예제 #1
0
	double SPDTensorDL::f(Variable *x) const
	{
		const double *xptr = x->ObtainReadData();
		/*each slice of Xaj is B alpha_j in [(6), CS15]*/
		SharedSpace *Xalpha = new SharedSpace(3, dim, dim, N);
		double *Xalphaptr = Xalpha->ObtainWriteEntireData();

		integer dd = dim * dim, nnum = num, NN = N;
		/*Xalpha <-- \mathbb{B} alpha*/
		dgemm_(GLOBAL::N, GLOBAL::N, &dd, &NN, &nnum, &GLOBAL::DONE, const_cast<double *> (xptr), &dd,
			alpha, &nnum, &GLOBAL::DZERO, Xalphaptr, &dd);
		x->AddToTempData("Xalpha", Xalpha);
		/*compute cholesky decomposition for all slices in Xalpha*/
		SPDTensor *Mani = dynamic_cast<SPDTensor *> (Domain);
		Mani->CholeskyRepresentation(x);

		const SharedSpace *SharedL = x->ObtainReadTempData("XaL");
		const double *L = SharedL->ObtainReadData();

		SharedSpace *SharedlogLXL = new SharedSpace(3, dim, dim, N);
		double *logLXL = SharedlogLXL->ObtainWriteEntireData();
		double *Ltmp = new double[dim * dim];
		integer length = dim * dim, ddim = dim, info;
		for (integer i = 0; i < N; i++)
		{
			dcopy_(&length, const_cast<double *> (L) + i * length, &GLOBAL::IONE, Ltmp, &GLOBAL::IONE);
			/*Solve the linear system Ls X = Li, i.e., X = Ls^{-1} Li. The solution X is stored in Li.
			Note that Li is a lower triangular matrix.
			Details: http://www.netlib.org/lapack/explore-html/d6/d6f/dtrtrs_8f.html */
			dtrtrs_(GLOBAL::L, GLOBAL::N, GLOBAL::N, &ddim, &ddim, Ls + dim * dim * i, &ddim, Ltmp, &ddim, &info);
			if (info != 0)
			{
				std::cout << "Warning: Solving linear system in SPDTensorDL::f failed with info:" << info << "!" << std::endl;
			}
			dgemm_(GLOBAL::N, GLOBAL::T, &ddim, &ddim, &ddim, &GLOBAL::DONE, Ltmp, &ddim, Ltmp, &ddim, &GLOBAL::DZERO, logLXL + ddim * ddim * i, &ddim);
			Matrix MMt(logLXL + ddim * ddim * i, ddim, ddim);
			Matrix::LogSymmetricM(GLOBAL::L, MMt, MMt);
		}
		delete[] Ltmp;

		length = dim * dim * N;
		double result = dnrm2_(&length, logLXL, &GLOBAL::IONE);
		x->AddToTempData("logLXL", SharedlogLXL);
		result *= result;
		result /= 2.0;
		/*add \Omega(X) = \sum \tr(X_i)*/
		for (integer i = 0; i < num; i++)
		{
			for (integer j = 0; j < dim; j++)
			{
				result += lambdaX * xptr[i * dim * dim + j * dim + j];
			}
		}
		return result;
	};
예제 #2
0
void L2Sphere::DiffRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
	if (IsEtaXiSameDir)
	{
		VectorTransport(x, etax, y, xix, result);

		if (IsEtaXiSameDir && (HasHHR || UpdBetaAlone))
		{
			const double *etaxTV = etax->ObtainReadData();
			const double *xixTV = xix->ObtainReadData();
			double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
			SharedSpace *beta = new SharedSpace(1, 3);
			double *betav = beta->ObtainWriteEntireData();
			betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
			betav[1] = Metric(x, etax, etax);
			betav[2] = Metric(x, result, result) * EtatoXi * EtatoXi;
			etax->AddToTempData("beta", beta);

			if (HasHHR)
			{
				Vector *TReta = result->ConstructEmpty();
				result->CopyTo(TReta);
				ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
				SharedSpace *SharedTReta = new SharedSpace(TReta);
				etax->AddToTempData("betaTReta", SharedTReta);
			}
		}
		return;
	}
	std::cout << "Warning: The differentiated retraction has not been implemented!" << std::endl;
	xix->CopyTo(result);
};
예제 #3
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::ObtainPerp(Variable *x) const
{
	const double *xM = x->ObtainReadData();
	SharedSpace *SharedSpacePerp = new SharedSpace(2, n, n - p);
	double *Perp = SharedSpacePerp->ObtainWriteEntireData();
	for (integer i = 0; i < n * (n - p); i++)
		Perp[i] = genrand_gaussian();
	double *temp = new double[p * (n - p)];
	char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
	double one = 1, zero = 0, neg_one = -1;
	integer P = p, N = n, NmP = n - p;
	// temp = X^T * Perp
	dgemm_(transt, transn, &P, &NmP, &N, &one, const_cast<double *> (xM), &N, Perp, &N, &zero, temp, &P);
	// Perp = Perp - X * temp
	dgemm_(transn, transn, &N, &NmP, &P, &neg_one, const_cast<double *> (xM), &N, temp, &P, &one, Perp, &N);
	delete[] temp;

	integer *jpvt = new integer[NmP];
	integer lwork = 2 * NmP + (1 + NmP) * INITIALBLOCKSIZE, info;
	double *tau = new double[NmP + lwork];
	double *work = tau + NmP;
	for (integer i = 0; i < NmP; i++)
		jpvt[i] = 0;
	dgeqp3_(&N, &NmP, Perp, &N, jpvt, tau, work, &lwork, &info);
	if (info < 0)
		Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
	dorgqr_(&N, &NmP, &NmP, Perp, &N, tau, work, &lwork, &info);
	if (info < 0)
		Rcpp::Rcout << "Error in forming Q matrix!" << std::endl;
	delete[] jpvt;
	delete[] tau;

	x->AddToTempData("Perp", SharedSpacePerp);
};
예제 #4
0
void ProductManifold::Retraction(Variable *x, Vector *etax, Variable *result) const
{
#ifdef TESTELASTICCURVESRO
	if (x->TempDataExist("w"))
	{
		const SharedSpace *Sharedw = x->ObtainReadTempData("w");
		const double *wptr = Sharedw->ObtainReadData();
		SharedSpace *Sharedww = new SharedSpace(1, 1);
		double *wwptr = Sharedww->ObtainWriteEntireData();
		wwptr[0] = wptr[0] * 0.8;
		result->AddToTempData("w", Sharedww);
	}
#endif

	ProdVariable *prodx = dynamic_cast<ProdVariable *> (x);
	ProdVector *prodetax = dynamic_cast<ProdVector *> (etax);
	ProdVector *prodresult = dynamic_cast<ProdVector *> (result);
	prodresult->NewMemoryOnWrite();
	for (integer i = 0; i < numofmani; i++)
	{
		for (integer j = powsinterval[i]; j < powsinterval[i + 1]; j++)
		{
			manifolds[i]->Retraction(prodx->GetElement(j), prodetax->GetElement(j), prodresult->GetElement(j));
		}
	}

#ifdef CHECKMEMORY
	prodresult->CheckMemory();
#endif
};
예제 #5
0
void mexProblem::ObtainElementFromMxArray(Element *X, const mxArray *Xmx)
{
	// copy the main data from mxArray to X
	double *Xmxptr = mxGetPr(GetFieldbyName(Xmx, 0, "main"));
	integer lengthX = X->Getlength();
	integer inc = 1;
	double *Xptr = X->ObtainWriteEntireData();
	dcopy_(&lengthX, Xmxptr, &inc, Xptr, &inc);

	// copy temp data from mxArray to X
	integer nfields = mxGetNumberOfFields(Xmx);
	const char **fnames;
	mxArray *tmp;

	fnames = static_cast<const char **> (mxCalloc(nfields, sizeof(*fnames)));
	for (integer i = 0; i < nfields; i++)
	{
		fnames[i] = mxGetFieldNameByNumber(Xmx, i);
		if (strcmp(fnames[i], "main") != 0)
		{
			tmp = GetFieldbyName(Xmx, 0, fnames[i]);
			double *tmpptr = mxGetPr(tmp);
			integer length = mxGetM(tmp);
			SharedSpace *Sharedtmp = new SharedSpace(1, length);
			double *Sharedtmpptr = Sharedtmp->ObtainWriteEntireData();
			dcopy_(&length, tmpptr, &inc, Sharedtmpptr, &inc);
			X->AddToTempData(fnames[i], Sharedtmp);
		}
	}
};
예제 #6
0
void ProductManifold::DiffRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
	ProdVariable *prodx = dynamic_cast<ProdVariable *> (x);
	ProdVector *prodetax = dynamic_cast<ProdVector *> (etax);
	ProdVariable *prody = dynamic_cast<ProdVariable *> (y);
	ProdVector *prodxix = dynamic_cast<ProdVector *> (xix);
	ProdVector *prodresult = dynamic_cast<ProdVector *> (result);
	if (xix == result)
	{
		ProdVector *prodresultTemp = prodresult->ConstructEmpty();
		prodresultTemp->NewMemoryOnWrite();
		for (integer i = 0; i < numofmani; i++)
		{
			for (integer j = powsinterval[i]; j < powsinterval[i + 1]; j++)
			{
				manifolds[i]->DiffRetraction(prodx->GetElement(j), prodetax->GetElement(j), prody->GetElement(j), prodxix->GetElement(j), prodresultTemp->GetElement(j), IsEtaXiSameDir);
			}
		}
		prodresultTemp->CopyTo(prodresult);
		delete prodresultTemp;
	}
	else
	{
		prodresult->NewMemoryOnWrite();
		for (integer i = 0; i < numofmani; i++)
		{
			for (integer j = powsinterval[i]; j < powsinterval[i + 1]; j++)
			{
				manifolds[i]->DiffRetraction(prodx->GetElement(j), prodetax->GetElement(j), prody->GetElement(j), prodxix->GetElement(j), prodresult->GetElement(j), IsEtaXiSameDir);
			}
		}
	}

#ifdef CHECKMEMORY
	prodresult->CheckMemory();
#endif

	if (IsEtaXiSameDir)
	{
		const double *etaxTV = etax->ObtainReadData();
		const double *xixTV = xix->ObtainReadData();
		double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
		SharedSpace *beta = new SharedSpace(1, 1);
		double *betav = beta->ObtainWriteEntireData();
		betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
		etax->AddToTempData("beta", beta);

		Vector *TReta = result->ConstructEmpty();
		result->CopyTo(TReta);
		ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
		SharedSpace *SharedTReta = new SharedSpace(TReta);
		etax->AddToTempData("betaTReta", SharedTReta);
	}
};
예제 #7
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::EucHvToHv(Variable *x, Vector *etax, Vector *exix, Vector *xix, const Problem *prob) const
{
	if (metric == EUCLIDEAN)
	{
		char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
		double one = 1, zero = 0;
		integer inc = 1, N = n, P = p, Length = N * P;
		double *symxtegfptr;
		SharedSpace *symxtegf;
		if (x->TempDataExist("symxtegf"))
		{
			symxtegf = const_cast<SharedSpace *> (x->ObtainReadTempData("symxtegf"));
			symxtegfptr = const_cast<double *> (symxtegf->ObtainReadData());
		}
		else
		{
			const double *xxM = x->ObtainReadData();
			const SharedSpace *Sharedegf = x->ObtainReadTempData("EGrad");
			Vector *egfVec = Sharedegf->GetSharedElement();
			const double *egf = egfVec->ObtainReadData();
			symxtegf = new SharedSpace(2, p, p);
			symxtegfptr = symxtegf->ObtainWriteEntireData();
			dgemm_(transt, transn, &P, &P, &N, &one, const_cast<double *> (xxM), &N, const_cast<double *> (egf), &N, &zero, symxtegfptr, &P);
			for (integer i = 0; i < p; i++)
			{
				for (integer j = i + 1; j < p; j++)
				{
					symxtegfptr[i + j * p] += symxtegfptr[j + i * p];
					symxtegfptr[i + j * p] /= 2.0;
					symxtegfptr[j + i * p] = symxtegfptr[i + j * p];
				}
			}
		}

		exix->CopyTo(xix);
		double *resultTV = xix->ObtainWritePartialData();
		const double *etaxTV = etax->ObtainReadData();

		double negone = -1;
		dgemm_(transn, transn, &N, &P, &P, &negone, const_cast<double *> (etaxTV), &N, symxtegfptr, &P, &one, resultTV, &N);
		ExtrProjection(x, xix, xix);
		if (!x->TempDataExist("symxtegf"))
		{
			x->AddToTempData("symxtegf", symxtegf);
		}
		return;
	}
	Rcpp::Rcout << "Warning:The function converting action of Eucidean Hessian to action of Riemannian Hessian has not been done!" << std::endl;
};
double EucQuadratic::f(Variable *x) const
{
	const double *v = x->ObtainReadData();
	SharedSpace *Temp = new SharedSpace(1, Dim);
	double *temp = Temp->ObtainWriteEntireData();

	char *transn = const_cast<char *> ("n");
	double one = 1, zero = 0;
	integer inc = 1, N = Dim;
	dgemv_(transn, &N, &N, &one, A, &N, const_cast<double *> (v), &inc, &zero, temp, &inc);

	x->AddToTempData("Ax", Temp);

	return ddot_(&N, const_cast<double *> (v), &inc, temp, &inc);
};
예제 #9
0
    void juliaProblem::EucHessianEta(Variable *x, Vector *etax, Vector *exix) const
    {
//        x->Print("cpp hf x");//---
//        etax->Print("cpp hf etax");//---
        jl_value_t* array_type = jl_apply_array_type(jl_float64_type, 1);
        double *xptr = x->ObtainWritePartialData();
        jl_array_t *arrx = jl_ptr_to_array_1d(array_type, xptr, x->Getlength(), 0);
        double *etaxptr = etax->ObtainWritePartialData();
        jl_array_t *arretax = jl_ptr_to_array_1d(array_type, etaxptr, etax->Getlength(), 0);

        jl_array_t *arrtmp = nullptr;
        if(x->TempDataExist(("Tmp")))
        {
            const SharedSpace *Tmp = x->ObtainReadTempData("Tmp");
//            Tmp->Print("cpp hf inTmp");//---
            const double *tmpptr = Tmp->ObtainReadData();
            arrtmp = jl_ptr_to_array_1d(array_type, const_cast<double *> (tmpptr), Tmp->Getlength(), 0);
        } else
        {
            arrtmp = jl_ptr_to_array_1d(array_type, nullptr, 0, 0);
        }

        jl_value_t *retresult = jl_call3(jl_Hess, (jl_value_t *) arrx, (jl_value_t *) arrtmp, (jl_value_t *) arretax);
        jl_array_t *jl_exix = (jl_array_t *) jl_get_nth_field(retresult, 0);
        jl_array_t *outtmp = (jl_array_t *) jl_get_nth_field(retresult, 1);

        if(jl_array_len(jl_exix) != etax->Getlength())
        {
            std::cout << "error: the size of the action of the Hessian is not correct!" << std::endl;
            exit(EXIT_FAILURE);
        }

        integer exixlen = exix->Getlength();
        double *exixptr = exix->ObtainWriteEntireData();
        dcopy_(&exixlen, (double*)jl_array_data(jl_exix), &GLOBAL::IONE, exixptr, &GLOBAL::IONE);
//        exix->Print("cpp hf exix:");//---

        integer outtmplen = jl_array_len(outtmp);
        if(outtmplen != 0)
        {
            SharedSpace *sharedouttmp = new SharedSpace(1, outtmplen);
            double *outtmpptr = sharedouttmp->ObtainWriteEntireData();
            dcopy_(&outtmplen, (double*)jl_array_data(outtmp), &GLOBAL::IONE, outtmpptr, &GLOBAL::IONE);
            x->RemoveFromTempData("Tmp");
            x->AddToTempData("Tmp", sharedouttmp);
        }
	};
예제 #10
0
	double EucQuadratic::f(Variable *x) const
	{
		const double *v = x->ObtainReadData();
		SharedSpace *Temp = new SharedSpace(1, Dim);
		double *temp = Temp->ObtainWriteEntireData();

		char *transn = const_cast<char *> ("n");
		double one = 1, zero = 0;
		integer inc = 1, N = Dim;
		// temp <- A * v, details: http://www.netlib.org/lapack/explore-html/dc/da8/dgemv_8f.html
		dgemv_(transn, &N, &N, &one, A, &N, const_cast<double *> (v), &inc, &zero, temp, &inc);

		x->AddToTempData("Ax", Temp);

		// output v^T temp, details: http://www.netlib.org/lapack/explore-html/d5/df6/ddot_8f.html
		return ddot_(&N, const_cast<double *> (v), &inc, temp, &inc);
	};
예제 #11
0
    double juliaProblem::f(Variable *x) const
    {
//        x->Print("cpp f x");//---
        jl_value_t* array_type = jl_apply_array_type(jl_float64_type, 1);
        double *xptr = x->ObtainWritePartialData();
        jl_array_t *arrx = jl_ptr_to_array_1d(array_type, xptr, x->Getlength(), 0);

        jl_array_t *arrtmp = nullptr;
        if(x->TempDataExist(("Tmp")))
        {
            const SharedSpace *Tmp = x->ObtainReadTempData("Tmp");
            const double *tmpptr = Tmp->ObtainReadData();
            arrtmp = jl_ptr_to_array_1d(array_type, const_cast<double *> (tmpptr), Tmp->Getlength(), 0);
        } else
        {
            arrtmp = jl_ptr_to_array_1d(array_type, nullptr, 0, 0);
        }

        jl_value_t *retresult = jl_call2(jl_f, (jl_value_t *) arrx, (jl_value_t *) arrtmp);
        jl_get_nth_field(retresult, 0);
        jl_value_t *fx = jl_get_nth_field(retresult, 0);
        jl_array_t *outtmp = (jl_array_t *) jl_get_nth_field(retresult, 1);

        integer outtmplen = jl_array_len(outtmp);
        SharedSpace *sharedouttmp = new SharedSpace(1, outtmplen);
        double *outtmpptr = sharedouttmp->ObtainWriteEntireData();
        dcopy_(&outtmplen, (double*)jl_array_data(outtmp), &GLOBAL::IONE, outtmpptr, &GLOBAL::IONE);
//        sharedouttmp->Print("cpp f tmp:");//----
        x->RemoveFromTempData("Tmp");
        x->AddToTempData("Tmp", sharedouttmp);

        if(jl_is_float64(fx))
        {
            double result = jl_unbox_float64(fx);
//            std::cout << "cpp f fx:" << result << std::endl;//-----
            return result;
        }
        std::cout << "Error: The objectve function must return a number of double precision!" << std::endl;
        exit(EXIT_FAILURE);
	};
예제 #12
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::ConRetraction(Variable *x, Vector *etax, Variable *result) const
{ // only accept intrinsic approach
	const double *V = etax->ObtainReadData();
	Vector *exetax = nullptr;
	double *M = new double[3 * n * n + 2 * n];
	double *wr = M + n * n;
	double *wi = wr + n;
	double *Vs = wi + n;
	double *VsT = Vs + n * n;

	double r2 = sqrt(2.0);
	integer idx = 0;
	for (integer i = 0; i < p; i++)
	{
		M[i + i * n] = 0;
		for (integer j = i + 1; j < p; j++)
		{
			M[j + i * n] = V[idx] / r2;
			M[i + j * n] = -M[j + i * n];
			idx++;
		}
	}

	for (integer i = 0; i < p; i++)
	{
		for (integer j = p; j < n; j++)
		{
			M[j + i * n] = V[idx];
			M[i + j * n] = -V[idx];
			idx++;
		}
	}
	for (integer i = p; i < n; i++)
	{
		for (integer j = p; j < n; j++)
		{
			M[j + i * n] = 0;
		}
	}
	char *jobv = const_cast<char *> ("V"), *sortn = const_cast<char *> ("N");
	integer N = n, P = p, NmP = n - p, sdim, info;
	integer lwork = -1;
	double lworkopt;

	dgees_(jobv, sortn, nullptr, &N, M, &N, &sdim, wr, wi, Vs, &N, &lworkopt, &lwork, nullptr, &info);
	lwork = static_cast<integer> (lworkopt);
	double *work = new double[lwork];
	dgees_(jobv, sortn, nullptr, &N, M, &N, &sdim, wr, wi, Vs, &N, work, &lwork, nullptr, &info);

	char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
	double cosv, sinv;
	integer two = 2, inc = 1;
	double one = 1, zero = 0;
	double block[4];
	for (integer i = 0; i < n; i++)
	{
		if (i + 1 < n && fabs(M[i + (i + 1) * n]) > std::numeric_limits<double>::epsilon())
		{
			cosv = cos(M[i + (i + 1) * n]);
			sinv = sin(M[i + (i + 1) * n]);
			block[0] = cosv; block[1] = -sinv; block[2] = sinv; block[3] = cosv;
			dgemm_(transn, transn, &N, &two, &two, &one, Vs + i * n, &N, block, &two, &zero, VsT + i * n, &N);
			i++;
		}
		else
		{
			dcopy_(&N, Vs + i * n, &inc, VsT + i * n, &inc);
		}
	}
	dgemm_(transn, transt, &N, &N, &N, &one, VsT, &N, Vs, &N, &zero, M, &N);

	if (!x->TempDataExist("Perp"))
	{
		ObtainPerp(x);
	}
	const SharedSpace *SharedSpacePerp = x->ObtainReadTempData("Perp");
	const double *Perp = SharedSpacePerp->ObtainReadData();

	const double *xM = x->ObtainReadData();
	double *resultM = result->ObtainWriteEntireData();
	SharedSpace *ResultSharedPerp = new SharedSpace(2, n, n - p);
	double *ResultPerp = ResultSharedPerp->ObtainWriteEntireData();

	dgemm_(transn, transn, &P, &P, &P, &one, const_cast<double *> (xM), &N, M, &N, &zero, resultM, &N);
	dgemm_(transn, transn, &P, &P, &NmP, &one, const_cast<double *> (Perp), &N, M + p, &N, &one, resultM, &N);

	dgemm_(transn, transn, &NmP, &P, &P, &one, const_cast<double *> (xM + p), &N, M, &N, &zero, resultM + p, &N);
	dgemm_(transn, transn, &NmP, &P, &NmP, &one, const_cast<double *> (Perp + p), &N, M + p, &N, &one, resultM + p, &N);

	dgemm_(transn, transn, &P, &NmP, &P, &one, const_cast<double *> (xM), &N, M + n * p, &N, &zero, ResultPerp, &N);
	dgemm_(transn, transn, &P, &NmP, &NmP, &one, const_cast<double *> (Perp), &N, M + n * p + p, &N, &one, ResultPerp, &N);

	dgemm_(transn, transn, &NmP, &NmP, &P, &one, const_cast<double *> (xM + p), &N, M + n * p, &N, &zero, ResultPerp + p, &N);
	dgemm_(transn, transn, &NmP, &NmP, &NmP, &one, const_cast<double *> (Perp + p), &N, M + n * p + p, &N, &one, ResultPerp + p, &N);

	result->AddToTempData("Perp", ResultSharedPerp);

	delete[] work;
	delete[] M;
};
예제 #13
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::ObtainExtrHHR(Variable *x, Vector *intretax, Vector *result) const
{
	if (!x->TempDataExist("HHR"))
	{
		const double *xM = x->ObtainReadData();
		SharedSpace *HouseHolderResult = new SharedSpace(2, x->Getsize()[0], x->Getsize()[1]);
		double *ptrHHR = HouseHolderResult->ObtainWriteEntireData();
		SharedSpace *HHRTau = new SharedSpace(1, x->Getsize()[1]);
		double *tau = HHRTau->ObtainWriteEntireData();

		integer N = x->Getsize()[0], P = x->Getsize()[1], Length = N * P, inc = 1;
		double one = 1, zero = 0;
		dcopy_(&Length, const_cast<double *> (xM), &inc, ptrHHR, &inc);
		integer *jpvt = new integer[P];
		integer info;
		integer lwork = -1;
		double lworkopt;
		for (integer i = 0; i < P; i++)
			jpvt[i] = i + 1;
		dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, &lworkopt, &lwork, &info);
		lwork = static_cast<integer> (lworkopt);
		double *work = new double[lwork];
		dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, work, &lwork, &info);
		x->AddToTempData("HHR", HouseHolderResult);
		x->AddToTempData("HHRTau", HHRTau);
		if (info < 0)
			Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
		for (integer i = 0; i < P; i++)
		{
			if (jpvt[i] != (i + 1))
				Rcpp::Rcout << "Error in qf retraction!" << std::endl;
		}
		delete[] jpvt;
		delete[] work;
	}

	const double *xM = x->ObtainReadData();
	const SharedSpace *HHR = x->ObtainReadTempData("HHR");
	const SharedSpace *HHRTau = x->ObtainReadTempData("HHRTau");
	const double *ptrHHR = HHR->ObtainReadData();
	const double *ptrHHRTau = HHRTau->ObtainReadData();
	const double *intretaxTV = intretax->ObtainReadData();
	double *resultTV = result->ObtainWriteEntireData();

	char *transn = const_cast<char *> ("n"), *sidel = const_cast<char *> ("l");
	integer N = x->Getsize()[0], P = x->Getsize()[1], inc = 1, Length = N * P;
	integer info;
	double r2 = sqrt(2.0);
	integer idx = 0;
	for (integer i = 0; i < p; i++)
	{
		resultTV[i + i * n] = 0;
		for (integer j = i + 1; j < p; j++)
		{
			resultTV[j + i * n] = intretaxTV[idx] / r2;
			resultTV[i + j * n] = -resultTV[j + i * n];
			idx++;
		}
	}

	for (integer i = 0; i < p; i++)
	{
		for (integer j = p; j < n; j++)
		{
			resultTV[j + i * n] = intretaxTV[idx];
			idx++;
		}
	}

	double sign;
	for (integer i = 0; i < p; i++)
	{
		sign = (ptrHHR[i + n * i] >= 0) ? 1 : -1;
		dscal_(&P, &sign, resultTV + i, &N);
	}
	integer lwork = -1;
	double lworkopt;
	dormqr_(sidel, transn, &N, &P, &P, const_cast<double *> (ptrHHR), &N, const_cast<double *> (ptrHHRTau), resultTV, &N, &lworkopt, &lwork, &info);
	lwork = static_cast<integer> (lworkopt);

	double *work = new double[lwork];
	dormqr_(sidel, transn, &N, &P, &P, const_cast<double *> (ptrHHR), &N, const_cast<double *> (ptrHHRTau), resultTV, &N, work, &lwork, &info);
	delete[] work;
};
예제 #14
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::DiffqfRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
	Vector *extempx = EMPTYEXTR->ConstructEmpty();
	const double *extempxTV;
	if (IsIntrApproach)
	{
		ObtainExtr(x, xix, extempx);
		extempxTV = extempx->ObtainReadData();
	}
	else
	{
		xix->CopyTo(extempx);
		extempxTV = extempx->ObtainWritePartialData();
	}
	const double *yM = y->ObtainReadData();
	double *resultTV = result->ObtainWriteEntireData();
	const SharedSpace *HHR = y->ObtainReadTempData("HHR");
	const double *ptrHHR = HHR->ObtainReadData();
	double *YtVRinv = new double[p * p];
	integer inc = 1, N = n, P = p;
	char *left = const_cast<char *> ("r"), *up = const_cast<char *> ("u"),
		*transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t"), *nonunit = const_cast<char *> ("n");
	double one = 1, zero = 0;
	dtrsm_(left, up, transn, nonunit, &N, &P, &one, const_cast<double *> (ptrHHR), &N, const_cast<double *> (extempxTV), &N);

	double sign;
	for (integer i = 0; i < P; i++)
	{
		sign = (ptrHHR[i + i * N] >= 0) ? 1 : -1;
		dscal_(&N, &sign, const_cast<double *> (extempxTV + i * N), &inc);
	}
	dgemm_(transt, transn, &P, &P, &N, &one, const_cast<double *> (yM), &N, const_cast<double *> (extempxTV), &N, &zero, YtVRinv, &P);
	for (integer i = 0; i < p; i++)
	{
		YtVRinv[i + p * i] = -YtVRinv[i + p * i];
		for (integer j = i + 1; j < p; j++)
		{
			YtVRinv[i + p * j] = -YtVRinv[j + p * i] - YtVRinv[i + p * j];
			YtVRinv[j + p * i] = 0;
		}
	}
	dgemm_(transn, transn, &N, &P, &P, &one, const_cast<double *> (yM), &N, YtVRinv, &P, &one, const_cast<double *> (extempxTV), &N);
	if (IsIntrApproach)
	{
		ObtainIntr(y, extempx, result);
	}
	else
	{
		extempx->CopyTo(result);
	}
	delete[] YtVRinv;
	delete extempx;

	if (IsEtaXiSameDir && (HasHHR || UpdBetaAlone))
	{
		const double *etaxTV = etax->ObtainReadData();
		const double *xixTV = xix->ObtainReadData();
		double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
		SharedSpace *beta = new SharedSpace(1, 3);
		double *betav = beta->ObtainWriteEntireData();
		betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
		betav[1] = Metric(x, etax, etax);
		betav[2] = Metric(x, result, result) * EtatoXi * EtatoXi;
		etax->AddToTempData("beta", beta);

		if (HasHHR)
		{
			Vector *TReta = result->ConstructEmpty();
			result->CopyTo(TReta);
			ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
			SharedSpace *SharedTReta = new SharedSpace(TReta);
			etax->AddToTempData("betaTReta", SharedTReta);
		}
	}
};
예제 #15
0
파일: Stiefel.cpp 프로젝트: cran/fdasrvf
void Stiefel::qfRetraction(Variable *x, Vector *etax, Variable *result) const
{
	//x->Print("x in qf:");//---
	const double *U = x->ObtainReadData();
	const double *V;
	Vector *exetax = nullptr;
	if (IsIntrApproach)
	{
		exetax = EMPTYEXTR->ConstructEmpty();
		ObtainExtr(x, etax, exetax);
		V = exetax->ObtainReadData();
		//exetax->Print("exetax:");//---
	}
	else
	{
		V = etax->ObtainReadData();
	}
	double *resultM = result->ObtainWriteEntireData();
	SharedSpace *HouseHolderResult = new SharedSpace(2, x->Getsize()[0], x->Getsize()[1]);
	double *ptrHHR = HouseHolderResult->ObtainWriteEntireData();
	SharedSpace *HHRTau = new SharedSpace(1, x->Getsize()[1]);
	double *tau = HHRTau->ObtainWriteEntireData();

	integer N = x->Getsize()[0], P = x->Getsize()[1], Length = N * P, inc = 1;
	double one = 1, zero = 0;
	dcopy_(&Length, const_cast<double *> (V), &inc, ptrHHR, &inc);
	daxpy_(&Length, &one, const_cast<double *> (U), &inc, ptrHHR, &inc);
	integer *jpvt = new integer[P];
	integer info;
	integer lwork = -1;
	double lworkopt;
	for (integer i = 0; i < P; i++)
		jpvt[i] = i + 1;
	dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, &lworkopt, &lwork, &info);
	lwork = static_cast<integer> (lworkopt);
	double *work = new double[lwork];
	dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, work, &lwork, &info);
	if (info < 0)
		Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
	for (integer i = 0; i < P; i++)
	{
		if (jpvt[i] != (i + 1))
			Rcpp::Rcout << "Error in qf retraction!" << std::endl;
	}
	double *signs = new double[P];
	for (integer i = 0; i < P; i++)
		signs[i] = (ptrHHR[i + i * N] >= 0) ? 1 : -1;
	dcopy_(&Length, ptrHHR, &inc, resultM, &inc);
	dorgqr_(&N, &P, &P, resultM, &N, tau, work, &lwork, &info);
	if (info < 0)
		Rcpp::Rcout << "Error in forming Q matrix!" << std::endl;
	for (integer i = 0; i < P; i++)
		dscal_(&N, signs + i, resultM + i * N, &inc);
	result->AddToTempData("HHR", HouseHolderResult);
	result->AddToTempData("HHRTau", HHRTau);
	delete[] jpvt;
	delete[] work;
	delete[] signs;
	if (exetax != nullptr)
		delete exetax;
	//result->Print("result in qf:");//---
};
예제 #16
0
	double ShapePathStraighten::f(Variable *x) const
	{
		const double *l = x->ObtainReadData();
		const double *O = l + numP;
		const double *m = O + dim * dim;
		//double *q2_new = new double[numP*dim];
        SharedSpace *Shared_q2_new = new SharedSpace(2, numP, dim); //===================
        double *q2_new = Shared_q2_new->ObtainWriteEntireData();   //==================

    
        Apply_Oml(O, m, l, numP, dim, q2_coefs, q2_new);
		//ForDebug::Print("q2q2=============", q2_new, numP, dim);
    
		//******************************compute path_x*********************************
		//initiate
		PSCVariable PSCV(numP, dim, numC);
		PSCV.Generate(q1, q2_new);
		//PSCV.Print();
		PreShapeCurves PSCurves(numP, dim, numC);
		PreShapePathStraighten PreSPSprob(numP, dim, numC);
		PreSPSprob.SetDomain(&PSCurves);
    
		//get updated preshape geodesic
		RSD *RSDsolver = new RSD(&PreSPSprob, &PSCV);
		//RSDsolver->LineSearch_LS = static_cast<LSAlgo> (i);
		RSDsolver->Debug= NOOUTPUT;
		RSDsolver->LineSearch_LS = INPUTFUN;
		RSDsolver->LinesearchInput = &ShapePathStraiLinesearchInput;
		RSDsolver->Max_Iteration = 16;
        RSDsolver->IsPureLSInput = true;
		//RSDsolver->Stop_Criterion = GRAD_F;
	//    RSDsolver->CheckParams();
		RSDsolver->Run();
		//std::cout << "energy:" << RSDsolver->Getfinalfun() << std::endl;//--
		//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% forcout %%%%%%%%%%%%%%%%%%%%%%
    
		//store preshape geodesic to compute distance and eta
		//current preshape geodesic between q1 and q2_new stored in PreGeodesic
		PSCVariable *PreGeodesic = PSCV.ConstructEmpty();
		RSDsolver->GetXopt()->CopyTo(PreGeodesic);
    
		//PreGeodesic->Print();
    
    
		//#############################Compute Distance##############################
		  //######Compute Dalpha######
		const double *GeoPath = PreGeodesic->ObtainReadData();
		//PreGeodesic->Print("kdsjfl;akjsdlfjals;dfjal;dsjfal;dsjfl;asdjfl;asdjfl;asjd");
		double *Dalpha = new double[numP*dim*numC];
		integer stp = numC - 1;
		for (integer t = 0; t < numC; t++)
		{
			if (t != 0) {
				for (integer j = 0; j < dim; j++)
				{
					for (integer i = 0; i < numP; i++)
					{
						Dalpha[t*numP*dim+j*numP+i] = stp*(GeoPath[t*numP*dim+j*numP+i] - GeoPath[(t-1)*numP*dim+j*numP+i]);
					}
				}
			}
			//Project c(tau/numC) into T_alpha(M)
		   if (t == 0)
		   {
			   for (integer j = 0; j < dim; j++)
			   {
					for (integer i = 0; i < numP; i++)
					{
						Dalpha[j*numP+i] = 0.0;
					}
				}
			}
			else
			{
				PreShapePathStraighten::Item_2(GeoPath + t*numP*dim, numP, dim, Dalpha + t*numP*dim);
			}
		}
		//ForDebug::Print("alphaalphalphalphalphalph", Dalpha, numP, dim, numC);
    
		//#######Compute Distance#########
		double intv;
		double *temp = new double[numC];
		double distance;
    
		for (integer i = 0; i < numC; i++)
		{
			temp[i] = PreShapePathStraighten::InnerProd_Q(Dalpha+i*numP*dim, Dalpha+i*numP*dim, numP, dim);
			temp[i] = sqrt(temp[i]);
		}
		intv = 1.0/(numC-1);
		distance = ElasticCurvesRO::Trapz(temp, numC, intv);
		//x->Print("================================");
		//std::cout << "++++++++++++++++++++++++++++++++"<< "distance" << distance<<std::endl;
		//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% forcout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
		//#############################Compute and store eta##############################
		integer NXD = numP*dim;
		double coeff;
		SharedSpace *SharedEta = new SharedSpace(2, numP, dim);
		double *eta = SharedEta->ObtainWriteEntireData();
		dcopy_(&NXD, const_cast<double *>(Dalpha+(numC-1)*numP*dim), &GLOBAL::IONE, eta, &GLOBAL::IONE);
		coeff = 1.0/std::sqrt(PreShapePathStraighten::InnerProd_Q(Dalpha+(numC-1)*numP*dim, Dalpha+(numC-1)*numP*dim, numP, dim));
		dscal_(&NXD, &coeff, eta, &GLOBAL::IONE);
		//std::cout <<"#########eta#####"<< PreShapePathStraighten::InnerProd_Q(eta, eta, numP, dim)<<std::endl;
    

		x->AddToTempData("eta", SharedEta);
        x->AddToTempData("q2_new", Shared_q2_new);
    
		//############################# Return ##############################
        

		delete RSDsolver;
		//delete [] q2_new;
		delete [] Dalpha;
		delete [] temp;
		return distance;
	}