/*
Copyright (c) 2009, UT-Battelle, LLC
All rights reserved

[DMRG++, Version 2.0.0]
[by G.A., Oak Ridge National Laboratory]

UT Battelle Open Source Software License 11242008

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*********************************************************
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*/

/** \ingroup DMRG */
/*@{*/

/*! \file ReflectionOperator
 *
 *  Critical problems:
 *
 *  - support for fermionic reflections
 *
 *  Low priority work that needs to be done:
 *
 *  - support for bases that change from site to site
 *
 */
#ifndef REFLECTION_OPERATOR_H
#define REFLECTION_OPERATOR_H

#include "LAPACK.h"
#include "Matrix.h"
#include "PackIndices.h" // in PsimagLite
#include "ProgressIndicator.h"
#include "ReflectionTransform.h"
#include "Sort.h"

namespace Dmrg
{

template <typename LeftRightSuperType, typename ConcurrencyType>
class ReflectionOperator
{

	typedef PsimagLite::PackIndices PackIndicesType;
	typedef typename LeftRightSuperType::SparseMatrixType
	    SparseMatrixType;
	typedef typename LeftRightSuperType::RealType RealType;
	typedef typename SparseMatrixType::value_type ComplexOrRealType;
	typedef typename PsimagLite::Vector<ComplexOrRealType>::Type VectorType;
	typedef SparseVector<typename VectorType::value_type> SparseVectorType;
	typedef ReflectionTransform<RealType, SparseMatrixType> ReflectionTransformType;

	enum { AVAILABLE,
		NOT_AVAILABLE,
		COLOR };

public:

	ReflectionOperator(LeftRightSuperType& lrs,
	    ConcurrencyType& concurrency,
	    SizeType n0,
	    bool isEnabled,
	    SizeType expandSys)
	    : lrs_(lrs)
	    , concurrency_(concurrency)
	    , n0_(n0)
	    , progress_("ReflectionOperator", 0)
	    , isEnabled_(isEnabled)
	    , expandSys_(expandSys)
	    , reflectedLeft_(n0_, n0_)
	    , reflectedRight_(n0_, n0_)
	    , reflectionTransform_(false)
	{
		SizeType counter = 0;
		for (SizeType i = 0; i < reflectedLeft_.rank(); i++) {
			reflectedLeft_.setRow(i, counter);
			reflectedLeft_.pushCol(i);
			reflectedLeft_.pushValue(1);
			counter++;
		}

		reflectedLeft_.setRow(reflectedLeft_.rank(), counter);
		reflectedRight_ = reflectedLeft_;
	}

	void update(const typename PsimagLite::Vector<SizeType>::Type& sectors)
	{
		if (!isEnabled_)
			return;
		//		SparseMatrixType sSuper;
		//		setS(sSuper);
		SparseMatrixType sSector;
		setSsector(sSector, sectors);
		updateReflected();
		//		extractCurrentSector(sSector,sSuper,sectors);
		reflectionTransform_.update(sSector);
	}

	template <typename SomeStructType>
	void updateKeptStates(SizeType& keptStates,
	    const SomeStructType& cacheLeft,
	    const SomeStructType& cacheRight)
	{
		const PsimagLite::Matrix<ComplexOrRealType>& transform1 = cacheLeft.transform;
		const PsimagLite::Matrix<ComplexOrRealType>& transform2 = cacheRight.transform;

		if (!isEnabled_)
			return;
		if (keptStates >= transform1.n_col())
			return;
		PsimagLite::OstringStream msg;
		msg << "updateKeptStates";
		progress_.printline(msg, std::cout);

		check(cacheLeft.removedIndices, reflectedLeft_, transform1, transform2);
		check(cacheRight.removedIndices, reflectedRight_, transform2, transform1);
	}

	void transform(SparseMatrixType& matrixA,
	    SparseMatrixType& matrixB,
	    const SparseMatrixType& matrix) const
	{
		assert(isEnabled_);
		reflectionTransform_.transform(matrixA, matrixB, matrix);
	}

	template <typename SomeVectorType>
	void setInitState(const SomeVectorType& initVector,
	    SomeVectorType& initVector1,
	    SomeVectorType& initVector2) const
	{
		assert(isEnabled_);
		return reflectionTransform_.setInitState(initVector, initVector1, initVector2);
	}

	RealType setGroundState(VectorType& gs,
	    const RealType& gsEnergy1,
	    const VectorType& gsVector1,
	    const RealType& gsEnergy2,
	    const VectorType& gsVector2) const
	{
		assert(isEnabled_);
		if (gsEnergy1 <= gsEnergy2) {
			reflectionTransform_.setGs(gs, gsVector1, 1.0);
			return gsEnergy1;
		}
		reflectionTransform_.setGs(gs, gsVector2, -1.0);
		return gsEnergy2;
	}

	const LeftRightSuperType& leftRightSuper() const { return lrs_; }

	bool isEnabled() const { return isEnabled_; }

	void changeBasis(const PsimagLite::Matrix<ComplexOrRealType>& transform1,
	    const PsimagLite::Matrix<ComplexOrRealType>& transform2)
	{
		if (!isEnabled_)
			return;

		SparseMatrixType newreflected;

		changeBasis(newreflected, reflectedLeft_, transform1, transform2);
		//		if (newreflected.rank()!=reflectedLeft_.rank()) {
		//			printFullMatrix(newreflected,"newreflectedLeft",0,1e-6);
		//			transform1.print(std::cerr,1e-6);
		//			transform2.print(std::cerr,1e-6);
		//		}
		reflectedLeft_ = newreflected;
		// normalize(reflectedLeft_);

		changeBasis(newreflected, reflectedRight_, transform2, transform1);
		reflectedRight_ = newreflected;
		// normalize(reflectedRight_);

		//		diagBasis();
	}

	void diagBasis()
	{
		//		SparseMatrixType sSector;
		//		setSsector(sSector);
		//		reflectionTransform_.update(sSector);

		//		const SparseMatrixType& Q1 = reflectionTransform_.getTransform(0);
		//		const SparseMatrixType& Qm = reflectionTransform_.getTransform(1);

		//		SparseMatrixType transf;
		//		transformPartialLeft(transf,Q1,Qm);
		//		PsimagLite::Matrix<ComplexOrRealType> fullm;
		//		crsMatrixToFullMatrix(fullm,transf);
		//		lrs_.leftNonConst().changeBasisDirect(fullm,concurrency_);

		//		transformPartialRight(transf,Q1,Qm);
		//		crsMatrixToFullMatrix(fullm,transf);
		//		lrs_.rightNonConst().changeBasisDirect(fullm,concurrency_);
	}

private:

	//	void transformPartialLeft(SparseMatrixType& tr,const SparseMatrixType& Q1,const SparseMatrix& Qm) const
	//	{

	//		SizeType ns = lrs_.left().size();
	//		PackIndicesType pack2(ns/n0_);
	//		PackIndicesType pack3(n0_);
	//		PackIndicesType pack1(ns);
	//		assert(reflectedLeft_.rank()==ns/n0_);
	//		assert(reflectedRight_.rank()==ns/n0_);
	//		typename PsimagLite::Vector<int>::Type ptr(total,-1);
	//		typename PsimagLite::Vector<SizeType>::Type index(total,0);
	//		typename PsimagLite::Vector<ComplexOrRealType>::Type temp(total,0);

	//		SizeType counter = 0;
	//		for (SizeType i=0;i<total;i++) {
	//			SizeType x = 0, y = 0;
	//			pack1.unpack(x,y,lrs_.super().permutation(i));
	//			tr.setRow(x,counter);
	//			for (int k=Q1.getRowPtr(i);k<Q1.getRowPtr(i+1);k++) {
	//				SizeType col = Q1.getCol(k);
	//				pack1.unpack(xprime,yprime,lrs_.super().permutation(i));

	//	}

	//	void transformPartial(SparseMatrixType& s1,const PsimagLite::Matrix<ComplexOrRealType>& fullm)
	//	{
	//		SparseMatrixType m1(fullm);
	//		SparseMatrixType m1Conj;
	//		transposeConjugate(m1Conj,m1);
	//		SparseMatrixType tmp = s1*m1Conj;
	//		s1 = m1*tmp;
	//		s1.checkValidity();
	//	}

	//	void transformPartial(SparseMatrixType& s1,const typename PsimagLite::Vector<RealType>::Type& eigs)
	//	{
	//		SizeType n = s1.rank();
	//		s1.resize(n);
	//		SizeType counter = 0;
	//		for (SizeType i=0;i<n;i++) {
	//			s1.setRow(i,counter);
	//			s1.pushCol(i);
	//			s1.pushValue(eigs[i]);
	//			counter++;
	//		}
	//		s1.setRow(n,counter);
	//		s1.checkValidity();
	//	}

	void check(const typename PsimagLite::Vector<SizeType>::Type& removedIndices,
	    const SparseMatrixType& reflected,
	    const PsimagLite::Matrix<ComplexOrRealType>& transform1,
	    const PsimagLite::Matrix<ComplexOrRealType>& transform2)
	{

		SparseMatrixType newreflected;

		changeBasis(newreflected, reflected, transform1, transform2);

		//		RealType eps = 1e-6;
		//		printFullMatrix(newreflected,"newreflected",0,eps);

		typename PsimagLite::Vector<SizeType>::Type x;
		for (SizeType ii = 0; ii < removedIndices.size(); ii++) {
			SizeType i = removedIndices[ii];
			for (int k = newreflected.getRowPtr(i); k < newreflected.getRowPtr(i + 1); k++) {
				ComplexOrRealType val = newreflected.getValue(k);
				if (isAlmostZero(val, 1e-8))
					continue;
				SizeType col = newreflected.getCol(k);
				x.push_back(col);
			}
		}
		Sort<typename PsimagLite::Vector<SizeType>::Type> sort;
		typename PsimagLite::Vector<SizeType>::Type iperm(x.size());
		sort.sort(x, iperm);

		typename PsimagLite::Vector<SizeType>::Type diffs;
		getDifferences(diffs, x, removedIndices);
		for (SizeType i = 0; i < diffs.size(); i++)
			std::cerr << "diffs[" << i << "]=" << diffs[i] << "\n";

		for (SizeType i = 0; i < x.size(); i++)
			std::cerr << "x[" << i << "]=" << x[i] << "\n";

		for (SizeType i = 0; i < removedIndices.size(); i++)
			std::cerr << "removed[" << i << "]=" << removedIndices[i] << "\n";
	}

	void getDifferences(typename PsimagLite::Vector<SizeType>::Type& diffs,
	    const typename PsimagLite::Vector<SizeType>::Type& x1,
	    const typename PsimagLite::Vector<SizeType>::Type& x2) const
	{
		typename PsimagLite::Vector<SizeType>::const_iterator::Type it2 = x2.begin();
		for (SizeType i = 0; i < x1.size(); i++) {
			typename PsimagLite::Vector<SizeType>::const_iterator::Type it = find(it2, x2.end(), x1[i]);
			if (it == x2.end()) {
				diffs.push_back(x1[i]);
				continue;
			}
			it2 = it + 1;
		}
	}

	void normalize(SparseMatrixType& A) const
	{
		SizeType n = A.rank();
		typename PsimagLite::Vector<ComplexOrRealType>::Type sum(n, 0.0);
		for (SizeType i = 0; i < n; i++) {
			for (int k = A.getRowPtr(i); k < A.getRowPtr(i + 1); k++) {
				ComplexOrRealType val = A.getValue(k);
				sum[i] += PsimagLite::conj(val) * val;
			}
		}

		for (SizeType i = 0; i < n; i++) {
			// assert(isAlmostZero(sum[i]-1.0,1e-6));
			assert(!isAlmostZero(sum[i], 1e-6));
			ComplexOrRealType x = 1.0 / sqrt(sum[i]);
			for (int k = A.getRowPtr(i); k < A.getRowPtr(i + 1); k++)
				A.setValues(k, A.getValue(k) * x);
		}
	}

	void changeBasis(SparseMatrixType& newreflected,
	    const SparseMatrixType& reflected,
	    const PsimagLite::Matrix<ComplexOrRealType>& transform1,
	    const PsimagLite::Matrix<ComplexOrRealType>& transform2)
	{
		assert(reflected.rank() == transform1.n_row());
		assert(reflected.rank() == transform2.n_row());

		SizeType total = transform1.n_col();
		newreflected.resize(total);
		typename PsimagLite::Vector<int>::Type ptr(total, -1);
		typename PsimagLite::Vector<SizeType>::Type index(total, 0);
		typename PsimagLite::Vector<ComplexOrRealType>::Type temp(total, 0);
		std::cerr << "transform1=" << transform1.n_row() << "x" << transform1.n_col() << "\n";
		std::cerr << "transform2=" << transform2.n_row() << "x" << transform2.n_col() << "\n";

		SizeType counter = 0;
		for (SizeType x = 0; x < total; x++) {
			newreflected.setRow(x, counter);

			SizeType itemp = 0;
			for (SizeType xprime = 0; xprime < transform1.n_row(); xprime++) {
				ComplexOrRealType wl1 = transform1(xprime, x);
				//				ComplexOrRealType wl1 =  transform(x,xprime);
				for (int k = reflected.getRowPtr(xprime); k < reflected.getRowPtr(xprime + 1); k++) {
					SizeType xsecond = reflected.getCol(k);
					ComplexOrRealType r = reflected.getValue(k);
					for (SizeType xthird = 0; xthird < transform2.n_col(); xthird++) {
						//						ComplexOrRealType val = wl1 * r * transform(xthird,xsecond);
						ComplexOrRealType val = wl1 * r * transform2(xsecond, xthird);
						// if (isAlmostZero(val)) continue;
						if (ptr[xthird] < 0) {
							ptr[xthird] = itemp;
							temp[ptr[xthird]] = val;
							index[ptr[xthird]] = xthird;
							itemp++;
						} else {
							temp[ptr[xthird]] += val;
						}
					}
				}
			}
			for (SizeType s = 0; s < itemp; s++) {
				newreflected.pushCol(index[s]);
				newreflected.pushValue(temp[s]);
				ptr[index[s]] = -1;
			}
			counter += itemp;
		}
		newreflected.setRow(newreflected.rank(), counter);
		newreflected.checkValidity();
	}

	void setSsector(SparseMatrixType& sSector, const typename PsimagLite::Vector<SizeType>::Type& sectors) const
	{
		assert(sectors.size() == 1);
		SizeType m = sectors[0];
		SizeType offset = lrs_.super().partition(m);
		SizeType total = lrs_.super().partition(m + 1) - offset;
		setSsector(sSector, total, offset);
	}

	void setSsector(SparseMatrixType& sSector, SizeType total = 0, SizeType offset = 0) const
	{
		if (total == 0)
			total = lrs_.super().size();
		sSector.resize(total);
		SizeType counter = 0;
		SizeType ns = lrs_.left().size();
		PackIndicesType pack2(ns / n0_);
		PackIndicesType pack3(n0_);
		PackIndicesType pack1(ns);
		assert(reflectedLeft_.rank() == ns / n0_);
		assert(reflectedRight_.rank() == ns / n0_);
		typename PsimagLite::Vector<int>::Type ptr(total, -1);
		typename PsimagLite::Vector<SizeType>::Type index(total, 0);
		typename PsimagLite::Vector<ComplexOrRealType>::Type temp(total, 0);

		for (SizeType i = 0; i < total; i++) {
			sSector.setRow(i, counter);
			SizeType x = 0, y = 0;
			pack1.unpack(x, y, lrs_.super().permutation(i + offset));

			SizeType x0 = 0, x1 = 0;
			pack2.unpack(x0, x1, lrs_.left().permutation(x));

			SizeType y0 = 0, y1 = 0;
			pack3.unpack(y0, y1, lrs_.right().permutation(y));

			SizeType itemp = 0;

			for (int k = reflectedLeft_.getRowPtr(x0); k < reflectedLeft_.getRowPtr(x0 + 1); k++) {
				ComplexOrRealType val1 = reflectedLeft_.getValue(k);
				for (int k2 = reflectedRight_.getRowPtr(y1); k2 < reflectedRight_.getRowPtr(y1 + 1); k2++) {
					ComplexOrRealType val2 = val1 * reflectedRight_.getValue(k2);
					if (isAlmostZero(val2))
						continue;
					SizeType x0prime = reflectedLeft_.getCol(k);
					SizeType xprime = pack3.pack(x1, x0prime, lrs_.right().permutationInverse());

					SizeType y1prime = reflectedRight_.getCol(k2);
					SizeType yprime = pack2.pack(y1prime, y0, lrs_.left().permutationInverse());

					SizeType iprime = pack1.pack(yprime, xprime, lrs_.super().permutationInverse());
					assert(iprime >= offset && iprime < offset + total);
					SizeType col = iprime - offset;
					if (ptr[col] < 0) {
						ptr[col] = itemp;
						temp[ptr[col]] = val2;
						index[ptr[col]] = col;
						itemp++;
					} else {
						temp[ptr[col]] += val2;
					}
				}
			}
			ComplexOrRealType val = 0.0;
			for (SizeType s = 0; s < itemp; s++) {
				sSector.pushCol(index[s]);
				sSector.pushValue(temp[s]);
				val += PsimagLite::conj(temp[s]) * temp[s];
				ptr[index[s]] = -1;
				counter++;
			}
			if (isAlmostZero(val, 1e-8)) {
				std::cerr << "i=" << i << " x0=" << x0 << " x1=" << x1 << " y0=" << y0 << " y1=" << y1 << "\n";
			}
		}
		sSector.setRow(total, counter);
		sSector.checkValidity();

//		printSparseMatrix(sSector,"sSector",1e-3);
#ifndef NDEBUG
		SparseMatrixType tmp;
		multiply(tmp, sSector, sSector);
		bool b = isTheIdentity(tmp, 1e-5);
		if (b)
			return;
		hasZeroRows(sSector, true);
		printFullMatrix(sSector, "sSector");
		printFullMatrix(tmp, "sSector*sSector");
		assert(false);
#endif
	}

	bool hasZeroRows(const SparseMatrixType& sSector, bool verbose) const
	{
		bool flag = false;
		SizeType n = sSector.rank();
		for (SizeType i = 0; i < n; i++) {
			ComplexOrRealType sum = 0.0;
			for (int k = sSector.getRowPtr(i); k < sSector.getRowPtr(i + 1); k++) {
				ComplexOrRealType val = sSector.getValue(k);
				sum += PsimagLite::conj(val) * val;
			}
			if (isAlmostZero(sum, 1e-4)) {
				flag = true;
				if (verbose)
					std::cerr << "zero row=" << i << "\n";
			}
		}
		return flag;
	}

	void printSparseMatrix(SparseMatrixType& s1, const PsimagLite::String& label, const RealType& eps) const
	{
		std::cout << label << "\n";
		for (SizeType i = 0; i < s1.rank(); i++) {
			for (int k = s1.getRowPtr(i); k < s1.getRowPtr(i + 1); k++) {
				ComplexOrRealType val = s1.getValue(k);
				if (isAlmostZero(val, eps))
					continue;
				std::cout << (i + 1) << " " << (1 + s1.getCol(k)) << " " << val << "\n";
			}
		}
	}

	void truncate(SparseMatrixType& reflectedFinal,
	    const SparseMatrixType& reflected,
	    SizeType keptstates)
	{
		//		SizeType n = reflected.rank();
		//		if (keptstates >= n) {
		reflectedFinal = reflected;
		return;
		//		}

		//		reflectedFinal.resize(keptstates);
		//		SizeType counterl = 0;

		//		typename PsimagLite::Vector<ComplexOrRealType>::Type sum(keptstates,0.0);
		//		for (SizeType i=0;i<keptstates;i++) {
		//			reflectedFinal.setRow(i,counterl);
		//			for (int k = reflected.getRowPtr(i); k < reflected.getRowPtr(i+1);k++) {
		//				SizeType col = reflected.getCol(k);
		//				if (col>=keptstates) continue;
		//				ComplexOrRealType val = reflected.getValue(k);
		//				reflectedFinal.pushCol(col);
		//				reflectedFinal.pushValue(val);
		//				counterl++;
		//				sum[i] += PsimagLite::conj(val) * val;
		//			}

		//		}
		//		reflectedFinal.setRow(reflectedFinal.rank(),counterl);
		//		reflectedFinal.checkValidity();

		//		// normalize
		//		for (SizeType i=0;i<reflectedFinal.rank();i++) {
		//			assert(!isAlmostZero(sum[i],1e-8));
		//			ComplexOrRealType x = 1.0/sqrt(sum[i]);
		//			for (int k = reflectedFinal.getRowPtr(i); k < reflectedFinal.getRowPtr(i+1);k++)
		//				reflectedFinal.setValues(k,reflectedFinal.getValue(k)*x);
		//		}
		//		reflectedFinal.checkValidity();
	}

	void updateReflected()
	{
		SizeType ns = lrs_.left().size();
		PackIndicesType pack2(ns / n0_);
		PackIndicesType pack3(n0_);
		SparseMatrixType reflectedLeft(ns, ns);

		SizeType counter = 0;
		for (SizeType x = 0; x < ns; x++) {
			reflectedLeft.setRow(x, counter);
			SizeType x0 = 0, x1 = 0;
			pack2.unpack(x0, x1, lrs_.left().permutation(x));
			for (int k = reflectedLeft_.getRowPtr(x0); k < reflectedLeft_.getRowPtr(x0 + 1); k++) {
				SizeType x0r = reflectedLeft_.getCol(k);
				SizeType col = pack3.pack(x1, x0r, lrs_.right().permutationInverse());
				ComplexOrRealType val = reflectedLeft_.getValue(k);
				// if (isAlmostZero(val)) continue;
				reflectedLeft.pushCol(col);
				reflectedLeft.pushValue(val);
				counter++;
			}
		}
		reflectedLeft.setRow(ns, counter);
		reflectedLeft.checkValidity();
		reflectedLeft_ = reflectedLeft;

		SparseMatrixType reflectedRight(ns, ns);
		counter = 0;
		for (SizeType x = 0; x < ns; x++) {
			SizeType x0 = 0, x1 = 0;
			reflectedRight.setRow(x, counter);
			pack3.unpack(x0, x1, lrs_.right().permutation(x));
			for (int k = reflectedRight_.getRowPtr(x1); k < reflectedRight_.getRowPtr(x1 + 1); k++) {
				SizeType x1r = reflectedRight_.getCol(k);
				ComplexOrRealType val = reflectedRight_.getValue(k);
				// if (isAlmostZero(val)) continue;
				SizeType col = pack2.pack(x1r, x0, lrs_.left().permutationInverse());
				reflectedRight.pushCol(col);
				reflectedRight.pushValue(val);
				counter++;
			}
		}
		reflectedRight.setRow(ns, counter);
		reflectedRight.checkValidity();
		reflectedRight_ = reflectedRight;
	}

	LeftRightSuperType& lrs_;
	ConcurrencyType& concurrency_;
	SizeType n0_; // hilbert size of one site
	PsimagLite::ProgressIndicator progress_;
	bool isEnabled_;
	SizeType expandSys_;
	SparseMatrixType reflectedLeft_, reflectedRight_;
	ReflectionTransformType reflectionTransform_;
}; // class ReflectionOperator

} // namespace Dmrg

/*@}*/
#endif // REFLECTION_OPERATOR_H