/*
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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*/

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

/*! \file ReflectionTransform
 *
 *
 */
#ifndef reflectionTRANSFORM_H
#define reflectionTRANSFORM_H

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

namespace Dmrg
{

template <typename RealType, typename SparseMatrixType>
class ReflectionTransform
{

	typedef typename SparseMatrixType::value_type ComplexOrRealType;
	typedef typename PsimagLite::Vector<ComplexOrRealType>::Type VectorType;
	typedef SparseVector<typename VectorType::value_type> SparseVectorType;
	typedef ReflectionBasis<RealType, SparseMatrixType> ReflectionBasisType;

public:

	ReflectionTransform(bool idebug)
	    : idebug_(idebug)
	{
	}

	void update(const SparseMatrixType& sSector)
	{
		ReflectionBasisType reflectionBasis(sSector, idebug_);
		plusSector_ = reflectionBasis.R(1.0).rank();
		computeTransform(Q1_, reflectionBasis, 1.0);
		computeTransform(Qm_, reflectionBasis, -1.0);
		//		SparseMatrixType Q;
		// computeFullQ(Q,Q1_,Qm_);
		//		split(Q);
		if (!idebug_)
			return;
		printFullMatrix(Q1_, "Q1");
		printFullMatrix(Qm_, "Qm");
	}

	void transform(SparseMatrixType& dest1,
	    SparseMatrixType& destm,
	    const SparseMatrixType& H) const
	{
		SparseMatrixType HQ1, HQm;
		multiply(HQ1, H, Q1_);

		multiply(HQm, H, Qm_);
		if (idebug_) {
			printFullMatrix(H, "OriginalHamiltonian");
			printFullMatrix(HQm, "HQm");
			printFullMatrix(HQ1, "HQ1");
		}

		SparseMatrixType Q1t, Qmt;
		transposeConjugate(Q1t, Q1_);
		transposeConjugate(Qmt, Qm_);

		RealType norm1 = getNorm(Q1t, Q1_);
		RealType normm = getNorm(Qmt, Qm_);

		multiply(dest1, Q1t, HQ1);
		reshape(dest1, plusSector_);
		dest1 *= (1.0 / norm1);
		assert(isHermitian(dest1));

		SizeType minusSector = H.rank() - plusSector_;

		multiply(destm, Qmt, HQm);
		reshape(destm, minusSector);
		destm *= (1.0 / normm);
		assert(isHermitian(destm));

		if (idebug_) {
			std::cerr << "norm1=" << norm1 << " normm=" << normm << "\n";
			std::cerr << "plusSector=" << plusSector_ << " minusSector=" << minusSector << "\n";
			printFullMatrix(dest1, "dest1");
			printFullMatrix(destm, "destm");
		}

#ifndef NDEBUG
//		checkTransform(Qmt,HQ1);
//		checkTransform(Q1t,HQm);
//		SparseMatrixType A;
//		multiply(A,Q1t,Q1_);
//		bool b = isThePartialIdentity(A,plusSector_,1e-5);
//		if (!b) {
//			printFullMatrix(A,"A");
//			assert(b);
//		}

//		multiply(A,Qmt,Qm_);
//		b = isThePartialIdentity(A,A.rank()-plusSector_,1e-5);
//		if (!b) {
//			printFullMatrix(A,"A");
//			assert(b);
//		}
#endif
	}

	bool isThePartialIdentity(const SparseMatrixType& A, SizeType partialSize, const RealType& eps = 1e-6) const
	{
		for (SizeType i = 0; i < partialSize; i++) {
			for (int k = A.getRowPtr(i); k < A.getRowPtr(i + 1); k++) {
				SizeType col = A.getCol(k);
				if (col >= partialSize)
					continue;
				ComplexOrRealType val = A.getValue(k);
				if (i == col && !isAlmostZero(val - 1.0, eps))
					return false;
				if (i != col && !isAlmostZero(val, eps))
					return false;
			}
		}
		return true;
	}

	void setGs(VectorType& gs, const VectorType& v, const RealType& sector) const
	{
		const SparseMatrixType& Q = (sector > 0) ? Q1_ : Qm_;
		multiply(gs, Q, v);
		RealType norma = PsimagLite::norm(gs);
		gs /= norma;
	}

	template <typename SomeVectorType>
	void setInitState(const SomeVectorType& initVector,
	    SomeVectorType& initVector1,
	    SomeVectorType& initVector2) const
	{
		SizeType minusSector = initVector.size() - plusSector_;
		initVector1.resize(plusSector_);
		initVector2.resize(minusSector);
		for (SizeType i = 0; i < initVector.size(); i++) {
			if (i < plusSector_)
				initVector1[i] = initVector[i];
			else
				initVector2[i - plusSector_] = initVector[i];
		}
	}

private:

	RealType getNorm(const SparseMatrixType& A, const SparseMatrixType& B) const
	{
		SparseMatrixType C;
		multiply(C, A, B);
		for (SizeType i = 0; i < C.rank(); i++) {
			for (int k = C.getRowPtr(i); k < C.getRowPtr(i + 1); k++) {
				SizeType col = C.getCol(k);
				if (col == i) {
					return PsimagLite::real(C.getValue(k));
				}
			}
		}
		assert(false);
		return 0;
	}

	void reshape(SparseMatrixType& A, SizeType n2) const
	{
		SparseMatrixType B(n2, n2);
		SizeType counter = 0;
		for (SizeType i = 0; i < n2; i++) {
			B.setRow(i, counter);
			for (int k = A.getRowPtr(i); k < A.getRowPtr(i + 1); k++) {
				SizeType col = A.getCol(k);
				ComplexOrRealType val = A.getValue(k);
				if (col >= n2) {
					assert(isAlmostZero(val, 1e-5));
					continue;
				}
				B.pushCol(col);
				B.pushValue(val);
				counter++;
			}
		}
#ifndef NDEBUG
		for (SizeType i = n2; i < A.rank(); i++) {
			for (int k = A.getRowPtr(i); k < A.getRowPtr(i + 1); k++) {
				ComplexOrRealType val = A.getValue(k);
				assert(isAlmostZero(val, 1e-5));
			}
		}
#endif
		B.setRow(n2, counter);
		B.checkValidity();
		A = B;
	}

	void checkTransform(const SparseMatrixType& A, const SparseMatrixType& B) const
	{
		SparseMatrixType C;
		multiply(C, A, B);
		bool b = isZero(C, 1e-5);
		if (b)
			return;
		printFullMatrix(A, "MatrixA");
		printFullMatrix(B, "MatrixB");
		printFullMatrix(C, "MatrixC");
		assert(b);
	}

	void computeTransform(SparseMatrixType& Q1,
	    const ReflectionBasisType& reflectionBasis,
	    const RealType& sector)
	{
		const SparseMatrixType& R1 = reflectionBasis.R(sector);
		SparseMatrixType R1Inverse;
		reflectionBasis.inverseTriangular(R1Inverse, R1, sector);

		SparseMatrixType T1;

		buildT1(T1, reflectionBasis, sector);
		bool strict = false; // matrices below have different ranks!!
		multiply(Q1, T1, R1Inverse, strict);
		if (!idebug_)
			return;
		printFullMatrix(R1Inverse, "R1Inverse");
		printFullMatrix(T1, "T1");
	}

	void computeFullQ(SparseMatrixType& Q,
	    const SparseMatrixType& Q1,
	    const SparseMatrixType& Qm) const
	{
		SizeType n = Q1.rank();
		typename PsimagLite::Vector<ComplexOrRealType>::Type sum(n, 0.0);
		SizeType counter = 0;
		Q.resize(n);
		SizeType minusSector = n - plusSector_;
		for (SizeType i = 0; i < n; i++) {
			Q.setRow(i, counter);
			// add Q1
			for (int k = Q1.getRowPtr(i); k < Q1.getRowPtr(i + 1); k++) {
				SizeType col = Q1.getCol(k);
				if (col >= plusSector_)
					continue;
				ComplexOrRealType val = Q1.getValue(k);
				Q.pushValue(val);
				Q.pushCol(col);
				sum[i] += PsimagLite::conj(val) * val;
				counter++;
			}
			// add Qm
			for (int k = Qm.getRowPtr(i); k < Qm.getRowPtr(i + 1); k++) {
				SizeType col = Qm.getCol(k);
				if (col >= minusSector)
					continue;
				ComplexOrRealType val = Qm.getValue(k);
				Q.pushValue(val);
				Q.pushCol(Qm.getCol(k) + plusSector_);
				sum[i] += PsimagLite::conj(val) * val;
				counter++;
			}
		}
		Q.setRow(Q.rank(), counter);
		// normalize
		//		for (SizeType i=0;i<n;i++) {
		//			if (isAlmostZero(sum[i],1e-10)) continue;
		//			sum[i] = 1.0/sqrt(sum[i]);
		//			for (int k = Q.getRowPtr(i);k<Q.getRowPtr(i+1);k++) {
		//				Q.setValues(k,Q.getValue(k)*sum[i]);
		//			}
		//		}
		Q.checkValidity();
#ifndef NDEBUG
		SparseMatrixType Qt;
		transposeConjugate(Qt, Q);
		SparseMatrixType A;
		multiply(A, Qt, Q);
		if (!isTheIdentity(A, 1e-5)) {
			printFullMatrix(Q, "Q");
			printFullMatrix(A, "A");
			assert(false);
		}
#endif
		if (!idebug_)
			return;
		printFullMatrix(Q, "Q");
	}

	void split(const SparseMatrixType& Q)
	{
		SizeType n = Q.rank();
		Q1_.resize(n);
		SizeType counter = 0;
		for (SizeType i = 0; i < n; i++) {
			Q1_.setRow(i, counter);
			for (int k = Q.getRowPtr(i); k < Q.getRowPtr(i + 1); k++) {
				SizeType col = Q.getCol(k);
				if (col >= plusSector_)
					continue;
				Q1_.pushCol(col);
				Q1_.pushValue(Q.getValue(k));
				counter++;
			}
		}
		Q1_.setRow(Q1_.rank(), counter);

		counter = 0;
		Qm_.resize(n);
		for (SizeType i = 0; i < n; i++) {
			Qm_.setRow(i, counter);
			for (int k = Q.getRowPtr(i); k < Q.getRowPtr(i + 1); k++) {
				SizeType col = Q.getCol(k);
				if (col < plusSector_)
					continue;
				Qm_.pushCol(col - plusSector_);
				Qm_.pushValue(Q.getValue(k));
				counter++;
			}
		}
		Qm_.setRow(Qm_.rank(), counter);
	}

	void buildT1(SparseMatrixType& T1final,
	    const ReflectionBasisType& reflectionBasis,
	    const RealType& sector) const
	{
		const typename PsimagLite::Vector<SizeType>::Type& ipPosOrNeg = reflectionBasis.ipPosOrNeg(sector);
		const SparseMatrixType& reflection = reflectionBasis.reflection();
		SizeType n = reflection.rank();

		SparseMatrixType T1(n, n);
		SizeType counter = 0;
		for (SizeType i = 0; i < n; i++) {
			T1.setRow(i, counter);
			bool hasDiagonal = false;
			for (int k = reflection.getRowPtr(i); k < reflection.getRowPtr(i + 1); k++) {
				SizeType col = reflection.getCol(k);
				ComplexOrRealType val = reflection.getValue(k);
				if (col == i) {
					val += sector;
					hasDiagonal = true;
				}
				val *= sector;
				if (isAlmostZero(val, 1e-10))
					continue;
				T1.pushCol(col);
				T1.pushValue(val);
				counter++;
			}
			if (!hasDiagonal) {
				T1.pushCol(i);
				T1.pushValue(1.0);
				counter++;
			}
		}
		T1.setRow(n, counter);
		T1.checkValidity();

		// permute columns now:
		typename PsimagLite::Vector<int>::Type inversePermutation(n, -1);
		for (SizeType i = 0; i < ipPosOrNeg.size(); i++)
			inversePermutation[ipPosOrNeg[i]] = i;

		T1final.resize(n);
		counter = 0;
		typename PsimagLite::Vector<ComplexOrRealType>::Type sum(n, 0.0);
		for (SizeType i = 0; i < n; i++) {
			T1final.setRow(i, counter);
			for (int k = T1.getRowPtr(i); k < T1.getRowPtr(i + 1); k++) {
				int col = inversePermutation[T1.getCol(k)];
				if (col < 0)
					continue;
				ComplexOrRealType val = T1.getValue(k);
				if (isAlmostZero(val, 1e-10))
					continue;
				assert(SizeType(col) < ipPosOrNeg.size());
				T1final.pushCol(col);
				T1final.pushValue(val);
				sum[i] += PsimagLite::conj(val) * val;
				counter++;
			}
		}
		T1final.setRow(n, counter);
		T1final.checkValidity();

		// normalize T1
		//		for (SizeType i=0;i<n;i++) {
		//			if (isAlmostZero(sum[i],1e-12)) continue;
		//			sum[i] = 1.0/sqrt(sum[i]);

		//			for (int k = T1final.getRowPtr(i);k<T1final.getRowPtr(i+1);k++)
		//				T1final.setValues(k,T1final.getValue(k) * sum[i]);

		//		}
	}

	bool idebug_;
	SizeType plusSector_;
	SparseMatrixType Q1_, Qm_;

}; // class ReflectionTransform

} // namespace Dmrg

/*@}*/
#endif // reflectionTRANSFORM_H