#include "toonz/ikjacobian.h"

#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <iostream>

#include "tstopwatch.h"
using namespace std;

inline bool NearZero(double x, double tolerance)
{
	return (fabs(x) <= tolerance);
}

/*
#ifdef _DYNAMIC
const double BASEMAXDIST = 0.02;
#else
const double MAXDIST = 0.08;	
#endif


const double DELTA = 0.4;
const long double LAMBDA = 2.0;		// solo per DLS. ottimale : 0.24
const double NEARZERO = 0.0000000001;
*/

//*******************************************************
// Class VectorRn

VectorRn VectorRn::WorkVector;

double VectorRn::MaxAbs() const
{
	double result = 0.0;
	double *t = x;
	for (long i = length; i > 0; i--) {
		if ((*t) > result) {
			result = *t;
		} else if (-(*t) > result) {
			result = -(*t);
		}
		t++;
	}
	return result;
}

//*************************************************************************
// MatrixRmn

MatrixRmn MatrixRmn::WorkMatrix; // Temporary work matrix

// Fill the diagonal entries with the value d.  The rest of the matrix is unchanged.
void MatrixRmn::SetDiagonalEntries(double d)
{
	long diagLen = std::min(NumRows, NumCols);
	double *dPtr = x;
	for (; diagLen > 0; diagLen--) {
		*dPtr = d;
		dPtr += NumRows + 1;
	}
}

// Fill the diagonal entries with values in vector d.  The rest of the matrix is unchanged.
void MatrixRmn::SetDiagonalEntries(const VectorRn &d)
{
	long diagLen = std::min(NumRows, NumCols);
	assert(d.length == diagLen);
	double *dPtr = x;
	double *from = d.x;
	for (; diagLen > 0; diagLen--) {
		*dPtr = *(from++);
		dPtr += NumRows + 1;
	}
}

// Fill the superdiagonal entries with the value d.  The rest of the matrix is unchanged.
void MatrixRmn::SetSuperDiagonalEntries(double d)
{
	long sDiagLen = std::min(NumRows, (long)(NumCols - 1));
	double *to = x + NumRows;
	for (; sDiagLen > 0; sDiagLen--) {
		*to = d;
		to += NumRows + 1;
	}
}

// Fill the superdiagonal entries with values in vector d.  The rest of the matrix is unchanged.
void MatrixRmn::SetSuperDiagonalEntries(const VectorRn &d)
{
	long sDiagLen = std::min((long)(NumRows - 1), NumCols);
	assert(sDiagLen == d.length);
	double *to = x + NumRows;
	double *from = d.x;
	for (; sDiagLen > 0; sDiagLen--) {
		*to = *(from++);
		to += NumRows + 1;
	}
}

// Fill the subdiagonal entries with the value d.  The rest of the matrix is unchanged.
void MatrixRmn::SetSubDiagonalEntries(double d)
{
	long sDiagLen = std::min(NumRows, NumCols) - 1;
	double *to = x + 1;
	for (; sDiagLen > 0; sDiagLen--) {
		*to = d;
		to += NumRows + 1;
	}
}

// Fill the subdiagonal entries with values in vector d.  The rest of the matrix is unchanged.
void MatrixRmn::SetSubDiagonalEntries(const VectorRn &d)
{
	long sDiagLen = std::min(NumRows, NumCols) - 1;
	assert(sDiagLen == d.length);
	double *to = x + 1;
	double *from = d.x;
	for (; sDiagLen > 0; sDiagLen--) {
		*to = *(from++);
		to += NumRows + 1;
	}
}

// Set the i-th column equal to d.
void MatrixRmn::SetColumn(long i, const VectorRn &d)
{
	assert(NumRows == d.GetLength());
	double *to = x + i * NumRows;
	const double *from = d.x;
	for (i = NumRows; i > 0; i--) {
		*(to++) = *(from++);
	}
}

// Set the i-th column equal to d.
void MatrixRmn::SetRow(long i, const VectorRn &d)
{
	assert(NumCols == d.GetLength());
	double *to = x + i;
	const double *from = d.x;
	for (i = NumRows; i > 0; i--) {
		*to = *(from++);
		to += NumRows;
	}
}

// Sets a "linear" portion of the array with the values from a vector d
// The first row and column position are given by startRow, startCol.
// Successive positions are found by using the deltaRow, deltaCol values
//	to increment the row and column indices.  There is no wrapping around.
void MatrixRmn::SetSequence(const VectorRn &d, long startRow, long startCol, long deltaRow, long deltaCol)
{
	long length = d.length;
	assert(startRow >= 0 && startRow < NumRows && startCol >= 0 && startCol < NumCols);
	assert(startRow + (length - 1) * deltaRow >= 0 && startRow + (length - 1) * deltaRow < NumRows);
	assert(startCol + (length - 1) * deltaCol >= 0 && startCol + (length - 1) * deltaCol < NumCols);
	double *to = x + startRow + NumRows * startCol;
	double *from = d.x;
	long stride = deltaRow + NumRows * deltaCol;
	for (; length > 0; length--) {
		*to = *(from++);
		to += stride;
	}
}

// The matrix A is loaded, in into "this" matrix, based at (0,0).
//  The size of "this" matrix must be large enough to accomodate A.
//	The rest of "this" matrix is left unchanged.  It is not filled with zeroes!

void MatrixRmn::LoadAsSubmatrix(const MatrixRmn &A)
{
	assert(A.NumRows <= NumRows && A.NumCols <= NumCols);
	int extraColStep = NumRows - A.NumRows;
	double *to = x;
	double *from = A.x;
	for (long i = A.NumCols; i > 0; i--) {	 // Copy columns of A, one per time thru loop
		for (long j = A.NumRows; j > 0; j--) { // Copy all elements of this column of A
			*(to++) = *(from++);
		}
		to += extraColStep;
	}
}

// The matrix A is loaded, in transposed order into "this" matrix, based at (0,0).
//  The size of "this" matrix must be large enough to accomodate A.
//	The rest of "this" matrix is left unchanged.  It is not filled with zeroes!
void MatrixRmn::LoadAsSubmatrixTranspose(const MatrixRmn &A)
{
	assert(A.NumRows <= NumCols && A.NumCols <= NumRows);
	double *rowPtr = x;
	double *from = A.x;
	for (long i = A.NumCols; i > 0; i--) { // Copy columns of A, once per loop
		double *to = rowPtr;
		for (long j = A.NumRows; j > 0; j--) { // Loop copying values from the column of A
			*to = *(from++);
			to += NumRows;
		}
		rowPtr++;
	}
}

// Calculate the Frobenius Norm (square root of sum of squares of entries of the matrix)
double MatrixRmn::FrobeniusNorm() const
{
	return sqrt(FrobeniusNormSq());
}

// Multiply this matrix by column vector v.
// Result is column vector "result"
void MatrixRmn::Multiply(const VectorRn &v, VectorRn &result) const
{
	assert(v.GetLength() == NumCols && result.GetLength() == NumRows);
	double *out = result.GetPtr(); // Points to entry in result vector
	const double *rowPtr = x;	  // Points to beginning of next row in matrix
	for (long j = NumRows; j > 0; j--) {
		const double *in = v.GetPtr();
		const double *m = rowPtr++;
		*out = 0.0f;
		for (long i = NumCols; i > 0; i--) {
			*out += (*(in++)) * (*m);
			m += NumRows;
		}
		out++;
	}
}

// Multiply transpose of this matrix by column vector v.
//    Result is column vector "result"
// Equivalent to mult by row vector on left
void MatrixRmn::MultiplyTranspose(const VectorRn &v, VectorRn &result) const
{
	assert(v.GetLength() == NumRows && result.GetLength() == NumCols);
	double *out = result.GetPtr(); // Points to entry in result vector
	const double *colPtr = x;	  // Points to beginning of next column in matrix
	for (long i = NumCols; i > 0; i--) {
		const double *in = v.GetPtr();
		*out = 0.0f;
		for (long j = NumRows; j > 0; j--) {
			*out += (*(in++)) * (*(colPtr++));
		}
		out++;
	}
}

// Form the dot product of a vector v with the i-th column of the array
double MatrixRmn::DotProductColumn(const VectorRn &v, long colNum) const
{
	assert(v.GetLength() == NumRows);
	double *ptrC = x + colNum * NumRows;
	double *ptrV = v.x;
	double ret = 0.0;
	for (long i = NumRows; i > 0; i--) {
		ret += (*(ptrC++)) * (*(ptrV++));
	}
	return ret;
}

// Add a constant to each entry on the diagonal
MatrixRmn &MatrixRmn::AddToDiagonal(double d) // Adds d to each diagonal entry
{
	long diagLen = std::min(NumRows, NumCols);
	double *dPtr = x;
	for (; diagLen > 0; diagLen--) {
		*dPtr += d;
		dPtr += NumRows + 1;
	}
	return *this;
}

// Aggiunge i temini del vettore alla diagonale
MatrixRmn &MatrixRmn::AddToDiagonal(const VectorRn &v) // Adds d to each diagonal entry
{
	long diagLen = std::min(NumRows, NumCols);
	double *dPtr = x;
	const double *dv = v.x;
	for (; diagLen > 0; diagLen--) {
		*dPtr += *(dv++);
		dPtr += NumRows + 1;
	}
	return *this;
}

MatrixRmn &MatrixRmn::MultiplyScalar(const MatrixRmn &A, double k, MatrixRmn &dst)
{

	long length = A.NumCols;
	double *dPtr = dst.x;
	for (long i = dst.NumCols; i > 0; i--) {
		double *aPtr = A.x; // Points to beginning of row in A

		for (long j = dst.NumRows; j > 0; j--) {
			*dPtr = *aPtr * k;
			dPtr++;
			aPtr++;
		}
		aPtr += A.NumRows;
	}

	return dst;
}
// Multiply two MatrixRmn's
MatrixRmn &MatrixRmn::Multiply(const MatrixRmn &A, const MatrixRmn &B, MatrixRmn &dst)
{
	assert(A.NumCols == B.NumRows && A.NumRows == dst.NumRows && B.NumCols == dst.NumCols);
	long length = A.NumCols;
	double *bPtr = B.x; // Points to beginning of column in B
	double *dPtr = dst.x;
	for (long i = dst.NumCols; i > 0; i--) {
		double *aPtr = A.x; // Points to beginning of row in A
		for (long j = dst.NumRows; j > 0; j--) {
			*dPtr = DotArray(length, aPtr, A.NumRows, bPtr, 1);
			dPtr++;
			aPtr++;
		}
		bPtr += B.NumRows;
	}

	return dst;
}

// Multiply two MatrixRmn's,  Transpose the first matrix before multiplying
MatrixRmn &MatrixRmn::TransposeMultiply(const MatrixRmn &A, const MatrixRmn &B, MatrixRmn &dst)
{
	assert(A.NumRows == B.NumRows && A.NumCols == dst.NumRows && B.NumCols == dst.NumCols);
	long length = A.NumRows;

	double *bPtr = B.x; // bPtr Points to beginning of column in B
	double *dPtr = dst.x;
	for (long i = dst.NumCols; i > 0; i--) {	 // Loop over all columns of dst
		double *aPtr = A.x;						 // aPtr Points to beginning of column in A
		for (long j = dst.NumRows; j > 0; j--) { // Loop over all rows of dst
			*dPtr = DotArray(length, aPtr, 1, bPtr, 1);
			dPtr++;
			aPtr += A.NumRows;
		}
		bPtr += B.NumRows;
	}

	return dst;
}

// Multiply two MatrixRmn's.  Transpose the second matrix before multiplying
MatrixRmn &MatrixRmn::MultiplyTranspose(const MatrixRmn &A, const MatrixRmn &B, MatrixRmn &dst)
{
	assert(A.NumCols == B.NumCols && A.NumRows == dst.NumRows && B.NumRows == dst.NumCols);
	long length = A.NumCols;

	double *bPtr = B.x; // Points to beginning of row in B
	double *dPtr = dst.x;
	for (long i = dst.NumCols; i > 0; i--) {
		double *aPtr = A.x; // Points to beginning of row in A
		for (long j = dst.NumRows; j > 0; j--) {
			*dPtr = DotArray(length, aPtr, A.NumRows, bPtr, B.NumRows);
			dPtr++;
			aPtr++;
		}
		bPtr++;
	}

	return dst;
}

// Solves the equation   (*this)*xVec = b;
// Uses row operations.  Assumes *this is square and invertible.
// No error checking for divide by zero or instability (except with asserts)
void MatrixRmn::Solve(const VectorRn &b, VectorRn *xVec) const
{
	assert(NumRows == NumCols && NumCols == xVec->GetLength() && NumRows == b.GetLength());

	// Copy this matrix and b into an Augmented Matrix
	MatrixRmn &AugMat = GetWorkMatrix(NumRows, NumCols + 1);
	AugMat.LoadAsSubmatrix(*this);
	AugMat.SetColumn(NumRows, b);

	// Put into row echelon form with row operations
	AugMat.ConvertToRefNoFree();

	// Solve for x vector values using back substitution
	double *xLast = xVec->x + NumRows - 1;			   // Last entry in xVec
	double *endRow = AugMat.x + NumRows * NumCols - 1; // Last entry in the current row of the coefficient part of Augmented Matrix
	double *bPtr = endRow + NumRows;				   // Last entry in augmented matrix (end of last column, in augmented part)
	for (long i = NumRows; i > 0; i--) {
		double accum = *(bPtr--);
		// Next loop computes back substitution terms
		double *rowPtr = endRow; // Points to entries of the current row for back substitution.
		double *xPtr = xLast;	// Points to entries in the x vector (also for back substitution)
		for (long j = NumRows - i; j > 0; j--) {
			accum -= (*rowPtr) * (*(xPtr--));
			rowPtr -= NumCols; // Previous entry in the row
		}
		assert(*rowPtr != 0.0); // Are not supposed to be any free variables in this matrix
		*xPtr = accum / (*rowPtr);
		endRow--;
	}
}

// ConvertToRefNoFree
// Converts the matrix (in place) to row echelon form
// For us, row echelon form allows any non-zero values, not just 1's, in the
//		position for a lead variable.
// The "NoFree" version operates on the assumption that no free variable will be found.
// Algorithm uses row operations and row pivoting (only).
// Augmented matrix is correctly accomodated.  Only the first square part participates
//		in the main work of row operations.
void MatrixRmn::ConvertToRefNoFree()
{
	// Loop over all columns (variables)
	// Find row with most non-zero entry.
	// Swap to the highest active row
	// Subtract appropriately from all the lower rows (row op of type 3)
	long numIters = std::min(NumRows, NumCols);
	double *rowPtr1 = x;
	const long diagStep = NumRows + 1;
	long lenRowLeft = NumCols;
	for (; numIters > 1; numIters--) {
		// Find row with most non-zero entry.
		double *rowPtr2 = rowPtr1;
		double maxAbs = fabs(*rowPtr1);
		double *rowPivot = rowPtr1;
		long i;
		for (i = numIters - 1; i > 0; i--) {
			const double &newMax = *(++rowPivot);
			if (newMax > maxAbs) {
				maxAbs = *rowPivot;
				rowPtr2 = rowPivot;
			} else if (-newMax > maxAbs) {
				maxAbs = -newMax;
				rowPtr2 = rowPivot;
			}
		}
		// Pivot step: Swap the row with highest entry to the current row
		if (rowPtr1 != rowPtr2) {
			double *to = rowPtr1;
			for (long i = lenRowLeft; i > 0; i--) {
				double temp = *to;
				*to = *rowPtr2;
				*rowPtr2 = temp;
				to += NumRows;
				rowPtr2 += NumRows;
			}
		}
		// Subtract this row appropriately from all the lower rows (row operation of type 3)
		rowPtr2 = rowPtr1;
		for (i = numIters - 1; i > 0; i--) {
			rowPtr2++;
			double *to = rowPtr2;
			double *from = rowPtr1;
			assert(*from != 0.0);
			double alpha = (*to) / (*from);
			*to = 0.0;
			for (long j = lenRowLeft - 1; j > 0; j--) {
				to += NumRows;
				from += NumRows;
				*to -= (*from) * alpha;
			}
		}
		// Update for next iteration of loop
		rowPtr1 += diagStep;
		lenRowLeft--;
	}
}

// Calculate the c=cosine and s=sine values for a Givens transformation.
// The matrix M = ( (c, -s), (s, c) ) in row order transforms the
//   column vector (a, b)^T to have y-coordinate zero.
void MatrixRmn::CalcGivensValues(double a, double b, double *c, double *s)
{
	double denomInv = sqrt(a * a + b * b);
	if (denomInv == 0.0) {
		*c = 1.0;
		*s = 0.0;
	} else {
		denomInv = 1.0 / denomInv;
		*c = a * denomInv;
		*s = -b * denomInv;
	}
}

// Applies Givens transform to columns i and i+1.
// Equivalent to postmultiplying by the matrix
//      ( c  -s )
//		( s   c )
// with non-zero entries in rows i and i+1 and columns i and i+1
void MatrixRmn::PostApplyGivens(double c, double s, long idx)
{
	assert(0 <= idx && idx < NumCols);
	double *colA = x + idx * NumRows;
	double *colB = colA + NumRows;
	for (long i = NumRows; i > 0; i--) {
		double temp = *colA;
		*colA = (*colA) * c + (*colB) * s;
		*colB = (*colB) * c - temp * s;
		colA++;
		colB++;
	}
}

// Applies Givens transform to columns idx1 and idx2.
// Equivalent to postmultiplying by the matrix
//      ( c  -s )
//		( s   c )
// with non-zero entries in rows idx1 and idx2 and columns idx1 and idx2
void MatrixRmn::PostApplyGivens(double c, double s, long idx1, long idx2)
{
	assert(idx1 != idx2 && 0 <= idx1 && idx1 < NumCols && 0 <= idx2 && idx2 < NumCols);
	double *colA = x + idx1 * NumRows;
	double *colB = x + idx2 * NumRows;
	for (long i = NumRows; i > 0; i--) {
		double temp = *colA;
		*colA = (*colA) * c + (*colB) * s;
		*colB = (*colB) * c - temp * s;
		colA++;
		colB++;
	}
}

// ********************************************************************************************
// Singular value decomposition.
// Return othogonal matrices U and V and diagonal matrix with diagonal w such that
//     (this) = U * Diag(w) * V^T     (V^T is V-transpose.)
// Diagonal entries have all non-zero entries before all zero entries, but are not
//		necessarily sorted.  (Someday, I will write ComputedSortedSVD that handles
//		sorting the eigenvalues by magnitude.)
// ********************************************************************************************
void MatrixRmn::ComputeSVD(MatrixRmn &U, VectorRn &w, MatrixRmn &V) const
{
	assert(U.NumRows == NumRows && V.NumCols == NumCols && U.NumRows == U.NumCols && V.NumRows == V.NumCols && w.GetLength() == std::min(NumRows, NumCols));

	double temp = 0.0;
	VectorRn &superDiag = VectorRn::GetWorkVector(w.GetLength() - 1); // Some extra work space.  Will get passed around.

	// Choose larger of U, V to hold intermediate results
	// If U is larger than V, use U to store intermediate results
	// Otherwise use V.  In the latter case, we form the SVD of A transpose,
	//		(which is essentially identical to the SVD of A).
	MatrixRmn *leftMatrix;
	MatrixRmn *rightMatrix;
	if (NumRows >= NumCols) {
		U.LoadAsSubmatrix(*this); // Copy A into U
		leftMatrix = &U;
		rightMatrix = &V;
	} else {
		V.LoadAsSubmatrixTranspose(*this); // Copy A-transpose into V
		leftMatrix = &V;
		rightMatrix = &U;
	}

	// Do the actual work to calculate the SVD
	// Now matrix has at least as many rows as columns

	CalcBidiagonal(*leftMatrix, *rightMatrix, w, superDiag);
	ConvertBidiagToDiagonal(*leftMatrix, *rightMatrix, w, superDiag);
}

// ************************************************ CalcBidiagonal **************************
// Helper routine for SVD computation
// U is a matrix to be bidiagonalized.
// On return, U and V are orthonormal and w holds the new diagonal
//	  elements and superDiag holds the super diagonal elements.

void MatrixRmn::CalcBidiagonal(MatrixRmn &U, MatrixRmn &V, VectorRn &w, VectorRn &superDiag)
{
	assert(U.NumRows >= V.NumRows);

	// The diagonal and superdiagonal entries of the bidiagonalized
	//	  version of the U matrix
	//	  are stored in the vectors w and superDiag (temporarily).

	// Apply Householder transformations to U.
	// Householder transformations come in pairs.
	//   First, on the left, we map a portion of a column to zeros
	//   Second, on the right, we map a portion of a row to zeros
	const long rowStep = U.NumCols;
	const long diagStep = U.NumCols + 1;
	double *diagPtr = U.x;
	double *wPtr = w.x;
	double *superDiagPtr = superDiag.x;
	long colLengthLeft = U.NumRows;
	long rowLengthLeft = V.NumCols;
	while (true) {
		// Apply a Householder xform on left to zero part of a column
		SvdHouseholder(diagPtr, colLengthLeft, rowLengthLeft, 1, rowStep, wPtr);

		if (rowLengthLeft == 2) {
			*superDiagPtr = *(diagPtr + rowStep);
			break;
		}

		// Apply a Householder xform on the right to zero part of a row
		SvdHouseholder(diagPtr + rowStep, rowLengthLeft - 1, colLengthLeft, rowStep, 1, superDiagPtr);

		rowLengthLeft--;
		colLengthLeft--;
		diagPtr += diagStep;
		wPtr++;
		superDiagPtr++;
	}

	int extra = 0;
	diagPtr += diagStep;
	wPtr++;
	if (colLengthLeft > 2) {
		extra = 1;
		// Do one last Householder transformation when the matrix is not square
		colLengthLeft--;
		SvdHouseholder(diagPtr, colLengthLeft, 1, 1, 0, wPtr);
	} else {
		*wPtr = *diagPtr;
	}

	// Form U and V from the Householder transformations
	V.ExpandHouseholders(V.NumCols - 2, 1, U.x + U.NumRows, U.NumRows, 1);
	U.ExpandHouseholders(V.NumCols - 1 + extra, 0, U.x, 1, U.NumRows);

	// Done with bidiagonalization
	return;
}

// Helper routine for CalcBidiagonal
// Performs a series of Householder transformations on a matrix
// Stores results compactly into the matrix:   The Householder vector u (normalized)
//   is stored into the first row/column being transformed.
// The leading term of that row (= plus/minus its magnitude is returned
//	 separately into "retFirstEntry"
void MatrixRmn::SvdHouseholder(double *basePt,
							   long colLength, long numCols, long colStride, long rowStride,
							   double *retFirstEntry)
{

	// Calc norm of vector u
	double *cPtr = basePt;
	double norm = 0.0;
	long i;

	double aa0 = *cPtr;
	double aa1 = *basePt;
	double aa2 = *retFirstEntry;

	for (i = colLength; i > 0; i--) {
		norm += Square(*cPtr);
		cPtr += colStride;
	}
	norm = sqrt(norm); // Norm of vector to reflect to axis  e_1

	// Handle sign issues
	double imageVal; // Choose sign to maximize distance
	if ((*basePt) < 0.0) {
		imageVal = norm;
		norm = 2.0 * norm * (norm - (*basePt));
	} else {
		imageVal = -norm;
		norm = 2.0 * norm * (norm + (*basePt));
	}
	norm = sqrt(norm); // Norm is norm of reflection vector

	if (norm == 0.0) { // If the vector being transformed is equal to zero
		// Force to zero in case of roundoff errors
		cPtr = basePt;
		for (i = colLength; i > 0; i--) {
			*cPtr = 0.0;
			cPtr += colStride;
		}
		*retFirstEntry = 0.0;
		return;
	}

	*retFirstEntry = imageVal;

	// Set up the normalized Householder vector
	*basePt -= imageVal; // First component changes. Rest stay the same.
	// Normalize the vector
	norm = 1.0 / norm; // Now it is the inverse norm
	cPtr = basePt;
	for (i = colLength; i > 0; i--) {
		*cPtr *= norm;
		cPtr += colStride;
	}

	// Transform the rest of the U matrix with the Householder transformation
	double *rPtr = basePt;
	for (long j = numCols - 1; j > 0; j--) {
		rPtr += rowStride;
		// Calc dot product with Householder transformation vector
		double dotP = DotArray(colLength, basePt, colStride, rPtr, colStride);
		// Transform with I - 2*dotP*(Householder vector)
		AddArrayScale(colLength, basePt, colStride, rPtr, colStride, -2.0 * dotP);
	}
}

// ********************************* ExpandHouseholders ********************************************
// The matrix will be square.
//   numXforms = number of Householder transformations to concatenate
//		Each Householder transformation is represented by a unit vector
//		Each successive Householder transformation starts one position later
//			and has one more implied leading zero
//	 basePt = beginning of the first Householder transform
//	 colStride, rowStride: Householder xforms are stored in "columns"
//   numZerosSkipped is the number of implicit zeros on the front each
//			Householder transformation vector (only values supported are 0 and 1).
void MatrixRmn::ExpandHouseholders(long numXforms, int numZerosSkipped, const double *basePt, long colStride, long rowStride)
{
	// Number of applications of the last Householder transform
	//     (That are not trivial!)
	long numToTransform = NumCols - numXforms + 1 - numZerosSkipped;
	assert(numToTransform > 0);

	if (numXforms == 0) {
		SetIdentity();
		return;
	}

	// Handle the first one separately as a special case,
	// "this" matrix will be treated to simulate being preloaded with the identity
	long hDiagStride = rowStride + colStride;
	const double *hBase = basePt + hDiagStride * (numXforms - 1);	  // Pointer to the last Householder vector
	const double *hDiagPtr = hBase + colStride * (numToTransform - 1); // Pointer to last entry in that vector
	long i;
	double *diagPtr = x + NumCols * NumRows - 1;	 // Last entry in matrix (points to diagonal entry)
	double *colPtr = diagPtr - (numToTransform - 1); // Pointer to column in matrix
	for (i = numToTransform; i > 0; i--) {
		CopyArrayScale(numToTransform, hBase, colStride, colPtr, 1, -2.0 * (*hDiagPtr));
		*diagPtr += 1.0;		  // Add back in 1 to the diagonal entry (since xforming the identity)
		diagPtr -= (NumRows + 1); // Next diagonal entry in this matrix
		colPtr -= NumRows;		  // Next column in this matrix
		hDiagPtr -= colStride;
	}

	// Now handle the general case
	// A row of zeros must be in effect added to the top of each old column (in each loop)
	double *colLastPtr = x + NumRows * NumCols - numToTransform - 1;
	for (i = numXforms - 1; i > 0; i--) {
		numToTransform++;	 // Number of non-trivial applications of this Householder transformation
		hBase -= hDiagStride; // Pointer to the beginning of the Householder transformation
		colPtr = colLastPtr;
		for (long j = numToTransform - 1; j > 0; j--) {
			// Get dot product
			double dotProd2N = -2.0 * DotArray(numToTransform - 1, hBase + colStride, colStride, colPtr + 1, 1);
			*colPtr = dotProd2N * (*hBase); // Adding onto zero at initial point
			AddArrayScale(numToTransform - 1, hBase + colStride, colStride, colPtr + 1, 1, dotProd2N);
			colPtr -= NumRows;
		}
		// Do last one as a special case (may overwrite the Householder vector)
		CopyArrayScale(numToTransform, hBase, colStride, colPtr, 1, -2.0 * (*hBase));
		*colPtr += 1.0; // Add back one one as identity
		// Done with this Householder transformation
		colLastPtr--;
	}

	if (numZerosSkipped != 0) {
		assert(numZerosSkipped == 1);
		// Fill first row and column with identity (More generally: first numZerosSkipped many rows and columns)
		double *d = x;
		*d = 1;
		double *d2 = d;
		for (i = NumRows - 1; i > 0; i--) {
			*(++d) = 0;
			*(d2 += NumRows) = 0;
		}
	}
}

// **************** ConvertBidiagToDiagonal ***********************************************
// Do the iterative transformation from bidiagonal form to diagonal form using
//		Givens transformation.  (Golub-Reinsch)
// U and V are square.  Size of U less than or equal to that of U.
void MatrixRmn::ConvertBidiagToDiagonal(MatrixRmn &U, MatrixRmn &V, VectorRn &w, VectorRn &superDiag) const
{
	// These two index into the last bidiagonal block  (last in the matrix, it will be
	//	first one handled.
	long lastBidiagIdx = V.NumRows - 1;
	long firstBidiagIdx = 0;
	//togliere
	double aa = w.MaxAbs();
	double bb = superDiag.MaxAbs();

	double eps = 1.0e-15 * std::max(w.MaxAbs(), superDiag.MaxAbs());

	while (true) {
		bool workLeft = UpdateBidiagIndices(&firstBidiagIdx, &lastBidiagIdx, w, superDiag, eps);
		if (!workLeft) {
			break;
		}

		// Get ready for first Givens rotation
		// Push non-zero to M[2,1] with Givens transformation
		double *wPtr = w.x + firstBidiagIdx;
		double *sdPtr = superDiag.x + firstBidiagIdx;
		double extraOffDiag = 0.0;
		if ((*wPtr) == 0.0) {
			ClearRowWithDiagonalZero(firstBidiagIdx, lastBidiagIdx, U, wPtr, sdPtr, eps);
			if (firstBidiagIdx > 0) {
				if (NearZero(*(--sdPtr), eps)) {
					*sdPtr = 0.0;
				} else {
					ClearColumnWithDiagonalZero(firstBidiagIdx, V, wPtr, sdPtr, eps);
				}
			}
			continue;
		}

		// Estimate an eigenvalue from bottom four entries of M
		// This gives a lambda value which will shift the Givens rotations
		// Last four entries of M^T * M are  ( ( A, B ), ( B, C ) ).
		double A;
		A = (firstBidiagIdx < lastBidiagIdx - 1) ? Square(superDiag[lastBidiagIdx - 2]) : 0.0;
		double BSq = Square(w[lastBidiagIdx - 1]);
		A += BSq; // The "A" entry of M^T * M
		double C = Square(superDiag[lastBidiagIdx - 1]);
		BSq *= C;									// The squared "B" entry
		C += Square(w[lastBidiagIdx]);				// The "C" entry
		double lambda;								// lambda will hold the estimated eigenvalue
		lambda = sqrt(Square((A - C) * 0.5) + BSq); // Use the lambda value that is closest to C.
		if (A > C) {
			lambda = -lambda;
		}
		lambda += (A + C) * 0.5; // Now lambda equals the estimate for the last eigenvalue
		double t11 = Square(w[firstBidiagIdx]);
		double t12 = w[firstBidiagIdx] * superDiag[firstBidiagIdx];

		double c, s;
		CalcGivensValues(t11 - lambda, t12, &c, &s);
		ApplyGivensCBTD(c, s, wPtr, sdPtr, &extraOffDiag, wPtr + 1);
		V.PostApplyGivens(c, -s, firstBidiagIdx);
		long i;
		for (i = firstBidiagIdx; i < lastBidiagIdx - 1; i++) {
			// Push non-zero from M[i+1,i] to M[i,i+2]
			CalcGivensValues(*wPtr, extraOffDiag, &c, &s);
			ApplyGivensCBTD(c, s, wPtr, sdPtr, &extraOffDiag, extraOffDiag, wPtr + 1, sdPtr + 1);
			U.PostApplyGivens(c, -s, i);
			// Push non-zero from M[i,i+2] to M[1+2,i+1]
			CalcGivensValues(*sdPtr, extraOffDiag, &c, &s);
			ApplyGivensCBTD(c, s, sdPtr, wPtr + 1, &extraOffDiag, extraOffDiag, sdPtr + 1, wPtr + 2);
			V.PostApplyGivens(c, -s, i + 1);
			wPtr++;
			sdPtr++;
		}
		// Push non-zero value from M[i+1,i] to M[i,i+1] for i==lastBidiagIdx-1
		CalcGivensValues(*wPtr, extraOffDiag, &c, &s);
		ApplyGivensCBTD(c, s, wPtr, &extraOffDiag, sdPtr, wPtr + 1);
		U.PostApplyGivens(c, -s, i);

		// DEBUG
		// DebugCalcBidiagCheck( V, w, superDiag, U );
	}
}

// This is called when there is a zero diagonal entry, with a non-zero superdiagonal entry on the same row.
// We use Givens rotations to "chase" the non-zero entry across the row; when it reaches the last
//	column, it is finally zeroed away.
// wPtr points to the zero entry on the diagonal.  sdPtr points to the non-zero superdiagonal entry on the same row.
void MatrixRmn::ClearRowWithDiagonalZero(long firstBidiagIdx, long lastBidiagIdx, MatrixRmn &U, double *wPtr, double *sdPtr, double eps)
{
	double curSd = *sdPtr; // Value being chased across the row
	*sdPtr = 0.0;
	long i = firstBidiagIdx + 1;
	while (true) {
		// Rotate row i and row firstBidiagIdx (Givens rotation)
		double c, s;
		CalcGivensValues(*(++wPtr), curSd, &c, &s);
		U.PostApplyGivens(c, -s, i, firstBidiagIdx);
		*wPtr = c * (*wPtr) - s * curSd;
		if (i == lastBidiagIdx) {
			break;
		}
		curSd = s * (*(++sdPtr)); // New value pops up one column over to the right
		*sdPtr = c * (*sdPtr);
		i++;
	}
}

// This is called when there is a zero diagonal entry, with a non-zero superdiagonal entry in the same column.
// We use Givens rotations to "chase" the non-zero entry up the column; when it reaches the last
//	column, it is finally zeroed away.
// wPtr points to the zero entry on the diagonal.  sdPtr points to the non-zero superdiagonal entry in the same column.
void MatrixRmn::ClearColumnWithDiagonalZero(long endIdx, MatrixRmn &V, double *wPtr, double *sdPtr, double eps)
{
	double curSd = *sdPtr; // Value being chased up the column
	*sdPtr = 0.0;
	long i = endIdx - 1;
	while (true) {
		double c, s;
		CalcGivensValues(*(--wPtr), curSd, &c, &s);
		V.PostApplyGivens(c, -s, i, endIdx);
		*wPtr = c * (*wPtr) - s * curSd;
		if (i == 0) {
			break;
		}
		curSd = s * (*(--sdPtr)); // New value pops up one row above
		if (NearZero(curSd, eps)) {
			break;
		}
		*sdPtr = c * (*sdPtr);
		i--;
	}
}

// Matrix A is  ( ( a c ) ( b d ) ), i.e., given in column order.
// Mult's G[c,s]  times  A, replaces A.
void MatrixRmn::ApplyGivensCBTD(double cosine, double sine, double *a, double *b, double *c, double *d)
{
	double temp = *a;
	*a = cosine * (*a) - sine * (*b);
	*b = sine * temp + cosine * (*b);
	temp = *c;
	*c = cosine * (*c) - sine * (*d);
	*d = sine * temp + cosine * (*d);
}

// Now matrix A given in row order, A = ( ( a b c ) ( d e f ) ).
// Return G[c,s] * A, replace A.  d becomes zero, no need to return.
//  Also, it is certain the old *c value is taken to be zero!
void MatrixRmn::ApplyGivensCBTD(double cosine, double sine, double *a, double *b, double *c,
								double d, double *e, double *f)
{
	*a = cosine * (*a) - sine * d;
	double temp = *b;
	*b = cosine * (*b) - sine * (*e);
	*e = sine * temp + cosine * (*e);
	*c = -sine * (*f);
	*f = cosine * (*f);
}

// Helper routine for SVD conversion from bidiagonal to diagonal
bool MatrixRmn::UpdateBidiagIndices(long *firstBidiagIdx, long *lastBidiagIdx, VectorRn &w, VectorRn &superDiag, double eps)
{
	long lastIdx = *lastBidiagIdx;
	double *sdPtr = superDiag.GetPtr(lastIdx - 1); // Entry above the last diagonal entry
	while (NearZero(*sdPtr, eps)) {
		*(sdPtr--) = 0.0;
		lastIdx--;
		if (lastIdx == 0) {
			return false;
		}
	}
	*lastBidiagIdx = lastIdx;
	long firstIdx = lastIdx - 1;
	double *wPtr = w.GetPtr(firstIdx);
	while (firstIdx > 0) {
		if (NearZero(*wPtr, eps)) { // If this diagonal entry (near) zero
			*wPtr = 0.0;
			break;
		}
		if (NearZero(*(--sdPtr), eps)) { // If the entry above the diagonal entry is (near) zero
			*sdPtr = 0.0;
			break;
		}
		wPtr--;
		firstIdx--;
	}
	*firstBidiagIdx = firstIdx;
	return true;
}

// ******************************************DEBUG STUFFF

bool MatrixRmn::DebugCheckSVD(const MatrixRmn &U, const VectorRn &w, const MatrixRmn &V) const
{
	// Special SVD test code

	MatrixRmn IV(V.getNumRows(), V.getNumColumns());
	IV.SetIdentity();
	MatrixRmn VTV(V.getNumRows(), V.getNumColumns());
	MatrixRmn::TransposeMultiply(V, V, VTV);
	IV -= VTV;
	double error = IV.FrobeniusNorm();

	MatrixRmn IU(U.getNumRows(), U.getNumColumns());
	IU.SetIdentity();
	MatrixRmn UTU(U.getNumRows(), U.getNumColumns());
	MatrixRmn::TransposeMultiply(U, U, UTU);
	IU -= UTU;
	error += IU.FrobeniusNorm();

	MatrixRmn Diag(U.getNumRows(), V.getNumRows());
	Diag.SetZero();
	Diag.SetDiagonalEntries(w);
	MatrixRmn B(U.getNumRows(), V.getNumRows());
	MatrixRmn C(U.getNumRows(), V.getNumRows());
	MatrixRmn::Multiply(U, Diag, B);
	MatrixRmn::MultiplyTranspose(B, V, C);
	C -= *this;
	error += C.FrobeniusNorm();

	bool ret = (fabs(error) <= 1.0e-13 * w.MaxAbs());
	assert(ret);
	return ret;
}

//=============================================================================

const double PI = 3.1415926535897932384626433832795028841972;
const double RadiansToDegrees = 180.0 / PI;
const double DegreesToRadians = PI / 180;

const double Jacobian::DefaultDampingLambda = 1.1;

const double Jacobian::PseudoInverseThresholdFactor = 0.001;
const double Jacobian::MaxAngleJtranspose = 30.0 * DegreesToRadians;
const double Jacobian::MaxAnglePseudoinverse = 5.0 * DegreesToRadians;
const double Jacobian::MaxAngleDLS = 5.0 * DegreesToRadians;
const double Jacobian::MaxAngleSDLS = 45.0 * DegreesToRadians;
const double Jacobian::BaseMaxTargetDist = 3.4;

Jacobian::Jacobian(IKSkeleton *skeleton, std::vector<TPointD> &targetPos)
{
	Jacobian::skeleton = skeleton;
	nEffector = skeleton->getNumEffector();
	nJoint = skeleton->getNodeCount() - nEffector; //numero dei giunti meno gli effettori
	nRow = 2 * nEffector;
	nCol = nJoint;

	target = (targetPos);

	Jend.SetSize(nRow, nCol); // Matrice jacobiana
	Jend.SetZero();

	Jtarget.SetSize(nRow, nCol); // Matrice jacobiana basta sulle posizioni dei targets (non usata)
	Jtarget.SetZero();

	U.SetSize(nRow, nRow); // matrice U per il calcolo SVD
	w.SetLength(min(nRow, nCol));
	V.SetSize(nCol, nCol); // matrice V per il calcolo SVD

	dS.SetLength(nRow);		// (Posizione Target ) - (posizione End effector)
	dTheta.SetLength(nCol); // Cambiamenti degli angoli dei Joints
	dPreTheta.SetLength(nCol);

	// Usato nel: metodo del trasposto dello Jacobiano  & DLS & SDLS
	dT.SetLength(nRow);

	// Usato nel Selectively Damped Least Squares Method
	dSclamp.SetLength(nEffector);

	Jnorms.SetSize(nEffector, nCol); // Memorizza le norme della matrice attiva J

	DampingLambdaSqV.SetLength(nRow);
	diagMatIdentity.SetLength(nCol);

	Reset();
}

void Jacobian::Reset()
{
	// Usato nel Damped Least Squares Method
	DampingLambda = DefaultDampingLambda;
	DampingLambdaSq = Square(DampingLambda);
	for (int i = 0; i < DampingLambdaSqV.GetLength(); i++)
		DampingLambdaSqV[i] = DampingLambdaSq;
	for (int i = 0; i < diagMatIdentity.GetLength(); i++)
		diagMatIdentity[i] = 1.0;
	//DampingLambdaSDLS = 1.5*DefaultDampingLambda;

	dSclamp.Fill(HUGE_VAL);
}

// Calcola il vettore deltaS vector, dS, (l' errore tra end effector e target
// Calcola le matrce jacobiana J
void Jacobian::computeJacobian()
{
	// Scorro tutto lo skeleton per trovare tutti gli end effectors

	int numNode = skeleton->getNodeCount();
	for (int index = 0; index < numNode; index++) {
		IKNode *n = skeleton->getNode(index);
		int effectorCount = skeleton->getNumEffector();
		if (n->IsEffector()) {
			int i = n->getEffectorNum();
			const TPointD &targetPos = target[i];
			TPointD temp;
			// Calcolo i valori di deltaS (differenza tra end effectors e target positions.)
			temp = targetPos;
			TPointD a = n->GetS();
			temp -= n->GetS();
			if (i < effectorCount - 1) {
				temp.x = 100 * temp.x;
				temp.y = 100 * temp.y;
			}
			dS.SetCouple(i, temp);

			// Find all ancestors (they will usually all be joints)
			// Set the corresponding entries in the Jacobians J, K.
			IKNode *m = skeleton->getParent(n);

			while (m) {
				int j = m->getJointNum();
				//assert(j>=0 && j<skeleton->GetNumJoint());
				int numnode = skeleton->getNodeCount();
				assert(0 <= i && i < nEffector && 0 <= j && j < (skeleton->getNodeCount() - skeleton->getNumEffector()));
				if (m->isFrozen()) {
					Jend.SetCouple(i, j, TPointD(0.0, 0.0));

				} else {
					temp = m->GetS();  // joint pos.
					temp -= n->GetS(); // -(end effector pos. - joint pos.)

					double tx = temp.x;
					temp.x = temp.y;
					temp.y = -tx;

					if (i < effectorCount - 1) {
						temp.x = 100 * temp.x;
						temp.y = 100 * temp.y;
					}
					Jend.SetCouple(i, j, temp);
				}
				m = skeleton->getParent(m);
			}
		}
	}
}

// The delta theta values have been computed in dTheta array
// Apply the delta theta values to the joints
// Nothing is done about joint limits for now.
void Jacobian::UpdateThetas()
{
	// Update the joint angles
	for (int index = 0; index < skeleton->getNodeCount(); index++) {
		IKNode *n = skeleton->getNode(index);
		if (n->IsJoint()) {
			int i = n->getJointNum();
			n->AddToTheta(dTheta[i]);
		}
	}
	// Aggiorno le posizioni dei joint
	skeleton->compute();
}

bool Jacobian::checkJointsLimit()
{
	bool clampingDetected = false;
	/*
	Node* n = skeleton->getNode(3);
	int indexJoint = n->getJointNum();
	double theta = n->getTheta();
	double upperLimit = PI;
	double lowerLimit = 0.0;
	if(theta >upperLimit || theta <lowerLimit)
	{
		if(theta<upperLimit)	upperLimit = lowerLimit;
		clampingDetected = true;
		double clampingVar = theta - upperLimit;
		for(int i=0;i<Jactive->getNumRows();i++)
		{
			double tmp = clampingVar*Jactive->Get(i,indexJoint);
			dS[i] -= tmp;
			Jactive->Set(i,indexJoint,0.0);
		}
		n->setTheta(upperLimit);
		diagMatIdentity.Set(indexJoint, 0.0);

	}*/
	return clampingDetected;
}

void Jacobian::ZeroDeltaThetas()
{
	dTheta.SetZero();
}

// Find the delta theta values using inverse Jacobian method
// Uses a greedy method to decide scaling factor
void Jacobian::CalcDeltaThetasTranspose()
{
	const MatrixRmn &J = Jend;

	J.MultiplyTranspose(dS, dTheta);

	// Scale back the dTheta values greedily
	J.Multiply(dTheta, dT); // dT = J * dTheta
	double alpha = Dot(dS, dT) / dT.NormSq();
	assert(alpha > 0.0);
	// Also scale back to be have max angle change less than MaxAngleJtranspose
	double maxChange = dTheta.MaxAbs();
	double beta = MaxAngleJtranspose / maxChange;
	dTheta *= min(alpha, beta);
}

void Jacobian::CalcDeltaThetasPseudoinverse()
{
	MatrixRmn &J = const_cast<MatrixRmn &>(Jend);

	// costruisco matrice J1
	MatrixRmn J1;
	J1.SetSize(2, J.getNumColumns());

	for (int i = 0; i < 2; i++)
		for (int j = 0; j < J.getNumColumns(); j++)
			J1.Set(i, j, J.Get(i, j));

	// COSTRUISCO VETTORI ds1 e ds2
	VectorRn dS1(2);

	for (int i = 0; i < 2; i++)
		dS1.Set(i, dS.Get(i));

	// calcolo dtheta1
	MatrixRmn U, V;
	VectorRn w;

	U.SetSize(J1.getNumRows(), J1.getNumRows());
	w.SetLength(min(J1.getNumRows(), J1.getNumColumns()));
	V.SetSize(J1.getNumColumns(), J1.getNumColumns());

	J1.ComputeSVD(U, w, V);

	// Next line for debugging only
	assert(J1.DebugCheckSVD(U, w, V));

	// Calculate response vector dTheta that is the DLS solution.
	//	Delta target values are the dS values
	//  We multiply by Moore-Penrose pseudo-inverse of the J matrix

	double pseudoInverseThreshold = PseudoInverseThresholdFactor * w.MaxAbs();

	long diagLength = w.GetLength();
	double *wPtr = w.GetPtr();
	dTheta.SetZero();
	for (long i = 0; i < diagLength; i++) {
		double dotProdCol = U.DotProductColumn(dS1, i); // Dot product with i-th column of U
		double alpha = *(wPtr++);
		if (fabs(alpha) > pseudoInverseThreshold) {
			alpha = 1.0 / alpha;
			MatrixRmn::AddArrayScale(V.getNumRows(), V.GetColumnPtr(i), 1, dTheta.GetPtr(), 1, dotProdCol * alpha);
		}
	}

	MatrixRmn JcurrentPinv(V.getNumRows(), J1.getNumRows());		   // pseudoinversa di J1
	MatrixRmn JProjPre(JcurrentPinv.getNumRows(), J1.getNumColumns()); // Proiezione di J1
	if (skeleton->getNumEffector() > 1) {
		// calcolo la pseudoinversa di J1
		MatrixRmn VD(V.getNumRows(), J1.getNumRows()); // matrice del prodotto V*w

		double *wPtr = w.GetPtr();
		pseudoInverseThreshold = PseudoInverseThresholdFactor * w.MaxAbs();
		for (int j = 0; j < VD.getNumColumns(); j++) {
			double *VPtr = V.GetColumnPtr(j);
			double alpha = *(wPtr++); // elemento matrice diagonale
			for (int i = 0; i < V.getNumRows(); i++) {
				if (fabs(alpha) > pseudoInverseThreshold) {
					double entry = *(VPtr++);
					VD.Set(i, j, entry * (1.0 / alpha));
				}
			}
		}
		MatrixRmn::MultiplyTranspose(VD, U, JcurrentPinv);

		// calcolo la proiezione J1
		MatrixRmn::Multiply(JcurrentPinv, J1, JProjPre);

		for (int j = 0; j < JProjPre.getNumColumns(); j++)
			for (int i = 0; i < JProjPre.getNumRows(); i++) {
				double temp = JProjPre.Get(i, j);
				JProjPre.Set(i, j, -1.0 * temp);
			}
		JProjPre.AddToDiagonal(diagMatIdentity);
	}

	//task priority strategy
	for (int i = 1; i < skeleton->getNumEffector(); i++) {
		// costruisco matrice Jcurrent (Ji)
		MatrixRmn Jcurrent(2, J.getNumColumns());
		for (int j = 0; j < J.getNumColumns(); j++)
			for (int k = 0; k < 2; k++)
				Jcurrent.Set(k, j, J.Get(k + 2 * i, j));

		// costruisco il vettore dScurrent
		VectorRn dScurrent(2);
		for (int k = 0; k < 2; k++)
			dScurrent.Set(k, dS.Get(k + 2 * i));

		// Moltiplico Jcurrent per la proiezione di J(i-1)
		MatrixRmn Jdst(Jcurrent.getNumRows(), JProjPre.getNumColumns());
		MatrixRmn::Multiply(Jcurrent, JProjPre, Jdst);

		// Calcolo la pseudoinversa di Jdst
		MatrixRmn UU(Jdst.getNumRows(), Jdst.getNumRows()), VV(Jdst.getNumColumns(), Jdst.getNumColumns());
		VectorRn ww(min(Jdst.getNumRows(), Jdst.getNumColumns()));

		Jdst.ComputeSVD(UU, ww, VV);
		assert(Jdst.DebugCheckSVD(UU, ww, VV));

		MatrixRmn VVD(VV.getNumRows(), J1.getNumRows()); // matrice V*w
		VVD.SetZero();
		pseudoInverseThreshold = PseudoInverseThresholdFactor * ww.MaxAbs();
		double *wwPtr = ww.GetPtr();
		for (int j = 0; j < VVD.getNumColumns(); j++) {
			double *VVPtr = VV.GetColumnPtr(j);
			double alpha = 50 * (*(wwPtr++)); // elemento matrice diagonale
			for (int i = 0; i < VV.getNumRows(); i++) {
				if (fabs(alpha) > 100 * pseudoInverseThreshold) {
					double entry = *(VVPtr++);
					VVD.Set(i, j, entry * (1.0 / alpha));
				}
			}
		}
		MatrixRmn JdstPinv(VV.getNumRows(), J1.getNumRows());
		MatrixRmn::MultiplyTranspose(VVD, UU, JdstPinv);

		VectorRn dTemp(J1.getNumRows());
		Jcurrent.Multiply(dTheta, dTemp);

		VectorRn dTemp2(dScurrent.GetLength());
		for (int k = 0; k < dScurrent.GetLength(); k++)
			dTemp2[k] = dScurrent[k] - dTemp[k];

		// Moltiplico JdstPinv per dTemp2
		VectorRn dThetaCurrent(JdstPinv.getNumRows());
		JdstPinv.Multiply(dTemp2, dThetaCurrent);
		for (int k = 0; k < dTheta.GetLength(); k++)
			dTheta[k] += dThetaCurrent[k];

		// Infine mi calcolo la pseudoinversa di Jcurrent e quindi la sua proiezione che servirà al passo successivo

		// calcolo la pseudoinversa di Jcurrent
		Jcurrent.ComputeSVD(U, w, V);
		assert(Jcurrent.DebugCheckSVD(U, w, V));

		MatrixRmn VD(V.getNumRows(), Jcurrent.getNumRows()); // matrice del prodotto V*w

		double *wPtr = w.GetPtr();
		pseudoInverseThreshold = PseudoInverseThresholdFactor * w.MaxAbs();
		for (int j = 0; j < VVD.getNumColumns(); j++) {
			double *VPtr = V.GetColumnPtr(j);
			double alpha = *(wPtr++); // elemento matrice diagonale
			for (int i = 0; i < V.getNumRows(); i++) {
				if (fabs(alpha) > pseudoInverseThreshold) {
					double entry = *(VPtr++);
					VD.Set(i, j, entry * (1.0 / alpha));
				}
			}
		}
		MatrixRmn::MultiplyTranspose(VD, U, JcurrentPinv);

		// calcolo la proiezione Jcurrent
		MatrixRmn::Multiply(JcurrentPinv, Jcurrent, JProjPre);

		for (int j = 0; j < JProjPre.getNumColumns(); j++)
			for (int k = 0; k < JProjPre.getNumRows(); k++) {
				double temp = JProjPre.Get(k, j);
				JProjPre.Set(k, j, -1.0 * temp);
			}
		JProjPre.AddToDiagonal(diagMatIdentity);
	}

	//sw.stop();
	//std::ofstream os("C:\\buttami.txt", std::ios::app);
	//sw.print(os);
	//os.close();

	// Scale back to not exceed maximum angle changes
	double maxChange = 10 * dTheta.MaxAbs();
	if (maxChange > MaxAnglePseudoinverse) {
		dTheta *= MaxAnglePseudoinverse / maxChange;
	}
}

void Jacobian::CalcDeltaThetasDLS()
{
	const MatrixRmn &J = Jend;

	MatrixRmn::MultiplyTranspose(J, J, U); // U = J * (J^T)

	U.AddToDiagonal(DampingLambdaSqV);

	// Use the next four lines instead of the succeeding two lines for the DLS method with clamped error vector e.
	// CalcdTClampedFromdS();
	// VectorRn dTextra(2*nEffector);
	// U.Solve( dT, &dTextra );
	// J.MultiplyTranspose( dTextra, dTheta );

	// Use these two lines for the traditional DLS method
	// gennaro

	U.Solve(dS, &dT);
	J.MultiplyTranspose(dT, dTheta);

	// Scalo per non superare l'nagolo massimod i cambiamento
	double maxChange = 100 * dTheta.MaxAbs();
	if (maxChange > MaxAngleDLS) {
		dTheta *= MaxAngleDLS / maxChange;
	}
}

void Jacobian::CalcDeltaThetasDLSwithSVD()
{
	const MatrixRmn &J = Jend;

	J.ComputeSVD(U, w, V);

	// For Debug
	assert(J.DebugCheckSVD(U, w, V));

	// Calculate response vector dTheta that is the DLS solution.
	//	Delta target values are the dS values
	//  We multiply by DLS inverse of the J matrix
	long diagLength = w.GetLength();
	double *wPtr = w.GetPtr();
	dTheta.SetZero();
	for (long i = 0; i < diagLength; i++) {
		double dotProdCol = U.DotProductColumn(dS, i); // Dot product with i-th column of U
		double alpha = *(wPtr++);
		alpha = alpha / (Square(alpha) + DampingLambdaSq);
		MatrixRmn::AddArrayScale(V.getNumRows(), V.GetColumnPtr(i), 1, dTheta.GetPtr(), 1, dotProdCol * alpha);
	}

	// Scale back to not exceed maximum angle changes
	double maxChange = dTheta.MaxAbs();
	if (maxChange > MaxAngleDLS) {
		dTheta *= MaxAngleDLS / maxChange;
	}
}

void Jacobian::CalcDeltaThetasSDLS()
{
	const MatrixRmn &J = Jend;

	// Compute Singular Value Decomposition

	J.ComputeSVD(U, w, V);

	// Next line for debugging only
	assert(J.DebugCheckSVD(U, w, V));

	// Calculate response vector dTheta that is the SDLS solution.
	//	Delta target values are the dS values
	int nRows = J.getNumRows();
	int numEndEffectors = skeleton->getNumEffector(); // Equals the number of rows of J divided by three
	int nCols = J.getNumColumns();
	dTheta.SetZero();

	// Calculate the norms of the 3-vectors in the Jacobian
	long i;
	const double *jx = J.GetPtr();
	double *jnx = Jnorms.GetPtr();
	for (i = nCols * numEndEffectors; i > 0; i--) {
		double accumSq = Square(*(jx++));
		accumSq += Square(*(jx++));
		accumSq += Square(*(jx++));
		*(jnx++) = sqrt(accumSq);
	}

	// Clamp the dS values
	CalcdTClampedFromdS();

	// Loop over each singular vector
	for (i = 0; i < nRows; i++) {

		double wiInv = w[i];
		if (NearZero(wiInv, 1.0e-10)) {
			continue;
		}
		wiInv = 1.0 / wiInv;

		double N = 0.0;		// N is the quasi-1-norm of the i-th column of U
		double alpha = 0.0; // alpha is the dot product of dT and the i-th column of U

		const double *dTx = dT.GetPtr();
		const double *ux = U.GetColumnPtr(i);
		long j;
		for (j = numEndEffectors; j > 0; j--) {
			double tmp;
			alpha += (*ux) * (*(dTx++));
			tmp = Square(*(ux++));
			alpha += (*ux) * (*(dTx++));
			tmp += Square(*(ux++));
			alpha += (*ux) * (*(dTx++));
			tmp += Square(*(ux++));
			N += sqrt(tmp);
		}

		// M is the quasi-1-norm of the response to angles changing according to the i-th column of V
		//		Then is multiplied by the wiInv value.
		double M = 0.0;
		double *vx = V.GetColumnPtr(i);
		jnx = Jnorms.GetPtr();
		for (j = nCols; j > 0; j--) {
			double accum = 0.0;
			for (long k = numEndEffectors; k > 0; k--) {
				accum += *(jnx++);
			}
			M += fabs((*(vx++))) * accum;
		}
		M *= fabs(wiInv);

		double gamma = MaxAngleSDLS;
		if (N < M) {
			gamma *= N / M; // Scale back maximum permissable joint angle
		}

		// Calculate the dTheta from pure pseudoinverse considerations
		double scale = alpha * wiInv; // This times i-th column of V is the psuedoinverse response
		dPreTheta.LoadScaled(V.GetColumnPtr(i), scale);
		// Now rescale the dTheta values.
		double max = dPreTheta.MaxAbs();
		double rescale = (gamma) / (gamma + max);
		dTheta.AddScaled(dPreTheta, rescale);
		/*if ( gamma<max) {
			dTheta.AddScaled( dPreTheta, gamma/max );
		}
		else {
			dTheta += dPreTheta;
		}*/
	}

	// Scale back to not exceed maximum angle changes
	double maxChange = dTheta.MaxAbs();
	if (maxChange > 100 * MaxAngleSDLS) {
		dTheta *= MaxAngleSDLS / (MaxAngleSDLS + maxChange);
		//dTheta *= MaxAngleSDLS/maxChange;
	}
}

void Jacobian::CalcdTClampedFromdS()
{
	long len = dS.GetLength();
	long j = 0;
	for (long i = 0; i < len; i += 2, j++) {
		double normSq = Square(dS[i]) + Square(dS[i + 1]); //+Square(dS[i+2]);
		if (normSq > Square(dSclamp[j])) {
			double factor = dSclamp[j] / sqrt(normSq);
			dT[i] = dS[i] * factor;
			dT[i + 1] = dS[i + 1] * factor;
			//dT[i+2] = dS[i+2]*factor;
		} else {
			dT[i] = dS[i];
			dT[i + 1] = dS[i + 1];
			//dT[i+2] = dS[i+2];
		}
	}
}

void Jacobian::UpdatedSClampValue()
{
	// Traverse skeleton to find all end effectors
	TPointD temp;

	int numNode = skeleton->getNodeCount();
	for (int i = 0; i < numNode; i++) {
		IKNode *n = skeleton->getNode(i);
		if (n->IsEffector()) {
			int i = n->getEffectorNum();
			const TPointD &targetPos = target[i];

			// Compute the delta S value (differences from end effectors to target positions.
			// While we are at it, also update the clamping values in dSclamp;
			temp = targetPos;
			temp -= n->GetS();
			double normSi = sqrt(Square(dS[i]) + Square(dS[i + 1]));
			double norma = sqrt(temp.x * temp.x + temp.y * temp.y);
			double changedDist = norma - normSi;

			if (changedDist > 0.0) {
				dSclamp[i] = BaseMaxTargetDist + changedDist;
			} else {
				dSclamp[i] = BaseMaxTargetDist;
			}
		}
	}
}