwb+icol) = source(rowlwb_s+irow,rowlwb_s+icol);
}
}
} else {
const Double_t *bp = source.GetMatrixArray();
Double_t *ap = this->GetMatrixArray()+(row_lwb-fRowLwb)*fNrows+(row_lwb-fRowLwb);
for (Int_t irow = 0; irow < nRows_source; irow++) {
Double_t *ap_sub = ap;
for (Int_t icol = 0; icol < nRows_source; icol++) {
*ap_sub++ = *bp++;
}
ap += fNrows;
}
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::SetSub(Int_t row_lwb,Int_t col_lwb,const TMatrixDBase &source)
{
// Insert matrix source starting at [row_lwb][col_lwb] in a symmetric fashion, thereby overwriting the part
// [row_lwb..row_lwb+nrows_source][row_lwb..row_lwb+nrows_source];
Assert(IsValid());
Assert(source.IsValid());
if (row_lwb < fRowLwb || row_lwb > fRowLwb+fNrows-1) {
Error("SetSub","row_lwb out of bounds");
Invalidate();
return *this;
}
if (col_lwb < fColLwb || col_lwb > fColLwb+fNcols-1) {
Error("SetSub","col_lwb out of bounds");
Invalidate();
return *this;
}
const Int_t nRows_source = source.GetNrows();
const Int_t nCols_source = source.GetNcols();
if (row_lwb+nRows_source > fRowLwb+fNrows || col_lwb+nCols_source > fRowLwb+fNrows) {
Error("SetSub","source matrix too large");
Invalidate();
return *this;
}
if (col_lwb+nCols_source > fRowLwb+fNrows || row_lwb+nRows_source > fRowLwb+fNrows) {
Error("SetSub","source matrix too large");
Invalidate();
return *this;
}
const Int_t rowlwb_s = source.GetRowLwb();
const Int_t collwb_s = source.GetColLwb();
if (row_lwb >= col_lwb) {
// lower triangle
Int_t irow;
for (irow = 0; irow < nRows_source; irow++) {
for (Int_t icol = 0; col_lwb+icol <= row_lwb+irow &&
icol < nCols_source; icol++) {
(*this)(row_lwb+irow,col_lwb+icol) = source(irow+rowlwb_s,icol+collwb_s);
}
}
// upper triangle
for (irow = 0; irow < nCols_source; irow++) {
for (Int_t icol = nRows_source-1; row_lwb+icol > irow+col_lwb &&
icol >= 0; icol--) {
(*this)(col_lwb+irow,row_lwb+icol) = source(icol+rowlwb_s,irow+collwb_s);
}
}
} else {
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::SetMatrixArray(const Double_t *data,Option_t *option)
{
TMatrixDBase::SetMatrixArray(data,option);
if (!this->IsSymmetric()) {
Error("SetMatrixArray","Matrix is not symmetric after Set");
Invalidate();
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::Shift(Int_t row_shift,Int_t col_shift)
{
if (row_shift != col_shift) {
Error("Shift","row_shift != col_shift");
Invalidate();
return *this;
}
return TMatrixDBase::Shift(row_shift,col_shift);
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::ResizeTo(Int_t nrows,Int_t ncols,Int_t /*nr_nonzeros*/)
{
// Set size of the matrix to nrows x ncols
// New dynamic elements are created, the overlapping part of the old ones are
// copied to the new structures, then the old elements are deleted.
Assert(IsValid());
if (!fIsOwner) {
Error("ResizeTo(Int_t,Int_t)","Not owner of data array,cannot resize");
Invalidate();
return *this;
}
if (nrows != ncols) {
Error("ResizeTo(Int_t,Int_t)","nrows != ncols");
Invalidate();
return *this;
}
if (fNelems > 0) {
if (fNrows == nrows && fNcols == ncols)
return *this;
else if (nrows == 0 || ncols == 0) {
fNrows = nrows; fNcols = ncols;
Clear();
return *this;
}
Double_t *elements_old = GetMatrixArray();
const Int_t nelems_old = fNelems;
const Int_t nrows_old = fNrows;
const Int_t ncols_old = fNcols;
Allocate(nrows,ncols);
Assert(IsValid());
Double_t *elements_new = GetMatrixArray();
// new memory should be initialized but be careful ot to wipe out the stack
// storage. Initialize all when old or new storage was on the heap
if (fNelems > kSizeMax || nelems_old > kSizeMax)
memset(elements_new,0,fNelems*sizeof(Double_t));
else if (fNelems > nelems_old)
memset(elements_new+nelems_old,0,(fNelems-nelems_old)*sizeof(Double_t));
// Copy overlap
const Int_t ncols_copy = TMath::Min(fNcols,ncols_old);
const Int_t nrows_copy = TMath::Min(fNrows,nrows_old);
const Int_t nelems_new = fNelems;
if (ncols_old < fNcols) {
for (Int_t i = nrows_copy-1; i >= 0; i--)
Memcpy_m(elements_new+i*fNcols,elements_old+i*ncols_old,ncols_copy,
nelems_new,nelems_old);
} else {
for (Int_t i = 0; i < nrows_copy; i++)
Memcpy_m(elements_new+i*fNcols,elements_old+i*ncols_old,ncols_copy,
nelems_new,nelems_old);
}
Delete_m(nelems_old,elements_old);
} else {
Allocate(nrows,ncols,0,0,1);
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::ResizeTo(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
Int_t /*nr_nonzeros*/)
{
// Set size of the matrix to [row_lwb:row_upb] x [col_lwb:col_upb]
// New dynamic elemenst are created, the overlapping part of the old ones are
// copied to the new structures, then the old elements are deleted.
Assert(IsValid());
if (!fIsOwner) {
Error("ResizeTo(Int_t,Int_t,Int_t,Int_t)","Not owner of data array,cannot resize");
Invalidate();
return *this;
}
if (row_lwb != col_lwb) {
Error("ResizeTo(Int_t,Int_t,Int_t,Int_t)","row_lwb != col_lwb");
Invalidate();
return *this;
}
if (row_upb != col_upb) {
Error("ResizeTo(Int_t,Int_t,Int_t,Int_t)","row_upb != col_upb");
Invalidate();
return *this;
}
const Int_t new_nrows = row_upb-row_lwb+1;
const Int_t new_ncols = col_upb-col_lwb+1;
if (fNelems > 0) {
if (fNrows == new_nrows && fNcols == new_ncols &&
fRowLwb == row_lwb && fColLwb == col_lwb)
return *this;
else if (new_nrows == 0 || new_ncols == 0) {
fNrows = new_nrows; fNcols = new_ncols;
fRowLwb = row_lwb; fColLwb = col_lwb;
Clear();
return *this;
}
Double_t *elements_old = GetMatrixArray();
const Int_t nelems_old = fNelems;
const Int_t nrows_old = fNrows;
const Int_t ncols_old = fNcols;
const Int_t rowLwb_old = fRowLwb;
const Int_t colLwb_old = fColLwb;
Allocate(new_nrows,new_ncols,row_lwb,col_lwb);
Assert(IsValid());
Double_t *elements_new = GetMatrixArray();
// new memory should be initialized but be careful ot to wipe out the stack
// storage. Initialize all when old or new storag ewas on the heap
if (fNelems > kSizeMax || nelems_old > kSizeMax)
memset(elements_new,0,fNelems*sizeof(Double_t));
else if (fNelems > nelems_old)
memset(elements_new+nelems_old,0,(fNelems-nelems_old)*sizeof(Double_t));
// Copy overlap
const Int_t rowLwb_copy = TMath::Max(fRowLwb,rowLwb_old);
const Int_t colLwb_copy = TMath::Max(fColLwb,colLwb_old);
const Int_t rowUpb_copy = TMath::Min(fRowLwb+fNrows-1,rowLwb_old+nrows_old-1);
const Int_t colUpb_copy = TMath::Min(fColLwb+fNcols-1,colLwb_old+ncols_old-1);
const Int_t nrows_copy = rowUpb_copy-rowLwb_copy+1;
const Int_t ncols_copy = colUpb_copy-colLwb_copy+1;
if (nrows_copy > 0 && ncols_copy > 0) {
const Int_t colOldOff = colLwb_copy-colLwb_old;
const Int_t colNewOff = colLwb_copy-fColLwb;
if (ncols_old < fNcols) {
for (Int_t i = nrows_copy-1; i >= 0; i--) {
const Int_t iRowOld = rowLwb_copy+i-rowLwb_old;
const Int_t iRowNew = rowLwb_copy+i-fRowLwb;
Memcpy_m(elements_new+iRowNew*fNcols+colNewOff,
elements_old+iRowOld*ncols_old+colOldOff,ncols_copy,fNelems,nelems_old);
}
} else {
for (Int_t i = 0; i < nrows_copy; i++) {
const Int_t iRowOld = rowLwb_copy+i-rowLwb_old;
const Int_t iRowNew = rowLwb_copy+i-fRowLwb;
Memcpy_m(elements_new+iRowNew*fNcols+colNewOff,
elements_old+iRowOld*ncols_old+colOldOff,ncols_copy,fNelems,nelems_old);
}
}
}
Delete_m(nelems_old,elements_old);
} else {
Allocate(new_nrows,new_ncols,row_lwb,col_lwb,1);
}
return *this;
}
//______________________________________________________________________________
Double_t TMatrixDSym::Determinant() const
{
const TMatrixD &tmp = *this;
TDecompLU lu(tmp,fTol);
Double_t d1,d2;
lu.Det(d1,d2);
if (TMath::Abs(d2) > 52.0)
::Warning("TMatrixDSym::Determinant","Determinant under/over-flows double: det= %.4f 2^%.0f",d1,d2);
return d1*TMath::Power(2.0,d2);
}
//______________________________________________________________________________
void TMatrixDSym::Determinant(Double_t &d1,Double_t &d2) const
{
const TMatrixD &tmp = *this;
TDecompLU lu(tmp,fTol);
lu.Det(d1,d2);
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Invert(Double_t *det)
{
// Invert the matrix and calculate its determinant
// Notice that we need to invoke an additional LU decomposition in order to
// calculate the determinant beacuse the Bunch-Kaufman does not result in a
// convenient triagularr matrix .
if (det)
*det = this->Determinant();
TDecompBK bk(*this,fTol);
bk.Invert(*this);
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::InvertFast(Double_t *det)
{
// Invert the matrix and calculate its determinant
Assert(IsValid());
const Char_t nRows = Char_t(GetNrows());
switch (nRows) {
case 1:
{
Double_t *pM = this->GetMatrixArray();
if (*pM == 0.) Invalidate();
else *pM = 1.0/(*pM);
return *this;
}
case 2:
{
TMatrixDSymCramerInv::Inv2x2(*this,det);
return *this;
}
case 3:
{
TMatrixDSymCramerInv::Inv3x3(*this,det);
return *this;
}
case 4:
{
TMatrixDSymCramerInv::Inv4x4(*this,det);
return *this;
}
case 5:
{
TMatrixDSymCramerInv::Inv5x5(*this,det);
return *this;
}
case 6:
{
TMatrixDSymCramerInv::Inv6x6(*this,det);
return *this;
}
default:
{
if (det)
*det = this->Determinant();
TDecompBK bk(*this,fTol);
bk.Invert(*this);
return *this;
}
}
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Transpose(const TMatrixDSym &source)
{
// Transpose a matrix.
Assert(IsValid());
Assert(source.IsValid());
if (fNrows != source.GetNcols() || fRowLwb != source.GetColLwb())
{
Error("Transpose","matrix has wrong shape");
Invalidate();
return *this;
}
*this = source;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Rank1Update(const TVectorD &v,Double_t alpha)
{
// Perform a rank 1 operation on the matrix:
// A += alpha * v * v^T
Assert(IsValid());
Assert(v.IsValid());
if (v.GetNoElements() < fNrows) {
Error("Rank1Update","vector too short");
Invalidate();
return *this;
}
const Double_t * const pv = v.GetMatrixArray();
Double_t *trp = this->GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < fNrows; i++) {
trp += i; // point to [i,i]
tcp += i*fNcols; // point to [i,i]
const Double_t tmp = alpha*pv[i];
for (Int_t j = i; j < fNcols; j++) {
if (j > i) *tcp += tmp*pv[j];
*trp++ += tmp*pv[j];
tcp += fNcols;
}
tcp -= fNelems-1; // point to [0,i]
}
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Similarity(const TMatrixD &b)
{
// Calculate B * (*this) * B^T , final matrix will be (nrowsb x nrowsb)
// This is a similarity transform when B is orthogonal . It is more
// efficient than applying the actual multiplication because this
// routine realizes that the final matrix is symmetric .
const TMatrixD ba(b,TMatrixD::kMult,*this);
const Int_t nrowsb = b.GetNrows();
if (nrowsb != fNrows)
this->ResizeTo(nrowsb,nrowsb);
#ifdef CBLAS
const Double_t *bap = ba.GetMatrixArray();
const Double_t *bp = b.GetMatrixArray();
Double_t *cp = this->GetMatrixArray();
cblas_dgemm (CblasRowMajor,CblasNoTrans,CblasTrans,fNrows,fNcols,ba.GetNcols(),
1.0,bap,ba.GetNcols(),bp,b.GetNcols(),1.0,cp,fNcols);
#else
const Int_t nba = ba.GetNoElements();
const Int_t nb = b.GetNoElements();
const Int_t ncolsba = ba.GetNcols();
const Int_t ncolsb = b.GetNcols();
const Double_t * const bap = ba.GetMatrixArray();
const Double_t * const bp = b.GetMatrixArray();
const Double_t * bi1p = bp;
Double_t * cp = this->GetMatrixArray();
Double_t * const cp0 = cp;
Int_t ishift = 0;
const Double_t *barp0 = bap;
while (barp0 < bap+nba) {
const Double_t *brp0 = bi1p;
while (brp0 < bp+nb) {
const Double_t *barp = barp0;
const Double_t *brp = brp0;
Double_t cij = 0;
while (brp < brp0+ncolsb)
cij += *barp++ * *brp++;
*cp++ = cij;
brp0 += ncolsb;
}
barp0 += ncolsba;
bi1p += ncolsb;
cp += ++ishift;
}
Assert(cp == cp0+fNelems+ishift && barp0 == bap+nba);
cp = cp0;
for (Int_t irow = 0; irow < fNrows; irow++) {
const Int_t rowOff1 = irow*fNrows;
for (Int_t icol = 0; icol < irow; icol++) {
const Int_t rowOff2 = icol*fNrows;
cp[rowOff1+icol] = cp[rowOff2+irow];
}
}
#endif
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::Similarity(const TMatrixDSym &b)
{
// Calculate B * (*this) * B^T , final matrix will be (nrowsb x nrowsb)
// This is a similarity transform when B is orthogonal . It is more
// efficient than applying the actual multiplication because this
// routine realizes that the final matrix is symmetric .
#ifdef CBLAS
const TMatrixD abt(*this,TMatrixD::kMultTranspose,b);
const Double_t *abtp = abt.GetMatrixArray();
const Double_t *bp = b.GetMatrixArray();
Double_t *cp = this->GetMatrixArray();
cblas_dsymm (CblasRowMajor,CblasLeft,CblasUpper,fNrows,fNcols,1.0,
bp,b.GetNcols(),abtp,abt.GetNcols(),0.0,cp,fNcols);
#else
const TMatrixD ba(b,TMatrixD::kMult,*this);
const Int_t nba = ba.GetNoElements();
const Int_t nb = b.GetNoElements();
const Int_t ncolsba = ba.GetNcols();
const Int_t ncolsb = b.GetNcols();
const Double_t * const bap = ba.GetMatrixArray();
const Double_t * const bp = b.GetMatrixArray();
const Double_t * bi1p = bp;
Double_t * cp = this->GetMatrixArray();
Double_t * const cp0 = cp;
Int_t ishift = 0;
const Double_t *barp0 = bap;
while (barp0 < bap+nba) {
const Double_t *brp0 = bi1p;
while (brp0 < bp+nb) {
const Double_t *barp = barp0;
const Double_t *brp = brp0;
Double_t cij = 0;
while (brp < brp0+ncolsb)
cij += *barp++ * *brp++;
*cp++ = cij;
brp0 += ncolsb;
}
barp0 += ncolsba;
bi1p += ncolsb;
cp += ++ishift;
}
Assert(cp == cp0+fNelems+ishift && barp0 == bap+nba);
cp = cp0;
for (Int_t irow = 0; irow < fNrows; irow++) {
const Int_t rowOff1 = irow*fNrows;
for (Int_t icol = 0; icol < irow; icol++) {
const Int_t rowOff2 = icol*fNrows;
cp[rowOff1+icol] = cp[rowOff2+irow];
}
}
#endif
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::SimilarityT(const TMatrixD &b)
{
// Calculate B^T * (*this) * B , final matrix will be (ncolsb x ncolsb)
// It is more efficient than applying the actual multiplication because this
// routine realizes that the final matrix is symmetric .
const TMatrixD bta(b,TMatrixD::kTransposeMult,*this);
const Int_t ncolsb = b.GetNcols();
if (ncolsb != fNcols)
this->ResizeTo(ncolsb,ncolsb);
#ifdef CBLAS
const Double_t *btap = bta.GetMatrixArray();
const Double_t *bp = b.GetMatrixArray();
Double_t *cp = this->GetMatrixArray();
cblas_dgemm (CblasRowMajor,CblasNoTrans,CblasNoTrans,fNrows,fNcols,bta.GetNcols(),
1.0,btap,bta.GetNcols(),bp,b.GetNcols(),1.0,cp,fNcols);
#else
const Int_t nbta = bta.GetNoElements();
const Int_t nb = b.GetNoElements();
const Int_t ncolsbta = bta.GetNcols();
const Double_t * const btap = bta.GetMatrixArray();
const Double_t * const bp = b.GetMatrixArray();
Double_t * cp = this->GetMatrixArray();
Double_t * const cp0 = cp;
Int_t ishift = 0;
const Double_t *btarp0 = btap; // Pointer to A[i,0];
const Double_t *bcp0 = bp;
while (btarp0 < btap+nbta) {
for (const Double_t *bcp = bcp0; bcp < bp+ncolsb; ) { // Pointer to the j-th column of B, Start bcp = B[0,0]
const Double_t *btarp = btarp0; // Pointer to the i-th row of A, reset to A[i,0]
Double_t cij = 0;
while (bcp < bp+nb) { // Scan the i-th row of A and
cij += *btarp++ * *bcp; // the j-th col of B
bcp += ncolsb;
}
*cp++ = cij;
bcp -= nb-1; // Set bcp to the (j+1)-th col
}
btarp0 += ncolsbta; // Set ap to the (i+1)-th row
bcp0++;
cp += ++ishift;
}
Assert(cp == cp0+fNelems+ishift && btarp0 == btap+nbta);
cp = cp0;
for (Int_t irow = 0; irow < fNrows; irow++) {
const Int_t rowOff1 = irow*fNrows;
for (Int_t icol = 0; icol < irow; icol++) {
const Int_t rowOff2 = icol*fNrows;
cp[rowOff1+icol] = cp[rowOff2+irow];
}
}
#endif
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator=(const TMatrixDSym &source)
{
if (!AreCompatible(*this,source)) {
Error("operator=","matrices not compatible");
Invalidate();
return *this;
}
if (this != &source) {
TObject::operator=(source);
memcpy(this->GetMatrixArray(),source.fElements,fNelems*sizeof(Double_t));
}
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator=(const TMatrixFSym &source)
{
if (!AreCompatible(*this,source)) {
Error("operator=","matrices not compatible");
Invalidate();
return *this;
}
if (dynamic_cast<TMatrixFSym *>(this) != &source) {
TObject::operator=(source);
const Float_t * const ps = source.GetMatrixArray();
Double_t * const pt = GetMatrixArray();
for (Int_t i = 0; i < fNelems; i++)
pt[i] = (Double_t) ps[i];
fTol = (Double_t)source.GetTol();
}
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator=(const TMatrixDSymLazy &lazy_constructor)
{
Assert(IsValid());
if (lazy_constructor.fRowUpb != GetRowUpb() ||
lazy_constructor.fRowLwb != GetRowLwb()) {
Error("operator=(const TMatrixDSymLazy&)", "matrix is incompatible with "
"the assigned Lazy matrix");
Invalidate();
return *this;
}
lazy_constructor.FillIn(*this);
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator=(Double_t val)
{
// Assign val to every element of the matrix.
Assert(IsValid());
Double_t *ep = fElements;
const Double_t * const ep_last = ep+fNelems;
while (ep < ep_last)
*ep++ = val;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator+=(Double_t val)
{
// Add val to every element of the matrix.
Assert(IsValid());
Double_t *ep = fElements;
const Double_t * const ep_last = ep+fNelems;
while (ep < ep_last)
*ep++ += val;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator-=(Double_t val)
{
// Subtract val from every element of the matrix.
Assert(IsValid());
Double_t *ep = fElements;
const Double_t * const ep_last = ep+fNelems;
while (ep < ep_last)
*ep++ -= val;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator*=(Double_t val)
{
// Multiply every element of the matrix with val.
Assert(IsValid());
Double_t *ep = fElements;
const Double_t * const ep_last = ep+fNelems;
while (ep < ep_last)
*ep++ *= val;
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator+=(const TMatrixDSym &source)
{
// Add the source matrix.
if (!AreCompatible(*this,source)) {
Error("operator+=","matrices not compatible");
Invalidate();
return *this;
}
const Double_t *sp = source.GetMatrixArray();
Double_t *trp = this->GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < fNrows; i++) {
sp += i;
trp += i; // point to [i,i]
tcp += i*fNcols; // point to [i,i]
for (Int_t j = i; j < fNcols; j++) {
if (j > i) *tcp += *sp;
*trp++ += *sp++;
tcp += fNcols;
}
tcp -= fNelems-1; // point to [0,i]
}
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::operator-=(const TMatrixDSym &source)
{
// Subtract the source matrix.
if (!AreCompatible(*this,source)) {
Error("operator-=","matrices not compatible");
Invalidate();
return *this;
}
const Double_t *sp = source.GetMatrixArray();
Double_t *trp = this->GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < fNrows; i++) {
sp += i;
trp += i; // point to [i,i]
tcp += i*fNcols; // point to [i,i]
for (Int_t j = i; j < fNcols; j++) {
if (j > i) *tcp -= *sp;
*trp++ -= *sp++;
tcp += fNcols;
}
tcp -= fNelems-1; // point to [0,i]
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::Apply(const TElementActionD &action)
{
Assert(IsValid());
Double_t val = 0;
Double_t *trp = this->GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < fNrows; i++) {
trp += i; // point to [i,i]
tcp += i*fNcols; // point to [i,i]
for (Int_t j = i; j < fNcols; j++) {
action.Operation(val);
if (j > i) *tcp = val;
*trp++ = val;
tcp += fNcols;
}
tcp -= fNelems-1; // point to [0,i]
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::Apply(const TElementPosActionD &action)
{
// Apply action to each element of the matrix. To action the location
// of the current element is passed.
Assert(IsValid());
Double_t val = 0;
Double_t *trp = this->GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < fNrows; i++) {
action.fI = i+fRowLwb;
trp += i; // point to [i,i]
tcp += i*fNcols; // point to [i,i]
for (Int_t j = i; j < fNcols; j++) {
action.fJ = j+fColLwb;
action.Operation(val);
if (j > i) *tcp = val;
*trp++ = val;
tcp += fNcols;
}
tcp -= fNelems-1; // point to [0,i]
}
return *this;
}
//______________________________________________________________________________
TMatrixDBase &TMatrixDSym::Randomize(Double_t alpha,Double_t beta,Double_t &seed)
{
// randomize matrix element values but keep matrix symmetric
Assert(IsValid());
if (fNrows != fNcols || fRowLwb != fColLwb) {
Error("Randomize(Double_t,Double_t,Double_t &","matrix should be square");
Invalidate();
return *this;
}
const Double_t scale = beta-alpha;
const Double_t shift = alpha/scale;
Double_t *ep = GetMatrixArray();
for (Int_t i = 0; i < fNrows; i++) {
const Int_t off = i*fNcols;
for (Int_t j = 0; j <= i; j++) {
ep[off+j] = scale*(Drand(seed)+shift);
if (i != j) {
ep[j*fNcols+i] = ep[off+j];
}
}
}
return *this;
}
//______________________________________________________________________________
TMatrixDSym &TMatrixDSym::RandomizePD(Double_t alpha,Double_t beta,Double_t &seed)
{
// randomize matrix element values but keep matrix symmetric positive definite
Assert(IsValid());
if (fNrows != fNcols || fRowLwb != fColLwb) {
Error("RandomizeSym(Double_t,Double_t,Double_t &","matrix should be square");
Invalidate();
return *this;
}
const Double_t scale = beta-alpha;
const Double_t shift = alpha/scale;
Double_t *ep = GetMatrixArray();
Int_t i;
for (i = 0; i < fNrows; i++) {
const Int_t off = i*fNcols;
for (Int_t j = 0; j <= i; j++)
ep[off+j] = scale*(Drand(seed)+shift);
}
for (i = fNrows-1; i >= 0; i--) {
const Int_t off1 = i*fNcols;
for (Int_t j = i; j >= 0; j--) {
const Int_t off2 = j*fNcols;
ep[off1+j] *= ep[off2+j];
for (Int_t k = j-1; k >= 0; k--) {
ep[off1+j] += ep[off1+k]*ep[off2+k];
}
if (i != j)
ep[off2+i] = ep[off1+j];
}
}
return *this;
}
//______________________________________________________________________________
const TMatrixD TMatrixDSym::EigenVectors(TVectorD &eigenValues) const
{
// Return a matrix containing the eigen-vectors ordered by descending eigen-values.
// For full functionality use TMatrixDSymEigen .
TMatrixDSymEigen eigen(*this);
eigenValues.ResizeTo(fNrows);
eigenValues = eigen.GetEigenValues();
return eigen.GetEigenVectors();
}
//______________________________________________________________________________
Bool_t operator==(const TMatrixDSym &m1,const TMatrixDSym &m2)
{
// Check to see if two matrices are identical.
if (!AreCompatible(m1,m2)) return kFALSE;
return (memcmp(m1.GetMatrixArray(),m2.GetMatrixArray(),
m1.GetNoElements()*sizeof(Double_t)) == 0);
}
//______________________________________________________________________________
TMatrixDSym operator+(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
TMatrixDSym target(source1);
target += source2;
return target;
}
//______________________________________________________________________________
TMatrixDSym operator+(const TMatrixDSym &source1,Double_t val)
{
TMatrixDSym target(source1);
target += val;
return target;
}
//______________________________________________________________________________
TMatrixDSym operator+(Double_t val,const TMatrixDSym &source1)
{
return operator+(source1,val);
}
//______________________________________________________________________________
TMatrixDSym operator-(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
TMatrixDSym target(source1);
target -= source2;
return target;
}
//______________________________________________________________________________
TMatrixDSym operator-(const TMatrixDSym &source1,Double_t val)
{
TMatrixDSym target(source1);
target -= val;
return target;
}
//______________________________________________________________________________
TMatrixDSym operator-(Double_t val,const TMatrixDSym &source1)
{
return -1.0*operator-(source1,val);
}
//______________________________________________________________________________
TMatrixDSym operator*(const TMatrixDSym &source1,Double_t val)
{
TMatrixDSym target(source1);
target *= val;
return target;
}
//______________________________________________________________________________
TMatrixDSym operator*(Double_t val,const TMatrixDSym &source1)
{
return operator*(source1,val);
}
//______________________________________________________________________________
TMatrixDSym operator&&(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// Logical AND
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator&&(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = (*scp1 != 0.0) & (*sp2 != 0.0);
*trp++ = (*srp1++ != 0.0 && *sp2++ != 0.0);
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator||(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// Logical Or
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator||(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = (*scp1 != 0.0) & (*sp2 != 0.0);
*trp++ = (*srp1++ != 0.0 || *sp2++ != 0.0);
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator>(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// source1 > source2
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator>(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = *scp1 > *sp2;
*trp++ = *srp1++ > *sp2++;
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
/*
//______________________________________________________________________________
TMatrixDSym operator>(const TMatrixDSym &source1,Double_t val)
{
// source1 > val
TMatrixDSym target; target.ResizeTo(source1);
const Double_t *sp = source1.GetMatrixArray();
Double_t *tp = target.GetMatrixArray();
const Double_t * const tp_last = tp+target.GetNoElements();
while (tp < tp_last) {
*tp++ = (*sp > val); sp++;
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator>(Double_t val,const TMatrixDSym &source1)
{
// val > source1
return operator<=(source1,val);
}
*/
//______________________________________________________________________________
TMatrixDSym operator>=(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// source1 >= source2
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator>=(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = *scp1 >= *sp2;
*trp++ = *srp1++ >= *sp2++;
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
/*
//______________________________________________________________________________
TMatrixDSym operator>=(const TMatrixDSym &source1,Double_t val)
{
// source1 >= val
TMatrixDSym target; target.ResizeTo(source1);
const Double_t *sp = source1.GetMatrixArray();
Double_t *tp = target.GetMatrixArray();
const Double_t * const tp_last = tp+target.GetNoElements();
while (tp < tp_last) {
*tp++ = (*sp >= val); sp++;
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator>=(Double_t val,const TMatrixDSym &source1)
{
// val >= source1
return operator<(source1,val);
}
*/
//______________________________________________________________________________
TMatrixDSym operator<=(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// source1 <= source2
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator<=(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = *scp1 <= *sp2;
*trp++ = *srp1++ <= *sp2++;
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
/*
//______________________________________________________________________________
TMatrixDSym operator<=(const TMatrixDSym &source1,Double_t val)
{
// source1 <= val
TMatrixDSym target; target.ResizeTo(source1);
const Double_t *sp = source1.GetMatrixArray();
Double_t *tp = target.GetMatrixArray();
const Double_t * const tp_last = tp+target.GetNoElements();
while (tp < tp_last) {
*tp++ = (*sp <= val); sp++;
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator<=(Double_t val,const TMatrixDSym &source1)
{
// val <= source1
return operator>(source1,val);
}
*/
//______________________________________________________________________________
TMatrixDSym operator<(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// source1 < source2
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator<(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = *scp1 < *sp2;
*trp++ = *srp1++ < *sp2++;
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
/*
//______________________________________________________________________________
TMatrixDSym operator<(const TMatrixDSym &source1,Double_t val)
{
// source1 < val
TMatrixDSym target; target.ResizeTo(source1);
const Double_t *sp = source1.GetMatrixArray();
Double_t *tp = target.GetMatrixArray();
const Double_t * const tp_last = tp+target.GetNoElements();
while (tp < tp_last) {
*tp++ = (*sp < val); sp++;
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator<(Double_t val,const TMatrixDSym &source1)
{
// val < source1
return operator>(source1,val);
}
*/
/*
//______________________________________________________________________________
TMatrixDSym operator==(const TMatrixDSym &source1,const TMatrixDSym &source2)
{
// source1 == source2
TMatrixDSym target;
if (!AreCompatible(source1,source2)) {
Error("operator==(const TMatrixDSym&,const TMatrixDSym&)","matrices not compatible");
target.Invalidate();
return target;
}
target.ResizeTo(source1);
const Int_t nelems = target.GetNoElements();
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Double_t *srp1 = source1.GetMatrixArray();
const Double_t *scp1 = srp1;
const Double_t *sp2 = source2.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = trp; // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp2 += i;
srp1 += i; trp += i; // point to [i,i]
scp1 += i*ncols; tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp = *scp1 == *sp2;
*trp++ = *srp1++ == *sp2++;
scp1 += ncols;
tcp += ncols;
}
scp1 -= nelems-1; // point to [0,i]
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator==(const TMatrixDSym &source1,Double_t val)
{
// source1 == val
TMatrixDSym target; target.ResizeTo(source1);
const Double_t *sp = source1.GetMatrixArray();
Double_t *tp = target.GetMatrixArray();
const Double_t * const tp_last = tp+target.GetNoElements();
while (tp < tp_last) {
*tp++ = (*sp == val); sp++;
}
return target;
}
//______________________________________________________________________________
TMatrixDSym operator==(Double_t val,const TMatrixDSym &source1)
{
// val == source1
return operator==(source1,val);
}
*/
//______________________________________________________________________________
TMatrixDSym &Add(TMatrixDSym &target,Double_t scalar,const TMatrixDSym &source)
{
// Modify addition: target += scalar * source.
if (!AreCompatible(target,source)) {
::Error("Add","matrices not compatible");
target.Invalidate();
return target;
}
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Int_t nelems = target.GetNoElements();
const Double_t *sp = source.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = target.GetMatrixArray(); // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp += i;
trp += i; // point to [i,i]
tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
const Double_t tmp = scalar * *sp++;
if (j > i) *tcp += tmp;
*trp++ += tmp;
tcp += ncols;
}
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
TMatrixDSym &ElementMult(TMatrixDSym &target,const TMatrixDSym &source)
{
// Multiply target by the source, element-by-element.
if (!AreCompatible(target,source)) {
::Error("ElementMult","matrices not compatible");
target.Invalidate();
return target;
}
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Int_t nelems = target.GetNoElements();
const Double_t *sp = source.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = target.GetMatrixArray(); // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp += i;
trp += i; // point to [i,i]
tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
if (j > i) *tcp *= *sp;
*trp++ *= *sp++;
tcp += ncols;
}
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
TMatrixDSym &ElementDiv(TMatrixDSym &target,const TMatrixDSym &source)
{
// Multiply target by the source, element-by-element.
if (!AreCompatible(target,source)) {
::Error("ElementDiv","matrices not compatible");
target.Invalidate();
return target;
}
const Int_t nrows = target.GetNrows();
const Int_t ncols = target.GetNcols();
const Int_t nelems = target.GetNoElements();
const Double_t *sp = source.GetMatrixArray();
Double_t *trp = target.GetMatrixArray(); // pointer to UR part and diagonal, traverse row-wise
Double_t *tcp = target.GetMatrixArray(); // pointer to LL part, traverse col-wise
for (Int_t i = 0; i < nrows; i++) {
sp += i;
trp += i; // point to [i,i]
tcp += i*ncols; // point to [i,i]
for (Int_t j = i; j < ncols; j++) {
Assert(*sp != 0.0);
if (j > i) *tcp /= *sp;
*trp++ /= *sp++;
tcp += ncols;
}
tcp -= nelems-1; // point to [0,i]
}
return target;
}
//______________________________________________________________________________
void TMatrixDSym::Streamer(TBuffer &R__b)
{
// Stream an object of class TMatrixDSym.
if (R__b.IsReading()) {
UInt_t R__s, R__c;
Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
Clear();
TMatrixDBase::Class()->ReadBuffer(R__b,this,R__v,R__s,R__c);
fElements = new Double_t[fNelems];
Int_t i;
for (i = 0; i < fNrows; i++) {
R__b.ReadFastArray(fElements+i*fNcols+i,fNcols-i);
}
// copy to Lower left triangle
for (i = 0; i < fNrows; i++) {
for (Int_t j = 0; j < i; j++) {
fElements[i*fNcols+j] = fElements[j*fNrows+i];
}
}
if (fNelems <= kSizeMax) {
memcpy(fDataStack,fElements,fNelems*sizeof(Double_t));
delete [] fElements;
fElements = fDataStack;
}
} else {
TMatrixDBase::Class()->WriteBuffer(R__b,this);
// Only write the Upper right triangle
for (Int_t i = 0; i < fNrows; i++) {
R__b.WriteFastArray(fElements+i*fNcols+i,fNcols-i);
}
}
}
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