diff options
author | Gael Guennebaud <g.gael@free.fr> | 2010-07-22 16:29:35 +0200 |
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committer | Gael Guennebaud <g.gael@free.fr> | 2010-07-22 16:29:35 +0200 |
commit | 7020f30da3ce2b646ddafa535c6564ed00fc762f (patch) | |
tree | 5d26ac3fd8b082dfe2d89903d58b760529632d72 /bench | |
parent | b9edd6fb85a4930f0291f1b52c7f84cb6684e063 (diff) | |
parent | 96ba7cd6557769e01778441cdf7855295542aad0 (diff) |
sync with default branch
Diffstat (limited to 'bench')
-rw-r--r-- | bench/bench_gemm.cpp | 4 | ||||
-rw-r--r-- | bench/btl/libs/C_BLAS/blas.h | 10 | ||||
-rw-r--r-- | bench/eig33.cpp | 139 | ||||
-rw-r--r-- | bench/quatmul.cpp | 47 |
4 files changed, 193 insertions, 7 deletions
diff --git a/bench/bench_gemm.cpp b/bench/bench_gemm.cpp index 922c3cd64..bc3089b9f 100644 --- a/bench/bench_gemm.cpp +++ b/bench/bench_gemm.cpp @@ -10,8 +10,8 @@ using namespace std; using namespace Eigen; #ifndef SCALAR -#define SCALAR std::complex<float> -// #define SCALAR float +// #define SCALAR std::complex<float> +#define SCALAR float #endif typedef SCALAR Scalar; diff --git a/bench/btl/libs/C_BLAS/blas.h b/bench/btl/libs/C_BLAS/blas.h index 1da288dd4..ab3d44052 100644 --- a/bench/btl/libs/C_BLAS/blas.h +++ b/bench/btl/libs/C_BLAS/blas.h @@ -11,7 +11,7 @@ typedef long BLASLONG; typedef unsigned long BLASULONG; #endif -int BLASFUNC(xerbla)(char *, int *info, int); +int BLASFUNC(xerbla)(const char *, int *info, int); float BLASFUNC(sdot) (int *, float *, int *, float *, int *); float BLASFUNC(sdsdot)(int *, float *, float *, int *, float *, int *); @@ -38,10 +38,10 @@ void BLASFUNC(zdotc) (double *, int *, double *, int *, double *, int *); void BLASFUNC(xdotu) (double *, int *, double *, int *, double *, int *); void BLASFUNC(xdotc) (double *, int *, double *, int *, double *, int *); #else -float BLASFUNC(cdotu) (int *, float *, int *, float *, int *); -float BLASFUNC(cdotc) (int *, float *, int *, float *, int *); -double BLASFUNC(zdotu) (int *, double *, int *, double *, int *); -double BLASFUNC(zdotc) (int *, double *, int *, double *, int *); +std::complex<float> BLASFUNC(cdotu) (int *, float *, int *, float *, int *); +std::complex<float> BLASFUNC(cdotc) (int *, float *, int *, float *, int *); +std::complex<double> BLASFUNC(zdotu) (int *, double *, int *, double *, int *); +std::complex<double> BLASFUNC(zdotc) (int *, double *, int *, double *, int *); double BLASFUNC(xdotu) (int *, double *, int *, double *, int *); double BLASFUNC(xdotc) (int *, double *, int *, double *, int *); #endif diff --git a/bench/eig33.cpp b/bench/eig33.cpp new file mode 100644 index 000000000..2016c2c01 --- /dev/null +++ b/bench/eig33.cpp @@ -0,0 +1,139 @@ +#include <iostream> +#include <Eigen/Core> +#include <Eigen/Eigenvalues> +#include <Eigen/Geometry> +#include <bench/BenchTimer.h> + +using namespace Eigen; +using namespace std; + +template<typename Matrix, typename Roots> +inline void computeRoots (const Matrix& rkA, Roots& adRoot) +{ + typedef typename Matrix::Scalar Scalar; + const Scalar msInv3 = 1.0/3.0; + const Scalar msRoot3 = ei_sqrt(Scalar(3.0)); + + Scalar dA00 = rkA(0,0); + Scalar dA01 = rkA(0,1); + Scalar dA02 = rkA(0,2); + Scalar dA11 = rkA(1,1); + Scalar dA12 = rkA(1,2); + Scalar dA22 = rkA(2,2); + + // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The + // eigenvalues are the roots to this equation, all guaranteed to be + // real-valued, because the matrix is symmetric. + Scalar dC0 = dA00*dA11*dA22 + Scalar(2)*dA01*dA02*dA12 - dA00*dA12*dA12 - dA11*dA02*dA02 - dA22*dA01*dA01; + Scalar dC1 = dA00*dA11 - dA01*dA01 + dA00*dA22 - dA02*dA02 + dA11*dA22 - dA12*dA12; + Scalar dC2 = dA00 + dA11 + dA22; + + // Construct the parameters used in classifying the roots of the equation + // and in solving the equation for the roots in closed form. + Scalar dC2Div3 = dC2*msInv3; + Scalar dADiv3 = (dC1 - dC2*dC2Div3)*msInv3; + if (dADiv3 > Scalar(0)) + dADiv3 = Scalar(0); + + Scalar dMBDiv2 = Scalar(0.5)*(dC0 + dC2Div3*(Scalar(2)*dC2Div3*dC2Div3 - dC1)); + + Scalar dQ = dMBDiv2*dMBDiv2 + dADiv3*dADiv3*dADiv3; + if (dQ > Scalar(0)) + dQ = Scalar(0); + + // Compute the eigenvalues by solving for the roots of the polynomial. + Scalar dMagnitude = ei_sqrt(-dADiv3); + Scalar dAngle = std::atan2(ei_sqrt(-dQ),dMBDiv2)*msInv3; + Scalar dCos = ei_cos(dAngle); + Scalar dSin = ei_sin(dAngle); + adRoot(0) = dC2Div3 + 2.f*dMagnitude*dCos; + adRoot(1) = dC2Div3 - dMagnitude*(dCos + msRoot3*dSin); + adRoot(2) = dC2Div3 - dMagnitude*(dCos - msRoot3*dSin); + + // Sort in increasing order. + if (adRoot(0) >= adRoot(1)) + std::swap(adRoot(0),adRoot(1)); + if (adRoot(1) >= adRoot(2)) + { + std::swap(adRoot(1),adRoot(2)); + if (adRoot(0) >= adRoot(1)) + std::swap(adRoot(0),adRoot(1)); + } +} + +template<typename Matrix, typename Vector> +void eigen33(const Matrix& mat, Matrix& evecs, Vector& evals) +{ + typedef typename Matrix::Scalar Scalar; + // Scale the matrix so its entries are in [-1,1]. The scaling is applied + // only when at least one matrix entry has magnitude larger than 1. + + Scalar scale = mat.cwiseAbs()/*.template triangularView<Lower>()*/.maxCoeff(); + scale = std::max(scale,Scalar(1)); + Matrix scaledMat = mat / scale; + + // Compute the eigenvalues +// scaledMat.setZero(); + computeRoots(scaledMat,evals); + + // compute the eigen vectors + // here we assume 3 differents eigenvalues + + // "optimized version" which appears to be slower with gcc! +// Vector base; +// Scalar alpha, beta; +// base << scaledMat(1,0) * scaledMat(2,1), +// scaledMat(1,0) * scaledMat(2,0), +// -scaledMat(1,0) * scaledMat(1,0); +// for(int k=0; k<2; ++k) +// { +// alpha = scaledMat(0,0) - evals(k); +// beta = scaledMat(1,1) - evals(k); +// evecs.col(k) = (base + Vector(-beta*scaledMat(2,0), -alpha*scaledMat(2,1), alpha*beta)).normalized(); +// } +// evecs.col(2) = evecs.col(0).cross(evecs.col(1)).normalized(); + + // naive version + Matrix tmp; + tmp = scaledMat; + tmp.diagonal().array() -= evals(0); + evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized(); + + tmp = scaledMat; + tmp.diagonal().array() -= evals(1); + evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized(); + + tmp = scaledMat; + tmp.diagonal().array() -= evals(2); + evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized(); + + // Rescale back to the original size. + evals *= scale; +} + +int main() +{ + BenchTimer t; + int tries = 10; + int rep = 400000; + typedef Matrix3f Mat; + typedef Vector3f Vec; + Mat A = Mat::Random(3,3); + A = A.adjoint() * A; + + SelfAdjointEigenSolver<Mat> eig(A); + BENCH(t, tries, rep, eig.compute(A)); + std::cout << "Eigen: " << t.best() << "s\n"; + + Mat evecs; + Vec evals; + BENCH(t, tries, rep, eigen33(A,evecs,evals)); + std::cout << "Direct: " << t.best() << "s\n\n"; + + std::cerr << "Eigenvalue/eigenvector diffs:\n"; + std::cerr << (evals - eig.eigenvalues()).transpose() << "\n"; + for(int k=0;k<3;++k) + if(evecs.col(k).dot(eig.eigenvectors().col(k))<0) + evecs.col(k) = -evecs.col(k); + std::cerr << evecs - eig.eigenvectors() << "\n\n"; +} diff --git a/bench/quatmul.cpp b/bench/quatmul.cpp new file mode 100644 index 000000000..d91a4b01b --- /dev/null +++ b/bench/quatmul.cpp @@ -0,0 +1,47 @@ +#include <iostream> +#include <Eigen/Core> +#include <Eigen/Geometry> +#include <bench/BenchTimer.h> + +using namespace Eigen; + +template<typename Quat> +EIGEN_DONT_INLINE void quatmul_default(const Quat& a, const Quat& b, Quat& c) +{ + c = a * b; +} + +template<typename Quat> +EIGEN_DONT_INLINE void quatmul_novec(const Quat& a, const Quat& b, Quat& c) +{ + c = ei_quat_product<0, Quat, Quat, typename Quat::Scalar, Aligned>::run(a,b); +} + +template<typename Quat> void bench(const std::string& label) +{ + int tries = 10; + int rep = 1000000; + BenchTimer t; + + Quat a(4, 1, 2, 3); + Quat b(2, 3, 4, 5); + Quat c; + + std::cout.precision(3); + + BENCH(t, tries, rep, quatmul_default(a,b,c)); + std::cout << label << " default " << 1e3*t.best(CPU_TIMER) << "ms \t" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << " M mul/s\n"; + + BENCH(t, tries, rep, quatmul_novec(a,b,c)); + std::cout << label << " novec " << 1e3*t.best(CPU_TIMER) << "ms \t" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << " M mul/s\n"; +} + +int main() +{ + bench<Quaternionf>("float "); + bench<Quaterniond>("double"); + + return 0; + +} + |