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Merge pull request #266 from prclibo:master

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Andrey Kamaev 12 years ago committed by OpenCV Buildbot
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  1. 124
      modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst
  2. 14
      modules/calib3d/include/opencv2/calib3d/calib3d.hpp
  3. 756
      modules/calib3d/src/five-point.cpp
  4. 363
      modules/calib3d/test/test_fundam.cpp

124
modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst
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@ -681,7 +681,125 @@ corresponding to the specified points. It can also be passed to
Mat fundamental_matrix =
findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
findEssentialMat
------------------
Calculates an essential matrix from the corresponding points in two images.
.. ocv:function:: Mat findEssentialMat( InputArray points1, InputArray points2, double focal = 1.0, Point2d pp = Point2d(0, 0), int method = FM_RANSAC, double prob = 0.999, double threshold = 1.0, OutputArray mask = noArray() )
:param points1: Array of ``N`` ``(N >= 5)`` 2D points from the first image. The point coordinates should be floating-point (single or double precision).
:param points2: Array of the second image points of the same size and format as ``points1`` .
:param focal: focal length of the camera. Note that this function assumes that ``points1`` and ``points2`` are feature points from cameras with same focal length and principle point.
:param pp: principle point of the camera.
:param method: Method for computing a fundamental matrix.
* **CV_RANSAC** for the RANSAC algorithm.
* **CV_LMEDS** for the LMedS algorithm.
:param threshold: Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
:param prob: Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
:param mask: Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods.
This function estimates essential matrix based on an implementation of five-point algorithm [Nister03]_ [SteweniusCFS]_.
The epipolar geometry is described by the following equation:
.. math::
[p_2; 1]^T K^T E K [p_1; 1] = 0 \\
K =
\begin{bmatrix}
f & 0 & x_{pp} \\
0 & f & y_{pp} \\
0 & 0 & 1
\end{bmatrix}
where
:math:`E` is an essential matrix,
:math:`p_1` and
:math:`p_2` are corresponding points in the first and the second images, respectively.
The result of this function may be passed further to ``decomposeEssentialMat()`` or ``recoverPose()`` to recover the relative pose between cameras.
decomposeEssentialMat
-------------------------
Decompose an essential matrix to possible rotations and translation.
.. ocv:function:: void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t )
:param E: The input essential matrix.
:param R1: One possible rotation matrix.
:param R2: Another possible rotation matrix.
:param t: One possible translation.
This function decompose an essential matrix ``E`` using svd decomposition [HartleyZ00]_. Generally 4 possible poses exists for a given ``E``.
They are
:math:`[R_1, t]`,
:math:`[R_1, -t]`,
:math:`[R_2, t]`,
:math:`[R_2, -t]`.
recoverPose
---------------
Recover relative camera rotation and translation from an estimated essential matrix and the corresponding points in two images, using cheirality check.
Returns the number of inliers which pass the check.
.. ocv:function:: int recoverPose( InputArray E, InputArray points1, InputArray points2, OutputArray R, OutputArray t, double focal = 1.0, Point2d pp = Point2d(0, 0), InputOutputArray mask = noArray())
:param E: The input essential matrix.
:param points1: Array of ``N`` 2D points from the first image. The point coordinates should be floating-point (single or double precision).
:param points2: Array of the second image points of the same size and format as ``points1`` .
:param R: Recovered relative rotation.
:param t: Recoverd relative translation.
:param focal: Focal length of the camera. Note that this function assumes that ``points1`` and ``points2`` are feature points from cameras with same focal length and principle point.
:param pp: Principle point of the camera.
:param mask: Input/output mask for inliers in ``points1`` and ``points2``.
If it is not empty, then it marks inliers in ``points1`` and ``points2`` for then given essential matrix ``E``.
Only these inliers will be used to recover pose.
In the output mask only inliers which pass the cheirality check.
This function decomposes an essential matrix using ``decomposeEssentialMat()`` and then verifies possible pose hypotheses by doing cheirality check.
The cheirality check basically means that the triangulated 3D points should have positive depth. Some details can be found from [Nister03]_.
This function can be used to process output ``E`` and ``mask`` from ``findEssentialMat()``.
In this scenario, ``points1`` and ``points2`` are the same input for ``findEssentialMat()``. ::
// Example. Estimation of fundamental matrix using the RANSAC algorithm
int point_count = 100;
vector<Point2f> points1(point_count);
vector<Point2f> points2(point_count);
// initialize the points here ... */
for( int i = 0; i < point_count; i++ )
{
points1[i] = ...;
points2[i] = ...;
}
double focal = 1.0;
cv::Point2d pp(0.0, 0.0);
Mat E, R, t, mask;
E = findEssentialMat(points1, points2, focal, pp, CV_RANSAC, 0.999, 1.0, mask);
recoverPose(E, points1, points2, R, t, focal, pp, mask);
findHomography
------------------
@ -1475,8 +1593,14 @@ The function reconstructs 3-dimensional points (in homogeneous coordinates) by u
.. [Hartley99] Hartley, R.I., Theory and Practice of Projective Rectification. IJCV 35 2, pp 115-127 (1999)
.. [HartleyZ00] Hartley, R. and Zisserman, A. Multiple View Geomtry in Computer Vision, Cambridge University Press, 2000.
.. [HH08] Hirschmuller, H. Stereo Processing by Semiglobal Matching and Mutual Information, PAMI(30), No. 2, February 2008, pp. 328-341.
.. [Nister03] Nistér, D. An efficient solution to the five-point relative pose problem, CVPR 2003.
.. [SteweniusCFS] Stewénius, H., Calibrated Fivepoint solver. http://www.vis.uky.edu/~stewe/FIVEPOINT/
.. [Slabaugh] Slabaugh, G.G. Computing Euler angles from a rotation matrix. http://gregslabaugh.name/publications/euler.pdf
.. [Zhang2000] Z. Zhang. A Flexible New Technique for Camera Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334, 2000.

14
modules/calib3d/include/opencv2/calib3d/calib3d.hpp
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@ -638,6 +638,20 @@ CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
OutputArray mask, int method=FM_RANSAC,
double param1=3., double param2=0.99);
//! finds essential matrix from a set of corresponding 2D points using five-point algorithm
CV_EXPORTS Mat findEssentialMat( InputArray points1, InputArray points2, double focal = 1.0, Point2d pp = Point2d(0, 0),
int method = CV_RANSAC,
double prob = 0.999, double threshold = 1.0, OutputArray mask = noArray() );
//! decompose essential matrix to possible rotation matrix and one translation vector
CV_EXPORTS void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t );
//! recover relative camera pose from a set of corresponding 2D points
CV_EXPORTS int recoverPose( InputArray E, InputArray points1, InputArray points2, OutputArray R, OutputArray t,
double focal = 1.0, Point2d pp = Point2d(0, 0),
InputOutputArray mask = noArray());
//! finds coordinates of epipolar lines corresponding the specified points
CV_EXPORTS void computeCorrespondEpilines( InputArray points,
int whichImage, InputArray F,

756
modules/calib3d/src/five-point.cpp
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@ -0,0 +1,756 @@
#include "precomp.hpp"
#include "_modelest.h"
#include <complex>
using namespace cv;
using namespace std;
class CvEMEstimator : public CvModelEstimator2
{
public:
CvEMEstimator();
virtual int runKernel( const CvMat* m1, const CvMat* m2, CvMat* model );
virtual int run5Point( const CvMat* _q1, const CvMat* _q2, CvMat* _ematrix );
protected:
bool reliable( const CvMat* m1, const CvMat* m2, const CvMat* model );
virtual void calibrated_fivepoint_helper( double *eet, double* at );
virtual void computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error );
};
// Input should be a vector of n 2D points or a Nx2 matrix
Mat cv::findEssentialMat( InputArray _points1, InputArray _points2, double focal, Point2d pp,
int method, double prob, double threshold, OutputArray _mask)
{
Mat points1, points2;
_points1.getMat().copyTo(points1);
_points2.getMat().copyTo(points2);
int npoints = points1.checkVector(2);
CV_Assert( npoints >= 5 && points2.checkVector(2) == npoints &&
points1.type() == points2.type());
if (points1.channels() > 1)
{
points1 = points1.reshape(1, npoints);
points2 = points2.reshape(1, npoints);
}
points1.convertTo(points1, CV_64F);
points2.convertTo(points2, CV_64F);
points1.col(0) = (points1.col(0) - pp.x) / focal;
points2.col(0) = (points2.col(0) - pp.x) / focal;
points1.col(1) = (points1.col(1) - pp.y) / focal;
points2.col(1) = (points2.col(1) - pp.y) / focal;
// Reshape data to fit opencv ransac function
points1 = points1.reshape(2, 1);
points2 = points2.reshape(2, 1);
Mat E(3, 3, CV_64F);
CvEMEstimator estimator;
CvMat p1 = points1;
CvMat p2 = points2;
CvMat _E = E;
CvMat* tempMask = cvCreateMat(1, npoints, CV_8U);
assert(npoints >= 5);
threshold /= focal;
int count = 1;
if (npoints == 5)
{
E.create(3 * 10, 3, CV_64F);
_E = E;
count = estimator.runKernel(&p1, &p2, &_E);
E = E.rowRange(0, 3 * count) * 1.0;
Mat(tempMask).setTo(true);
}
else if (method == CV_RANSAC)
{
estimator.runRANSAC(&p1, &p2, &_E, tempMask, threshold, prob);
}
else
{
estimator.runLMeDS(&p1, &p2, &_E, tempMask, prob);
}
if (_mask.needed())
{
_mask.create(1, npoints, CV_8U, -1, true);
Mat mask = _mask.getMat();
Mat(tempMask).copyTo(mask);
}
return E;
}
int cv::recoverPose( InputArray E, InputArray _points1, InputArray _points2, OutputArray _R, OutputArray _t,
double focal, Point2d pp,
InputOutputArray _mask)
{
Mat points1, points2;
_points1.getMat().copyTo(points1);
_points2.getMat().copyTo(points2);
int npoints = points1.checkVector(2);
CV_Assert( npoints >= 0 && points2.checkVector(2) == npoints &&
points1.type() == points2.type());
if (points1.channels() > 1)
{
points1 = points1.reshape(1, npoints);
points2 = points2.reshape(1, npoints);
}
points1.convertTo(points1, CV_64F);
points2.convertTo(points2, CV_64F);
points1.col(0) = (points1.col(0) - pp.x) / focal;
points2.col(0) = (points2.col(0) - pp.x) / focal;
points1.col(1) = (points1.col(1) - pp.y) / focal;
points2.col(1) = (points2.col(1) - pp.y) / focal;
points1 = points1.t();
points2 = points2.t();
Mat R1, R2, t;
decomposeEssentialMat(E, R1, R2, t);
Mat P0 = Mat::eye(3, 4, R1.type());
Mat P1(3, 4, R1.type()), P2(3, 4, R1.type()), P3(3, 4, R1.type()), P4(3, 4, R1.type());
P1(Range::all(), Range(0, 3)) = R1 * 1.0; P1.col(3) = t * 1.0;
P2(Range::all(), Range(0, 3)) = R2 * 1.0; P2.col(3) = t * 1.0;
P3(Range::all(), Range(0, 3)) = R1 * 1.0; P3.col(3) = -t * 1.0;
P4(Range::all(), Range(0, 3)) = R2 * 1.0; P4.col(3) = -t * 1.0;
// Do the cheirality check.
// Notice here a threshold dist is used to filter
// out far away points (i.e. infinite points) since
// there depth may vary between postive and negtive.
double dist = 50.0;
Mat Q;
triangulatePoints(P0, P1, points1, points2, Q);
Mat mask1 = Q.row(2).mul(Q.row(3)) > 0;
Q.row(0) /= Q.row(3);
Q.row(1) /= Q.row(3);
Q.row(2) /= Q.row(3);
Q.row(3) /= Q.row(3);
mask1 = (Q.row(2) < dist) & mask1;
Q = P1 * Q;
mask1 = (Q.row(2) > 0) & mask1;
mask1 = (Q.row(2) < dist) & mask1;
triangulatePoints(P0, P2, points1, points2, Q);
Mat mask2 = Q.row(2).mul(Q.row(3)) > 0;
Q.row(0) /= Q.row(3);
Q.row(1) /= Q.row(3);
Q.row(2) /= Q.row(3);
Q.row(3) /= Q.row(3);
mask2 = (Q.row(2) < dist) & mask2;
Q = P2 * Q;
mask2 = (Q.row(2) > 0) & mask2;
mask2 = (Q.row(2) < dist) & mask2;
triangulatePoints(P0, P3, points1, points2, Q);
Mat mask3 = Q.row(2).mul(Q.row(3)) > 0;
Q.row(0) /= Q.row(3);
Q.row(1) /= Q.row(3);
Q.row(2) /= Q.row(3);
Q.row(3) /= Q.row(3);
mask3 = (Q.row(2) < dist) & mask3;
Q = P3 * Q;
mask3 = (Q.row(2) > 0) & mask3;
mask3 = (Q.row(2) < dist) & mask3;
triangulatePoints(P0, P4, points1, points2, Q);
Mat mask4 = Q.row(2).mul(Q.row(3)) > 0;
Q.row(0) /= Q.row(3);
Q.row(1) /= Q.row(3);
Q.row(2) /= Q.row(3);
Q.row(3) /= Q.row(3);
mask4 = (Q.row(2) < dist) & mask4;
Q = P4 * Q;
mask4 = (Q.row(2) > 0) & mask4;
mask4 = (Q.row(2) < dist) & mask4;
// If _mask is given, then use it to filter outliers.
if (_mask.needed())
{
_mask.create(1, npoints, CV_8U, -1, true);
Mat mask = _mask.getMat();
bitwise_and(mask, mask1, mask1);
bitwise_and(mask, mask2, mask2);
bitwise_and(mask, mask3, mask3);
bitwise_and(mask, mask4, mask4);
}
CV_Assert(_R.needed() && _t.needed());
_R.create(3, 3, R1.type());
_t.create(3, 1, t.type());
int good1 = countNonZero(mask1);
int good2 = countNonZero(mask2);
int good3 = countNonZero(mask3);
int good4 = countNonZero(mask4);
if (good1 >= good2 && good1 >= good3 && good1 >= good4)
{
R1.copyTo(_R.getMat());
t.copyTo(_t.getMat());
if (_mask.needed()) mask1.copyTo(_mask.getMat());
return good1;
}
else if (good2 >= good1 && good2 >= good3 && good2 >= good4)
{
R2.copyTo(_R.getMat());
t.copyTo(_t.getMat());
if (_mask.needed()) mask2.copyTo(_mask.getMat());
return good2;
}
else if (good3 >= good1 && good3 >= good2 && good3 >= good4)
{
t = -t;
R1.copyTo(_R.getMat());
t.copyTo(_t.getMat());
if (_mask.needed()) mask3.copyTo(_mask.getMat());
return good3;
}
else
{
t = -t;
R2.copyTo(_R.getMat());
t.copyTo(_t.getMat());
if (_mask.needed()) mask4.copyTo(_mask.getMat());
return good4;
}
}
void cv::decomposeEssentialMat( InputArray _E, OutputArray _R1, OutputArray _R2, OutputArray _t )
{
Mat E;
_E.getMat().copyTo(E);
E = E.reshape(1, 3);
assert(E.cols == 3 && E.rows == 3);
Mat D, U, Vt;
SVD::compute(E, D, U, Vt);
if (determinant(U) < 0) U = -U;
if (determinant(Vt) < 0) Vt = -Vt;
Mat W = (Mat_<double>(3, 3) << 0, 1, 0, -1, 0, 0, 0, 0, 1);
W.convertTo(W, E.type());
Mat R1, R2, t;
R1 = U * W * Vt;
R2 = U * W.t() * Vt;
t = U.col(2) * 1.0;
_R1.create(3, 3, E.type());
_R2.create(3, 3, E.type());
_t.create(3, 1, E.type());
R1.copyTo(_R1.getMat());
R2.copyTo(_R2.getMat());
t.copyTo(_t.getMat());
}
CvEMEstimator::CvEMEstimator()
: CvModelEstimator2( 5, cvSize(3,3), 10 )
{
}
int CvEMEstimator::runKernel( const CvMat* m1, const CvMat* m2, CvMat* model )
{
return run5Point(m1, m2, model);
}
// Notice to keep compatibility with opencv ransac, q1 and q2 have
// to be of 1 row x n col x 2 channel.
int CvEMEstimator::run5Point( const CvMat* q1, const CvMat* q2, CvMat* ematrix )
{
Mat Q1 = Mat(q1).reshape(1, q1->cols);
Mat Q2 = Mat(q2).reshape(1, q2->cols);
int n = Q1.rows;
Mat Q(n, 9, CV_64F);
Q.col(0) = Q1.col(0).mul( Q2.col(0) );
Q.col(1) = Q1.col(1).mul( Q2.col(0) );
Q.col(2) = Q2.col(0) * 1.0;
Q.col(3) = Q1.col(0).mul( Q2.col(1) );
Q.col(4) = Q1.col(1).mul( Q2.col(1) );
Q.col(5) = Q2.col(1) * 1.0;
Q.col(6) = Q1.col(0) * 1.0;
Q.col(7) = Q1.col(1) * 1.0;
Q.col(8) = 1.0;
Mat U, W, Vt;
SVD::compute(Q, W, U, Vt, SVD::MODIFY_A | SVD::FULL_UV);
Mat EE = Mat(Vt.t()).colRange(5, 9) * 1.0;
Mat AA(20, 10, CV_64F);
EE = EE.t();
calibrated_fivepoint_helper((double*)EE.data, (double*)AA.data);
AA = AA.t();
EE = EE.t();
Mat A(10, 20, CV_64F);
int perm[20] = {0, 3, 1, 2, 4, 10, 6, 12, 5, 11, 7, 13, 16, 8, 14, 17, 9, 15, 18, 19};
for (int i = 0; i < 20; i++)
A.col(i) = AA.col(perm[i]) * 1.0;
A = A.colRange(0, 10).inv() * A.colRange(10, 20);
double b[3 * 13];
Mat B(3, 13, CV_64F, b);
for (int i = 0; i < 3; i++)
{
Mat arow1 = A.row(i * 2 + 4) * 1.0;
Mat arow2 = A.row(i * 2 + 5) * 1.0;
Mat row1(1, 13, CV_64F, Scalar(0.0));
Mat row2(1, 13, CV_64F, Scalar(0.0));
row1.colRange(1, 4) = arow1.colRange(0, 3) * 1.0;
row1.colRange(5, 8) = arow1.colRange(3, 6) * 1.0;
row1.colRange(9, 13) = arow1.colRange(6, 10) * 1.0;
row2.colRange(0, 3) = arow2.colRange(0, 3) * 1.0;
row2.colRange(4, 7) = arow2.colRange(3, 6) * 1.0;
row2.colRange(8, 12) = arow2.colRange(6, 10) * 1.0;
B.row(i) = row1 - row2;
}
double c[11];
Mat coeffs(1, 11, CV_64F, c);
c[10] = (b[0]*b[17]*b[34]+b[26]*b[4]*b[21]-b[26]*b[17]*b[8]-b[13]*b[4]*b[34]-b[0]*b[21]*b[30]+b[13]*b[30]*b[8]);
c[9] = (b[26]*b[4]*b[22]+b[14]*b[30]*b[8]+b[13]*b[31]*b[8]+b[1]*b[17]*b[34]-b[13]*b[5]*b[34]+b[26]*b[5]*b[21]-b[0]*b[21]*b[31]-b[26]*b[17]*b[9]-b[1]*b[21]*b[30]+b[27]*b[4]*b[21]+b[0]*b[17]*b[35]-b[0]*b[22]*b[30]+b[13]*b[30]*b[9]+b[0]*b[18]*b[34]-b[27]*b[17]*b[8]-b[14]*b[4]*b[34]-b[13]*b[4]*b[35]-b[26]*b[18]*b[8]);
c[8] = (b[14]*b[30]*b[9]+b[14]*b[31]*b[8]+b[13]*b[31]*b[9]-b[13]*b[4]*b[36]-b[13]*b[5]*b[35]+b[15]*b[30]*b[8]-b[13]*b[6]*b[34]+b[13]*b[30]*b[10]+b[13]*b[32]*b[8]-b[14]*b[4]*b[35]-b[14]*b[5]*b[34]+b[26]*b[4]*b[23]+b[26]*b[5]*b[22]+b[26]*b[6]*b[21]-b[26]*b[17]*b[10]-b[15]*b[4]*b[34]-b[26]*b[18]*b[9]-b[26]*b[19]*b[8]+b[27]*b[4]*b[22]+b[27]*b[5]*b[21]-b[27]*b[17]*b[9]-b[27]*b[18]*b[8]-b[1]*b[21]*b[31]-b[0]*b[23]*b[30]-b[0]*b[21]*b[32]+b[28]*b[4]*b[21]-b[28]*b[17]*b[8]+b[2]*b[17]*b[34]+b[0]*b[18]*b[35]-b[0]*b[22]*b[31]+b[0]*b[17]*b[36]+b[0]*b[19]*b[34]-b[1]*b[22]*b[30]+b[1]*b[18]*b[34]+b[1]*b[17]*b[35]-b[2]*b[21]*b[30]);
c[7] = (b[14]*b[30]*b[10]+b[14]*b[32]*b[8]-b[3]*b[21]*b[30]+b[3]*b[17]*b[34]+b[13]*b[32]*b[9]+b[13]*b[33]*b[8]-b[13]*b[4]*b[37]-b[13]*b[5]*b[36]+b[15]*b[30]*b[9]+b[15]*b[31]*b[8]-b[16]*b[4]*b[34]-b[13]*b[6]*b[35]-b[13]*b[7]*b[34]+b[13]*b[30]*b[11]+b[13]*b[31]*b[10]+b[14]*b[31]*b[9]-b[14]*b[4]*b[36]-b[14]*b[5]*b[35]-b[14]*b[6]*b[34]+b[16]*b[30]*b[8]-b[26]*b[20]*b[8]+b[26]*b[4]*b[24]+b[26]*b[5]*b[23]+b[26]*b[6]*b[22]+b[26]*b[7]*b[21]-b[26]*b[17]*b[11]-b[15]*b[4]*b[35]-b[15]*b[5]*b[34]-b[26]*b[18]*b[10]-b[26]*b[19]*b[9]+b[27]*b[4]*b[23]+b[27]*b[5]*b[22]+b[27]*b[6]*b[21]-b[27]*b[17]*b[10]-b[27]*b[18]*b[9]-b[27]*b[19]*b[8]+b[0]*b[17]*b[37]-b[0]*b[23]*b[31]-b[0]*b[24]*b[30]-b[0]*b[21]*b[33]-b[29]*b[17]*b[8]+b[28]*b[4]*b[22]+b[28]*b[5]*b[21]-b[28]*b[17]*b[9]-b[28]*b[18]*b[8]+b[29]*b[4]*b[21]+b[1]*b[19]*b[34]-b[2]*b[21]*b[31]+b[0]*b[20]*b[34]+b[0]*b[19]*b[35]+b[0]*b[18]*b[36]-b[0]*b[22]*b[32]-b[1]*b[23]*b[30]-b[1]*b[21]*b[32]+b[1]*b[18]*b[35]-b[1]*b[22]*b[31]-b[2]*b[22]*b[30]+b[2]*b[17]*b[35]+b[1]*b[17]*b[36]+b[2]*b[18]*b[34]);
c[6] = (-b[14]*b[6]*b[35]-b[14]*b[7]*b[34]-b[3]*b[22]*b[30]-b[3]*b[21]*b[31]+b[3]*b[17]*b[35]+b[3]*b[18]*b[34]+b[13]*b[32]*b[10]+b[13]*b[33]*b[9]-b[13]*b[4]*b[38]-b[13]*b[5]*b[37]-b[15]*b[6]*b[34]+b[15]*b[30]*b[10]+b[15]*b[32]*b[8]-b[16]*b[4]*b[35]-b[13]*b[6]*b[36]-b[13]*b[7]*b[35]+b[13]*b[31]*b[11]+b[13]*b[30]*b[12]+b[14]*b[32]*b[9]+b[14]*b[33]*b[8]-b[14]*b[4]*b[37]-b[14]*b[5]*b[36]+b[16]*b[30]*b[9]+b[16]*b[31]*b[8]-b[26]*b[20]*b[9]+b[26]*b[4]*b[25]+b[26]*b[5]*b[24]+b[26]*b[6]*b[23]+b[26]*b[7]*b[22]-b[26]*b[17]*b[12]+b[14]*b[30]*b[11]+b[14]*b[31]*b[10]+b[15]*b[31]*b[9]-b[15]*b[4]*b[36]-b[15]*b[5]*b[35]-b[26]*b[18]*b[11]-b[26]*b[19]*b[10]-b[27]*b[20]*b[8]+b[27]*b[4]*b[24]+b[27]*b[5]*b[23]+b[27]*b[6]*b[22]+b[27]*b[7]*b[21]-b[27]*b[17]*b[11]-b[27]*b[18]*b[10]-b[27]*b[19]*b[9]-b[16]*b[5]*b[34]-b[29]*b[17]*b[9]-b[29]*b[18]*b[8]+b[28]*b[4]*b[23]+b[28]*b[5]*b[22]+b[28]*b[6]*b[21]-b[28]*b[17]*b[10]-b[28]*b[18]*b[9]-b[28]*b[19]*b[8]+b[29]*b[4]*b[22]+b[29]*b[5]*b[21]-b[2]*b[23]*b[30]+b[2]*b[18]*b[35]-b[1]*b[22]*b[32]-b[2]*b[21]*b[32]+b[2]*b[19]*b[34]+b[0]*b[19]*b[36]-b[0]*b[22]*b[33]+b[0]*b[20]*b[35]-b[0]*b[23]*b[32]-b[0]*b[25]*b[30]+b[0]*b[17]*b[38]+b[0]*b[18]*b[37]-b[0]*b[24]*b[31]+b[1]*b[17]*b[37]-b[1]*b[23]*b[31]-b[1]*b[24]*b[30]-b[1]*b[21]*b[33]+b[1]*b[20]*b[34]+b[1]*b[19]*b[35]+b[1]*b[18]*b[36]+b[2]*b[17]*b[36]-b[2]*b[22]*b[31]);
c[5] = (-b[14]*b[6]*b[36]-b[14]*b[7]*b[35]+b[14]*b[31]*b[11]-b[3]*b[23]*b[30]-b[3]*b[21]*b[32]+b[3]*b[18]*b[35]-b[3]*b[22]*b[31]+b[3]*b[17]*b[36]+b[3]*b[19]*b[34]+b[13]*b[32]*b[11]+b[13]*b[33]*b[10]-b[13]*b[5]*b[38]-b[15]*b[6]*b[35]-b[15]*b[7]*b[34]+b[15]*b[30]*b[11]+b[15]*b[31]*b[10]+b[16]*b[31]*b[9]-b[13]*b[6]*b[37]-b[13]*b[7]*b[36]+b[13]*b[31]*b[12]+b[14]*b[32]*b[10]+b[14]*b[33]*b[9]-b[14]*b[4]*b[38]-b[14]*b[5]*b[37]-b[16]*b[6]*b[34]+b[16]*b[30]*b[10]+b[16]*b[32]*b[8]-b[26]*b[20]*b[10]+b[26]*b[5]*b[25]+b[26]*b[6]*b[24]+b[26]*b[7]*b[23]+b[14]*b[30]*b[12]+b[15]*b[32]*b[9]+b[15]*b[33]*b[8]-b[15]*b[4]*b[37]-b[15]*b[5]*b[36]+b[29]*b[5]*b[22]+b[29]*b[6]*b[21]-b[26]*b[18]*b[12]-b[26]*b[19]*b[11]-b[27]*b[20]*b[9]+b[27]*b[4]*b[25]+b[27]*b[5]*b[24]+b[27]*b[6]*b[23]+b[27]*b[7]*b[22]-b[27]*b[17]*b[12]-b[27]*b[18]*b[11]-b[27]*b[19]*b[10]-b[28]*b[20]*b[8]-b[16]*b[4]*b[36]-b[16]*b[5]*b[35]-b[29]*b[17]*b[10]-b[29]*b[18]*b[9]-b[29]*b[19]*b[8]+b[28]*b[4]*b[24]+b[28]*b[5]*b[23]+b[28]*b[6]*b[22]+b[28]*b[7]*b[21]-b[28]*b[17]*b[11]-b[28]*b[18]*b[10]-b[28]*b[19]*b[9]+b[29]*b[4]*b[23]-b[2]*b[22]*b[32]-b[2]*b[21]*b[33]-b[1]*b[24]*b[31]+b[0]*b[18]*b[38]-b[0]*b[24]*b[32]+b[0]*b[19]*b[37]+b[0]*b[20]*b[36]-b[0]*b[25]*b[31]-b[0]*b[23]*b[33]+b[1]*b[19]*b[36]-b[1]*b[22]*b[33]+b[1]*b[20]*b[35]+b[2]*b[19]*b[35]-b[2]*b[24]*b[30]-b[2]*b[23]*b[31]+b[2]*b[20]*b[34]+b[2]*b[17]*b[37]-b[1]*b[25]*b[30]+b[1]*b[18]*b[37]+b[1]*b[17]*b[38]-b[1]*b[23]*b[32]+b[2]*b[18]*b[36]);
c[4] = (-b[14]*b[6]*b[37]-b[14]*b[7]*b[36]+b[14]*b[31]*b[12]+b[3]*b[17]*b[37]-b[3]*b[23]*b[31]-b[3]*b[24]*b[30]-b[3]*b[21]*b[33]+b[3]*b[20]*b[34]+b[3]*b[19]*b[35]+b[3]*b[18]*b[36]-b[3]*b[22]*b[32]+b[13]*b[32]*b[12]+b[13]*b[33]*b[11]-b[15]*b[6]*b[36]-b[15]*b[7]*b[35]+b[15]*b[31]*b[11]+b[15]*b[30]*b[12]+b[16]*b[32]*b[9]+b[16]*b[33]*b[8]-b[13]*b[6]*b[38]-b[13]*b[7]*b[37]+b[14]*b[32]*b[11]+b[14]*b[33]*b[10]-b[14]*b[5]*b[38]-b[16]*b[6]*b[35]-b[16]*b[7]*b[34]+b[16]*b[30]*b[11]+b[16]*b[31]*b[10]-b[26]*b[19]*b[12]-b[26]*b[20]*b[11]+b[26]*b[6]*b[25]+b[26]*b[7]*b[24]+b[15]*b[32]*b[10]+b[15]*b[33]*b[9]-b[15]*b[4]*b[38]-b[15]*b[5]*b[37]+b[29]*b[5]*b[23]+b[29]*b[6]*b[22]+b[29]*b[7]*b[21]-b[27]*b[20]*b[10]+b[27]*b[5]*b[25]+b[27]*b[6]*b[24]+b[27]*b[7]*b[23]-b[27]*b[18]*b[12]-b[27]*b[19]*b[11]-b[28]*b[20]*b[9]-b[16]*b[4]*b[37]-b[16]*b[5]*b[36]+b[0]*b[19]*b[38]-b[0]*b[24]*b[33]+b[0]*b[20]*b[37]-b[29]*b[17]*b[11]-b[29]*b[18]*b[10]-b[29]*b[19]*b[9]+b[28]*b[4]*b[25]+b[28]*b[5]*b[24]+b[28]*b[6]*b[23]+b[28]*b[7]*b[22]-b[28]*b[17]*b[12]-b[28]*b[18]*b[11]-b[28]*b[19]*b[10]-b[29]*b[20]*b[8]+b[29]*b[4]*b[24]+b[2]*b[18]*b[37]-b[0]*b[25]*b[32]+b[1]*b[18]*b[38]-b[1]*b[24]*b[32]+b[1]*b[19]*b[37]+b[1]*b[20]*b[36]-b[1]*b[25]*b[31]+b[2]*b[17]*b[38]+b[2]*b[19]*b[36]-b[2]*b[24]*b[31]-b[2]*b[22]*b[33]-b[2]*b[23]*b[32]+b[2]*b[20]*b[35]-b[1]*b[23]*b[33]-b[2]*b[25]*b[30]);
c[3] = (-b[14]*b[6]*b[38]-b[14]*b[7]*b[37]+b[3]*b[19]*b[36]-b[3]*b[22]*b[33]+b[3]*b[20]*b[35]-b[3]*b[23]*b[32]-b[3]*b[25]*b[30]+b[3]*b[17]*b[38]+b[3]*b[18]*b[37]-b[3]*b[24]*b[31]-b[15]*b[6]*b[37]-b[15]*b[7]*b[36]+b[15]*b[31]*b[12]+b[16]*b[32]*b[10]+b[16]*b[33]*b[9]+b[13]*b[33]*b[12]-b[13]*b[7]*b[38]+b[14]*b[32]*b[12]+b[14]*b[33]*b[11]-b[16]*b[6]*b[36]-b[16]*b[7]*b[35]+b[16]*b[31]*b[11]+b[16]*b[30]*b[12]+b[15]*b[32]*b[11]+b[15]*b[33]*b[10]-b[15]*b[5]*b[38]+b[29]*b[5]*b[24]+b[29]*b[6]*b[23]-b[26]*b[20]*b[12]+b[26]*b[7]*b[25]-b[27]*b[19]*b[12]-b[27]*b[20]*b[11]+b[27]*b[6]*b[25]+b[27]*b[7]*b[24]-b[28]*b[20]*b[10]-b[16]*b[4]*b[38]-b[16]*b[5]*b[37]+b[29]*b[7]*b[22]-b[29]*b[17]*b[12]-b[29]*b[18]*b[11]-b[29]*b[19]*b[10]+b[28]*b[5]*b[25]+b[28]*b[6]*b[24]+b[28]*b[7]*b[23]-b[28]*b[18]*b[12]-b[28]*b[19]*b[11]-b[29]*b[20]*b[9]+b[29]*b[4]*b[25]-b[2]*b[24]*b[32]+b[0]*b[20]*b[38]-b[0]*b[25]*b[33]+b[1]*b[19]*b[38]-b[1]*b[24]*b[33]+b[1]*b[20]*b[37]-b[2]*b[25]*b[31]+b[2]*b[20]*b[36]-b[1]*b[25]*b[32]+b[2]*b[19]*b[37]+b[2]*b[18]*b[38]-b[2]*b[23]*b[33]);
c[2] = (b[3]*b[18]*b[38]-b[3]*b[24]*b[32]+b[3]*b[19]*b[37]+b[3]*b[20]*b[36]-b[3]*b[25]*b[31]-b[3]*b[23]*b[33]-b[15]*b[6]*b[38]-b[15]*b[7]*b[37]+b[16]*b[32]*b[11]+b[16]*b[33]*b[10]-b[16]*b[5]*b[38]-b[16]*b[6]*b[37]-b[16]*b[7]*b[36]+b[16]*b[31]*b[12]+b[14]*b[33]*b[12]-b[14]*b[7]*b[38]+b[15]*b[32]*b[12]+b[15]*b[33]*b[11]+b[29]*b[5]*b[25]+b[29]*b[6]*b[24]-b[27]*b[20]*b[12]+b[27]*b[7]*b[25]-b[28]*b[19]*b[12]-b[28]*b[20]*b[11]+b[29]*b[7]*b[23]-b[29]*b[18]*b[12]-b[29]*b[19]*b[11]+b[28]*b[6]*b[25]+b[28]*b[7]*b[24]-b[29]*b[20]*b[10]+b[2]*b[19]*b[38]-b[1]*b[25]*b[33]+b[2]*b[20]*b[37]-b[2]*b[24]*b[33]-b[2]*b[25]*b[32]+b[1]*b[20]*b[38]);
c[1] = (b[29]*b[7]*b[24]-b[29]*b[20]*b[11]+b[2]*b[20]*b[38]-b[2]*b[25]*b[33]-b[28]*b[20]*b[12]+b[28]*b[7]*b[25]-b[29]*b[19]*b[12]-b[3]*b[24]*b[33]+b[15]*b[33]*b[12]+b[3]*b[19]*b[38]-b[16]*b[6]*b[38]+b[3]*b[20]*b[37]+b[16]*b[32]*b[12]+b[29]*b[6]*b[25]-b[16]*b[7]*b[37]-b[3]*b[25]*b[32]-b[15]*b[7]*b[38]+b[16]*b[33]*b[11]);
c[0] = -b[29]*b[20]*b[12]+b[29]*b[7]*b[25]+b[16]*b[33]*b[12]-b[16]*b[7]*b[38]+b[3]*b[20]*b[38]-b[3]*b[25]*b[33];
std::vector<std::complex<double> > roots;
solvePoly(coeffs, roots);
std::vector<double> xs, ys, zs;
int count = 0;
double * e = ematrix->data.db;
for (size_t i = 0; i < roots.size(); i++)
{
if (fabs(roots[i].imag()) > 1e-10) continue;
double z1 = roots[i].real();
double z2 = z1 * z1;
double z3 = z2 * z1;
double z4 = z3 * z1;
double bz[3][3];
for (int j = 0; j < 3; j++)
{
const double * br = b + j * 13;
bz[j][0] = br[0] * z3 + br[1] * z2 + br[2] * z1 + br[3];
bz[j][1] = br[4] * z3 + br[5] * z2 + br[6] * z1 + br[7];
bz[j][2] = br[8] * z4 + br[9] * z3 + br[10] * z2 + br[11] * z1 + br[12];
}
Mat Bz(3, 3, CV_64F, bz);
cv::Mat xy1;
SVD::solveZ(Bz, xy1);
if (fabs(xy1.at<double>(2)) < 1e-10) continue;
xs.push_back(xy1.at<double>(0) / xy1.at<double>(2));
ys.push_back(xy1.at<double>(1) / xy1.at<double>(2));
zs.push_back(z1);
cv::Mat Evec = EE.col(0) * xs.back() + EE.col(1) * ys.back() + EE.col(2) * zs.back() + EE.col(3);
Evec /= norm(Evec);
memcpy(e + count * 9, Evec.data, 9 * sizeof(double));
count++;
}
return count;
}
// Same as the runKernel (run5Point), m1 and m2 should be
// 1 row x n col x 2 channels.
// And also, error has to be of CV_32FC1.
void CvEMEstimator::computeReprojError( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* error )
{
Mat X1(m1), X2(m2);
int n = X1.cols;
X1 = X1.reshape(1, n);
X2 = X2.reshape(1, n);
X1.convertTo(X1, CV_64F);
X2.convertTo(X2, CV_64F);
Mat E(model);
for (int i = 0; i < n; i++)
{
Mat x1 = (Mat_<double>(3, 1) << X1.at<double>(i, 0), X1.at<double>(i, 1), 1.0);
Mat x2 = (Mat_<double>(3, 1) << X2.at<double>(i, 0), X2.at<double>(i, 1), 1.0);
double x2tEx1 = x2.dot(E * x1);
Mat Ex1 = E * x1;
Mat Etx2 = E * x2;
double a = Ex1.at<double>(0) * Ex1.at<double>(0);
double b = Ex1.at<double>(1) * Ex1.at<double>(1);
double c = Etx2.at<double>(0) * Etx2.at<double>(0);
double d = Etx2.at<double>(0) * Etx2.at<double>(0);
error->data.fl[i] = (float)(x2tEx1 * x2tEx1 / (a + b + c + d));
}
}
void CvEMEstimator::calibrated_fivepoint_helper( double *EE, double* A )
{
double e00,e01,e02,e03,e04,e05,e06,e07,e08;
double e10,e11,e12,e13,e14,e15,e16,e17,e18;
double e20,e21,e22,e23,e24,e25,e26,e27,e28;
double e30,e31,e32,e33,e34,e35,e36,e37,e38;
double e002,e012,e022,e032,e042,e052,e062,e072,e082;
double e102,e112,e122,e132,e142,e152,e162,e172,e182;
double e202,e212,e222,e232,e242,e252,e262,e272,e282;
double e302,e312,e322,e332,e342,e352,e362,e372,e382;
double e003,e013,e023,e033,e043,e053,e063,e073,e083;
double e103,e113,e123,e133,e143,e153,e163,e173,e183;
double e203,e213,e223,e233,e243,e253,e263,e273,e283;
double e303,e313,e323,e333,e343,e353,e363,e373,e383;
e00 = EE[0*9 + 0 ];
e10 = EE[1*9 + 0 ];
e20 = EE[2*9 + 0 ];
e30 = EE[3*9 + 0 ];
e01 = EE[0*9 + 1 ];
e11 = EE[1*9 + 1 ];
e21 = EE[2*9 + 1 ];
e31 = EE[3*9 + 1 ];
e02 = EE[0*9 + 2 ];
e12 = EE[1*9 + 2 ];
e22 = EE[2*9 + 2 ];
e32 = EE[3*9 + 2 ];
e03 = EE[0*9 + 3 ];
e13 = EE[1*9 + 3 ];
e23 = EE[2*9 + 3 ];
e33 = EE[3*9 + 3 ];
e04 = EE[0*9 + 4 ];
e14 = EE[1*9 + 4 ];
e24 = EE[2*9 + 4 ];
e34 = EE[3*9 + 4 ];
e05 = EE[0*9 + 5 ];
e15 = EE[1*9 + 5 ];
e25 = EE[2*9 + 5 ];
e35 = EE[3*9 + 5 ];
e06 = EE[0*9 + 6 ];
e16 = EE[1*9 + 6 ];
e26 = EE[2*9 + 6 ];
e36 = EE[3*9 + 6 ];
e07 = EE[0*9 + 7 ];
e17 = EE[1*9 + 7 ];
e27 = EE[2*9 + 7 ];
e37 = EE[3*9 + 7 ];
e08 = EE[0*9 + 8 ];
e18 = EE[1*9 + 8 ];
e28 = EE[2*9 + 8 ];
e38 = EE[3*9 + 8 ];
e002 =e00*e00;
e102 =e10*e10;
e202 =e20*e20;
e302 =e30*e30;
e012 =e01*e01;
e112 =e11*e11;
e212 =e21*e21;
e312 =e31*e31;
e022 =e02*e02;
e122 =e12*e12;
e222 =e22*e22;
e322 =e32*e32;
e032 =e03*e03;
e132 =e13*e13;
e232 =e23*e23;
e332 =e33*e33;
e042 =e04*e04;
e142 =e14*e14;
e242 =e24*e24;
e342 =e34*e34;
e052 =e05*e05;
e152 =e15*e15;
e252 =e25*e25;
e352 =e35*e35;
e062 =e06*e06;
e162 =e16*e16;
e262 =e26*e26;
e362 =e36*e36;
e072 =e07*e07;
e172 =e17*e17;
e272 =e27*e27;
e372 =e37*e37;
e082 =e08*e08;
e182 =e18*e18;
e282 =e28*e28;
e382 =e38*e38;
e003 =e00*e00*e00;
e103 =e10*e10*e10;
e203 =e20*e20*e20;
e303 =e30*e30*e30;
e013 =e01*e01*e01;
e113 =e11*e11*e11;
e213 =e21*e21*e21;
e313 =e31*e31*e31;
e023 =e02*e02*e02;
e123 =e12*e12*e12;
e223 =e22*e22*e22;
e323 =e32*e32*e32;
e033 =e03*e03*e03;
e133 =e13*e13*e13;
e233 =e23*e23*e23;
e333 =e33*e33*e33;
e043 =e04*e04*e04;
e143 =e14*e14*e14;
e243 =e24*e24*e24;
e343 =e34*e34*e34;
e053 =e05*e05*e05;
e153 =e15*e15*e15;
e253 =e25*e25*e25;
e353 =e35*e35*e35;
e063 =e06*e06*e06;
e163 =e16*e16*e16;
e263 =e26*e26*e26;
e363 =e36*e36*e36;
e073 =e07*e07*e07;
e173 =e17*e17*e17;
e273 =e27*e27*e27;
e373 =e37*e37*e37;
e083 =e08*e08*e08;
e183 =e18*e18*e18;
e283 =e28*e28*e28;
e383 =e38*e38*e38;
A[0 + 10*0]=0.5*e003+0.5*e00*e012+0.5*e00*e022+0.5*e00*e032+e03*e01*e04+e03*e02*e05+0.5*e00*e062+e06*e01*e07+e06*e02*e08-0.5*e00*e042-0.5*e00*e052-0.5*e00*e072-0.5*e00*e082;
A[0 + 10*1]=e00*e11*e01+e00*e12*e02+e03*e00*e13+e03*e11*e04+e03*e01*e14+e03*e12*e05+e03*e02*e15+e13*e01*e04+e13*e02*e05+e06*e00*e16+1.5*e10*e002+0.5*e10*e012+0.5*e10*e022+0.5*e10*e062-0.5*e10*e042-0.5*e10*e052-0.5*e10*e072+0.5*e10*e032+e06*e11*e07+e06*e01*e17+e06*e12*e08+e06*e02*e18+e16*e01*e07+e16*e02*e08-e00*e14*e04-e00*e17*e07-e00*e15*e05-e00*e18*e08-0.5*e10*e082;
A[0 + 10*2]=e16*e02*e18+e03*e12*e15+e10*e11*e01+e10*e12*e02+e03*e10*e13+e03*e11*e14+e13*e11*e04+e13*e01*e14+e13*e12*e05+e13*e02*e15+e06*e10*e16+e06*e12*e18+e06*e11*e17+e16*e11*e07+e16*e01*e17+e16*e12*e08-e10*e14*e04-e10*e17*e07-e10*e15*e05-e10*e18*e08+1.5*e00*e102+0.5*e00*e122+0.5*e00*e112+0.5*e00*e132+0.5*e00*e162-0.5*e00*e152-0.5*e00*e172-0.5*e00*e182-0.5*e00*e142;
A[0 + 10*3]=0.5*e103+0.5*e10*e122+0.5*e10*e112+0.5*e10*e132+e13*e12*e15+e13*e11*e14+0.5*e10*e162+e16*e12*e18+e16*e11*e17-0.5*e10*e152-0.5*e10*e172-0.5*e10*e182-0.5*e10*e142;
A[0 + 10*4]=-e00*e28*e08-e00*e25*e05-e00*e27*e07-e00*e24*e04+e26*e02*e08+e26*e01*e07+e06*e02*e28+e06*e22*e08+e06*e01*e27+e06*e21*e07+e23*e02*e05+e23*e01*e04+e03*e02*e25+e03*e22*e05+e03*e01*e24+e03*e21*e04+e00*e22*e02+e00*e21*e01-0.5*e20*e082-0.5*e20*e052-0.5*e20*e072-0.5*e20*e042+e06*e00*e26+0.5*e20*e062+e03*e00*e23+0.5*e20*e022+1.5*e20*e002+0.5*e20*e032+0.5*e20*e012;
A[0 + 10*5]=-e10*e24*e04-e10*e27*e07-e10*e25*e05-e10*e28*e08-e20*e14*e04-e20*e17*e07-e20*e15*e05-e20*e18*e08-e00*e24*e14-e00*e25*e15-e00*e27*e17-e00*e28*e18+e06*e21*e17+e06*e22*e18+e06*e12*e28+e16*e00*e26+e16*e21*e07+e16*e01*e27+e16*e22*e08+e16*e02*e28+e26*e11*e07+e26*e01*e17+e26*e12*e08+e26*e02*e18+e06*e11*e27+e23*e11*e04+e23*e01*e14+e23*e12*e05+e23*e02*e15+e06*e20*e16+e06*e10*e26+e03*e21*e14+e03*e22*e15+e03*e12*e25+e13*e00*e23+e13*e21*e04+e13*e01*e24+e13*e22*e05+e13*e02*e25+e03*e11*e24+e03*e20*e13+e03*e10*e23+e00*e21*e11+3*e00*e20*e10+e00*e22*e12+e20*e12*e02+e20*e11*e01+e10*e22*e02+e10*e21*e01;
A[0 + 10*6]=-0.5*e20*e152+e26*e11*e17-e10*e24*e14-e10*e25*e15-e10*e27*e17-e10*e28*e18+0.5*e20*e162+e13*e10*e23+e13*e22*e15+e23*e12*e15+e23*e11*e14+e16*e10*e26+e16*e21*e17+e16*e11*e27+e16*e22*e18+e16*e12*e28+e26*e12*e18+e13*e12*e25+0.5*e20*e132+1.5*e20*e102+0.5*e20*e122+0.5*e20*e112+e10*e21*e11+e10*e22*e12+e13*e11*e24-0.5*e20*e172-0.5*e20*e182-0.5*e20*e142+e13*e21*e14;
A[0 + 10*7]=-e20*e25*e05-e20*e28*e08-0.5*e00*e272-0.5*e00*e282-0.5*e00*e242+0.5*e00*e262-0.5*e00*e252+e06*e20*e26+0.5*e00*e232+e06*e22*e28+e06*e21*e27+e26*e21*e07+e26*e01*e27+e26*e22*e08+e26*e02*e28-e20*e24*e04-e20*e27*e07+e03*e20*e23+e03*e22*e25+e03*e21*e24+e23*e21*e04+e23*e01*e24+e23*e22*e05+e23*e02*e25+e20*e21*e01+e20*e22*e02+1.5*e00*e202+0.5*e00*e222+0.5*e00*e212;
A[0 + 10*8]=e23*e21*e14+e23*e11*e24+e23*e22*e15+e23*e12*e25+e16*e20*e26+e16*e22*e28+e16*e21*e27+e26*e21*e17+e26*e11*e27+e26*e22*e18+e26*e12*e28+1.5*e10*e202+0.5*e10*e222+0.5*e10*e212+0.5*e10*e232+e20*e21*e11+e20*e22*e12+e13*e20*e23+e13*e22*e25+e13*e21*e24-e20*e24*e14-e20*e25*e15-e20*e27*e17-e20*e28*e18-0.5*e10*e272-0.5*e10*e282-0.5*e10*e242-0.5*e10*e252+0.5*e10*e262;
A[0 + 10*9]=0.5*e203+0.5*e20*e222+0.5*e20*e212+0.5*e20*e232+e23*e22*e25+e23*e21*e24+0.5*e20*e262+e26*e22*e28+e26*e21*e27-0.5*e20*e252-0.5*e20*e272-0.5*e20*e282-0.5*e20*e242;
A[0 + 10*10]=e06*e32*e08-0.5*e30*e082-0.5*e30*e042-0.5*e30*e052-0.5*e30*e072+0.5*e30*e012+0.5*e30*e022+0.5*e30*e032+0.5*e30*e062+1.5*e30*e002+e00*e31*e01+e00*e32*e02+e03*e31*e04+e03*e01*e34+e03*e32*e05+e03*e02*e35+e33*e01*e04+e33*e02*e05+e06*e00*e36+e06*e31*e07+e06*e01*e37+e06*e02*e38+e36*e01*e07+e36*e02*e08-e00*e34*e04-e00*e37*e07-e00*e35*e05-e00*e38*e08+e03*e00*e33;
A[0 + 10*11]=e06*e30*e16+e03*e30*e13+e16*e31*e07+e06*e10*e36-e10*e37*e07+3*e00*e30*e10+e00*e32*e12-e00*e38*e18-e10*e34*e04-e10*e35*e05-e10*e38*e08-e30*e14*e04-e30*e17*e07-e30*e15*e05-e30*e18*e08+e00*e31*e11+e10*e31*e01+e10*e32*e02+e30*e11*e01+e30*e12*e02+e03*e10*e33-e00*e34*e14-e00*e35*e15-e00*e37*e17+e03*e31*e14+e03*e11*e34+e03*e32*e15+e03*e12*e35+e13*e00*e33+e13*e31*e04+e13*e01*e34+e13*e32*e05+e13*e02*e35+e33*e11*e04+e33*e01*e14+e33*e12*e05+e33*e02*e15+e06*e31*e17+e06*e11*e37+e06*e32*e18+e06*e12*e38+e16*e00*e36+e16*e01*e37+e16*e32*e08+e16*e02*e38+e36*e11*e07+e36*e01*e17+e36*e12*e08+e36*e02*e18;
A[0 + 10*12]=e13*e10*e33+e33*e11*e14+e16*e10*e36+e16*e31*e17+e16*e11*e37+e16*e32*e18+e16*e12*e38+e36*e12*e18+e36*e11*e17-e10*e34*e14-e10*e35*e15-e10*e37*e17-e10*e38*e18+e10*e31*e11+e10*e32*e12+e13*e31*e14+e13*e11*e34+e13*e32*e15+e13*e12*e35+e33*e12*e15+1.5*e30*e102+0.5*e30*e122+0.5*e30*e112+0.5*e30*e132+0.5*e30*e162-0.5*e30*e152-0.5*e30*e172-0.5*e30*e182-0.5*e30*e142;
A[0 + 10*13]=e00*e32*e22+3*e00*e30*e20+e00*e31*e21+e20*e31*e01+e20*e32*e02+e30*e21*e01+e30*e22*e02+e03*e20*e33+e03*e32*e25+e03*e22*e35+e03*e31*e24+e03*e21*e34+e23*e00*e33+e23*e31*e04+e23*e01*e34+e23*e32*e05+e23*e02*e35+e33*e21*e04+e33*e01*e24+e33*e22*e05+e33*e02*e25+e06*e30*e26+e06*e20*e36+e06*e32*e28+e06*e22*e38+e06*e31*e27+e06*e21*e37+e26*e00*e36+e26*e31*e07+e03*e30*e23+e26*e01*e37+e26*e32*e08+e26*e02*e38+e36*e21*e07+e36*e01*e27+e36*e22*e08+e36*e02*e28-e00*e35*e25-e00*e37*e27-e00*e38*e28-e00*e34*e24-e20*e34*e04-e20*e37*e07-e20*e35*e05-e20*e38*e08-e30*e24*e04-e30*e27*e07-e30*e25*e05-e30*e28*e08;
A[0 + 10*14]=e16*e30*e26+e13*e21*e34+3*e10*e30*e20+e10*e32*e22+e10*e31*e21+e20*e31*e11+e20*e32*e12+e30*e21*e11+e30*e22*e12+e13*e30*e23+e13*e20*e33+e13*e32*e25+e13*e22*e35+e13*e31*e24+e23*e10*e33+e23*e31*e14+e23*e11*e34+e23*e32*e15+e23*e12*e35+e33*e21*e14+e33*e11*e24+e33*e22*e15+e33*e12*e25+e16*e20*e36+e16*e32*e28+e16*e22*e38+e16*e31*e27+e16*e21*e37+e26*e10*e36+e26*e31*e17+e26*e11*e37+e26*e32*e18+e26*e12*e38+e36*e21*e17+e36*e11*e27+e36*e22*e18+e36*e12*e28-e10*e35*e25-e10*e37*e27-e10*e38*e28-e10*e34*e24-e20*e34*e14-e20*e35*e15-e20*e37*e17-e20*e38*e18-e30*e24*e14-e30*e25*e15-e30*e27*e17-e30*e28*e18;
A[0 + 10*15]=-e20*e34*e24+0.5*e30*e262-0.5*e30*e252-0.5*e30*e272-0.5*e30*e282-0.5*e30*e242+1.5*e30*e202+0.5*e30*e222+0.5*e30*e212+0.5*e30*e232+e20*e32*e22+e20*e31*e21+e23*e20*e33+e23*e32*e25+e23*e22*e35+e23*e31*e24+e23*e21*e34+e33*e22*e25+e33*e21*e24+e26*e20*e36+e26*e32*e28+e26*e22*e38+e26*e31*e27+e26*e21*e37+e36*e22*e28+e36*e21*e27-e20*e35*e25-e20*e37*e27-e20*e38*e28;
A[0 + 10*16]=0.5*e00*e322+e30*e32*e02+e30*e31*e01+1.5*e00*e302+0.5*e00*e312+e03*e32*e35+e33*e31*e04+e33*e01*e34+e33*e32*e05+e33*e02*e35+e06*e30*e36+e06*e31*e37+e06*e32*e38+e36*e31*e07+e36*e01*e37+e36*e32*e08+e36*e02*e38-e30*e34*e04-e30*e37*e07-e30*e35*e05-e30*e38*e08+0.5*e00*e332+0.5*e00*e362-0.5*e00*e382-0.5*e00*e352-0.5*e00*e342-0.5*e00*e372+e03*e30*e33+e03*e31*e34;
A[0 + 10*17]=0.5*e10*e362-0.5*e10*e382-0.5*e10*e352-0.5*e10*e342-0.5*e10*e372+e36*e31*e17+e36*e11*e37+e36*e32*e18+e36*e12*e38-e30*e34*e14-e30*e35*e15-e30*e37*e17-e30*e38*e18+1.5*e10*e302+0.5*e10*e312+0.5*e10*e322+0.5*e10*e332+e30*e31*e11+e30*e32*e12+e13*e30*e33+e13*e31*e34+e13*e32*e35+e33*e31*e14+e33*e11*e34+e33*e32*e15+e33*e12*e35+e16*e30*e36+e16*e31*e37+e16*e32*e38;
A[0 + 10*18]=e33*e31*e24+e33*e21*e34+e26*e30*e36+e26*e31*e37+e26*e32*e38+e36*e32*e28+e36*e22*e38+e36*e31*e27+e36*e21*e37-e30*e35*e25-e30*e37*e27-e30*e38*e28-e30*e34*e24+e33*e22*e35+1.5*e20*e302+0.5*e20*e312+0.5*e20*e322+0.5*e20*e332+0.5*e20*e362-0.5*e20*e382-0.5*e20*e352-0.5*e20*e342-0.5*e20*e372+e30*e32*e22+e30*e31*e21+e23*e30*e33+e23*e31*e34+e23*e32*e35+e33*e32*e25;
A[0 + 10*19]=0.5*e303+0.5*e30*e312+0.5*e30*e322+0.5*e30*e332+e33*e31*e34+e33*e32*e35+0.5*e30*e362+e36*e31*e37+e36*e32*e38-0.5*e30*e382-0.5*e30*e352-0.5*e30*e342-0.5*e30*e372;
A[1 + 10*0]=e00*e01*e04+0.5*e002*e03+e00*e02*e05+0.5*e033+0.5*e03*e042+0.5*e03*e052+0.5*e03*e062+e06*e04*e07+e06*e05*e08-0.5*e03*e012-0.5*e03*e072-0.5*e03*e022-0.5*e03*e082;
A[1 + 10*1]=e03*e14*e04+e10*e01*e04+e16*e05*e08+e00*e10*e03+e00*e11*e04+e00*e01*e14+e00*e12*e05+e00*e02*e15+e10*e02*e05+e03*e15*e05+e06*e03*e16+e06*e14*e07+e06*e04*e17+e06*e15*e08+e06*e05*e18+0.5*e002*e13+1.5*e13*e032+0.5*e13*e042+0.5*e13*e052+0.5*e13*e062-0.5*e13*e012-0.5*e13*e072-0.5*e13*e022-0.5*e13*e082+e16*e04*e07-e03*e12*e02-e03*e11*e01-e03*e17*e07-e03*e18*e08;
A[1 + 10*2]=-e13*e11*e01+e00*e10*e13+e00*e12*e15+e00*e11*e14+e10*e11*e04+e10*e01*e14+e10*e12*e05+e10*e02*e15+e13*e14*e04+e13*e15*e05+e06*e13*e16+e06*e15*e18+e06*e14*e17+e16*e14*e07+e16*e04*e17+e16*e15*e08+e16*e05*e18-e13*e12*e02-e13*e17*e07-e13*e18*e08+0.5*e102*e03+1.5*e03*e132+0.5*e03*e152+0.5*e03*e142+0.5*e03*e162-0.5*e03*e112-0.5*e03*e172-0.5*e03*e122-0.5*e03*e182;
A[1 + 10*3]=0.5*e102*e13+e10*e11*e14+e10*e12*e15+0.5*e133+0.5*e13*e152+0.5*e13*e142+0.5*e13*e162+e16*e15*e18+e16*e14*e17-0.5*e13*e112-0.5*e13*e122-0.5*e13*e172-0.5*e13*e182;
A[1 + 10*4]=-e03*e28*e08-e03*e27*e07-e03*e21*e01-e03*e22*e02+e26*e05*e08+e26*e04*e07+e06*e05*e28+e06*e25*e08+e06*e04*e27+e06*e24*e07+e03*e25*e05+e03*e24*e04+e20*e02*e05+e20*e01*e04+e00*e02*e25+e00*e22*e05+e00*e01*e24+e00*e21*e04+e00*e20*e03-0.5*e23*e072-0.5*e23*e082-0.5*e23*e022-0.5*e23*e012+e06*e03*e26+0.5*e23*e052+0.5*e23*e062+1.5*e23*e032+0.5*e23*e042+0.5*e002*e23;
A[1 + 10*5]=e00*e21*e14+e00*e11*e24+e00*e10*e23+e00*e22*e15+e00*e12*e25+e20*e12*e05+e20*e01*e14+e20*e11*e04+e00*e20*e13+e10*e02*e25+e10*e22*e05+e10*e01*e24+e10*e21*e04+e10*e20*e03+e23*e15*e05+e23*e14*e04+e13*e25*e05+e13*e24*e04+e03*e24*e14+e03*e25*e15+3*e03*e23*e13+e20*e02*e15+e16*e03*e26+e06*e14*e27-e23*e18*e08+e06*e24*e17+e06*e15*e28+e06*e25*e18+e06*e13*e26+e06*e23*e16+e26*e04*e17+e26*e14*e07+e16*e05*e28+e16*e25*e08+e16*e04*e27+e16*e24*e07-e03*e22*e12-e03*e21*e11+e26*e05*e18+e26*e15*e08-e03*e27*e17-e03*e28*e18-e13*e22*e02-e13*e28*e08-e13*e27*e07-e13*e21*e01-e23*e17*e07-e23*e11*e01-e23*e12*e02;
A[1 + 10*6]=-0.5*e23*e182-0.5*e23*e172-0.5*e23*e112-0.5*e23*e122-e13*e22*e12-e13*e27*e17-e13*e28*e18+e26*e15*e18+e26*e14*e17-e13*e21*e11+e20*e12*e15+e13*e25*e15+e13*e24*e14+e16*e13*e26+e16*e25*e18+e16*e15*e28+e16*e24*e17+e16*e14*e27+1.5*e23*e132+0.5*e23*e152+0.5*e23*e142+0.5*e23*e162+e10*e20*e13+e10*e21*e14+e10*e11*e24+e10*e22*e15+e10*e12*e25+e20*e11*e14+0.5*e102*e23;
A[1 + 10*7]=e26*e04*e27+e00*e22*e25-e23*e28*e08+0.5*e03*e262-0.5*e03*e212-0.5*e03*e272-0.5*e03*e222-0.5*e03*e282+e23*e24*e04+e23*e25*e05+0.5*e202*e03+e06*e23*e26+e06*e24*e27+e06*e25*e28+e26*e24*e07+e26*e25*e08+e26*e05*e28-e23*e22*e02-e23*e21*e01-e23*e27*e07+e00*e20*e23+e00*e21*e24+e20*e21*e04+e20*e01*e24+e20*e22*e05+e20*e02*e25+1.5*e03*e232+0.5*e03*e242+0.5*e03*e252;
A[1 + 10*8]=e20*e11*e24-0.5*e13*e212-0.5*e13*e272-0.5*e13*e222-0.5*e13*e282-e23*e27*e17-e23*e28*e18+e26*e25*e18+e26*e24*e17+e26*e14*e27-e23*e21*e11-e23*e22*e12+e26*e15*e28+e23*e25*e15+e23*e24*e14+e16*e23*e26+e16*e24*e27+e16*e25*e28+0.5*e13*e262+e20*e21*e14+e20*e22*e15+e20*e12*e25+0.5*e13*e242+0.5*e13*e252+0.5*e202*e13+1.5*e13*e232+e10*e20*e23+e10*e22*e25+e10*e21*e24;
A[1 + 10*9]=0.5*e202*e23+e20*e22*e25+e20*e21*e24+0.5*e233+0.5*e23*e242+0.5*e23*e252+0.5*e23*e262+e26*e24*e27+e26*e25*e28-0.5*e23*e212-0.5*e23*e272-0.5*e23*e222-0.5*e23*e282;
A[1 + 10*10]=e00*e30*e03+0.5*e33*e062-0.5*e33*e012-0.5*e33*e022-0.5*e33*e072+e03*e35*e05+e06*e03*e36+e06*e34*e07+e06*e04*e37+e06*e35*e08+e06*e05*e38+e36*e04*e07+e36*e05*e08-e03*e32*e02-e03*e31*e01-e03*e37*e07+e00*e31*e04+e00*e01*e34+e00*e32*e05+e00*e02*e35+e30*e01*e04+e30*e02*e05+e03*e34*e04-e03*e38*e08+0.5*e002*e33+1.5*e33*e032+0.5*e33*e042+0.5*e33*e052-0.5*e33*e082;
A[1 + 10*11]=e06*e35*e18+e06*e33*e16+e00*e30*e13+e00*e10*e33+e00*e31*e14+e00*e11*e34+e00*e32*e15+e00*e12*e35+e10*e30*e03-e33*e17*e07-e33*e18*e08+e10*e31*e04+e10*e01*e34+e10*e32*e05+e10*e02*e35+e30*e11*e04+e30*e01*e14+e30*e12*e05+e30*e02*e15+3*e03*e33*e13+e03*e35*e15+e03*e34*e14+e13*e34*e04+e13*e35*e05+e33*e14*e04+e33*e15*e05+e06*e13*e36+e06*e15*e38+e06*e34*e17+e06*e14*e37+e16*e03*e36+e16*e34*e07+e16*e04*e37+e16*e35*e08+e16*e05*e38+e36*e14*e07+e36*e04*e17+e36*e15*e08+e36*e05*e18-e03*e31*e11-e03*e32*e12-e03*e37*e17-e03*e38*e18-e13*e32*e02-e13*e31*e01-e13*e37*e07-e13*e38*e08-e33*e12*e02-e33*e11*e01;
A[1 + 10*12]=e16*e13*e36+e10*e11*e34+0.5*e33*e152+0.5*e33*e142+0.5*e33*e162-0.5*e33*e112-0.5*e33*e122-0.5*e33*e172-0.5*e33*e182+0.5*e102*e33+1.5*e33*e132+e10*e30*e13+e10*e31*e14+e10*e32*e15+e10*e12*e35+e30*e11*e14+e30*e12*e15+e13*e35*e15+e13*e34*e14+e16*e35*e18+e16*e15*e38+e16*e34*e17+e16*e14*e37+e36*e15*e18+e36*e14*e17-e13*e31*e11-e13*e32*e12-e13*e37*e17-e13*e38*e18;
A[1 + 10*13]=e06*e35*e28+e36*e04*e27+e00*e20*e33+e00*e30*e23+3*e03*e33*e23+e03*e34*e24+e03*e35*e25+e23*e34*e04+e23*e35*e05+e33*e24*e04+e33*e25*e05+e06*e33*e26+e06*e23*e36+e06*e34*e27+e06*e24*e37+e06*e25*e38+e26*e03*e36+e26*e34*e07+e26*e04*e37+e26*e35*e08+e26*e05*e38+e36*e24*e07+e36*e25*e08+e36*e05*e28-e03*e31*e21-e03*e37*e27-e03*e32*e22-e03*e38*e28-e23*e32*e02-e23*e31*e01-e23*e37*e07-e23*e38*e08-e33*e22*e02-e33*e21*e01-e33*e27*e07-e33*e28*e08+e00*e32*e25+e00*e22*e35+e00*e31*e24+e00*e21*e34+e20*e30*e03+e20*e31*e04+e20*e01*e34+e20*e32*e05+e20*e02*e35+e30*e21*e04+e30*e01*e24+e30*e22*e05+e30*e02*e25;
A[1 + 10*14]=e10*e30*e23+e10*e20*e33+e10*e22*e35+e10*e32*e25+e10*e31*e24+e10*e21*e34+e20*e30*e13+e20*e31*e14+e20*e11*e34+e20*e32*e15+e20*e12*e35+e30*e21*e14+e30*e11*e24+e30*e22*e15+e30*e12*e25+3*e13*e33*e23+e13*e34*e24+e13*e35*e25+e23*e35*e15+e23*e34*e14+e33*e25*e15+e33*e24*e14+e16*e33*e26+e16*e23*e36+e16*e34*e27+e16*e24*e37+e16*e35*e28+e16*e25*e38+e26*e13*e36+e26*e35*e18+e26*e15*e38+e26*e34*e17+e26*e14*e37+e36*e25*e18+e36*e15*e28+e36*e24*e17+e36*e14*e27-e13*e31*e21-e13*e37*e27-e13*e32*e22-e13*e38*e28-e23*e31*e11-e23*e32*e12-e23*e37*e17-e23*e38*e18-e33*e21*e11-e33*e22*e12-e33*e27*e17-e33*e28*e18;
A[1 + 10*15]=-0.5*e33*e212-0.5*e33*e272-0.5*e33*e222-0.5*e33*e282+e26*e23*e36+e20*e30*e23+e20*e32*e25+e20*e22*e35+e20*e31*e24+e20*e21*e34+e30*e22*e25+e30*e21*e24+e23*e34*e24+e23*e35*e25+e26*e34*e27+e26*e24*e37+e26*e35*e28+e26*e25*e38+e36*e24*e27+e36*e25*e28-e23*e31*e21-e23*e37*e27-e23*e32*e22-e23*e38*e28+0.5*e202*e33+1.5*e33*e232+0.5*e33*e242+0.5*e33*e252+0.5*e33*e262;
A[1 + 10*16]=e33*e35*e05+e30*e32*e05+0.5*e03*e362+0.5*e302*e03+1.5*e03*e332+0.5*e03*e352+0.5*e03*e342+e00*e30*e33+e00*e31*e34+e00*e32*e35+e30*e31*e04+e30*e01*e34+e30*e02*e35+e33*e34*e04+e06*e33*e36+e06*e35*e38+e06*e34*e37+e36*e34*e07+e36*e04*e37+e36*e35*e08+e36*e05*e38-e33*e32*e02-e33*e31*e01-e33*e37*e07-e33*e38*e08-0.5*e03*e322-0.5*e03*e382-0.5*e03*e312-0.5*e03*e372;
A[1 + 10*17]=-e33*e31*e11-e33*e32*e12-e33*e38*e18+e30*e11*e34+e30*e32*e15+e30*e12*e35+e33*e35*e15+e33*e34*e14+e16*e33*e36+e16*e35*e38+e16*e34*e37+e36*e35*e18+e36*e15*e38+e36*e34*e17+e36*e14*e37-e33*e37*e17+0.5*e302*e13+1.5*e13*e332+0.5*e13*e352+0.5*e13*e342+0.5*e13*e362-0.5*e13*e322-0.5*e13*e382-0.5*e13*e312-0.5*e13*e372+e10*e30*e33+e10*e31*e34+e10*e32*e35+e30*e31*e14;
A[1 + 10*18]=e36*e25*e38+0.5*e302*e23+1.5*e23*e332+0.5*e23*e352+0.5*e23*e342+0.5*e23*e362-0.5*e23*e322-0.5*e23*e382-0.5*e23*e312-0.5*e23*e372+e20*e30*e33+e20*e31*e34+e20*e32*e35+e30*e32*e25+e30*e22*e35+e30*e31*e24+e30*e21*e34+e33*e34*e24+e33*e35*e25+e26*e33*e36+e26*e35*e38+e26*e34*e37+e36*e34*e27+e36*e24*e37+e36*e35*e28-e33*e31*e21-e33*e37*e27-e33*e32*e22-e33*e38*e28;
A[1 + 10*19]=0.5*e302*e33+e30*e31*e34+e30*e32*e35+0.5*e333+0.5*e33*e352+0.5*e33*e342+0.5*e33*e362+e36*e35*e38+e36*e34*e37-0.5*e33*e322-0.5*e33*e382-0.5*e33*e312-0.5*e33*e372;
A[2 + 10*0]=0.5*e002*e06+e00*e01*e07+e00*e02*e08+0.5*e032*e06+e03*e04*e07+e03*e05*e08+0.5*e063+0.5*e06*e072+0.5*e06*e082-0.5*e06*e012-0.5*e06*e022-0.5*e06*e042-0.5*e06*e052;
A[2 + 10*1]=e00*e10*e06+0.5*e002*e16+0.5*e032*e16+1.5*e16*e062+0.5*e16*e072+0.5*e16*e082-0.5*e16*e012-0.5*e16*e022-0.5*e16*e042-0.5*e16*e052+e00*e11*e07+e00*e01*e17+e00*e12*e08+e00*e02*e18+e10*e01*e07+e10*e02*e08+e03*e13*e06+e03*e14*e07+e03*e04*e17+e03*e15*e08+e03*e05*e18+e13*e04*e07+e13*e05*e08+e06*e17*e07+e06*e18*e08-e06*e12*e02-e06*e11*e01-e06*e14*e04-e06*e15*e05;
A[2 + 10*2]=e13*e14*e07+0.5*e102*e06+e00*e10*e16+e00*e12*e18+e00*e11*e17+e10*e11*e07+e10*e01*e17+e10*e12*e08+e10*e02*e18+e03*e13*e16+e03*e15*e18+e03*e14*e17+e13*e04*e17+e13*e15*e08+e13*e05*e18+e16*e17*e07+e16*e18*e08-e16*e12*e02-e16*e11*e01-e16*e14*e04-e16*e15*e05+0.5*e132*e06+1.5*e06*e162+0.5*e06*e182+0.5*e06*e172-0.5*e06*e112-0.5*e06*e122-0.5*e06*e142-0.5*e06*e152;
A[2 + 10*3]=0.5*e102*e16+e10*e12*e18+e10*e11*e17+0.5*e132*e16+e13*e15*e18+e13*e14*e17+0.5*e163+0.5*e16*e182+0.5*e16*e172-0.5*e16*e112-0.5*e16*e122-0.5*e16*e142-0.5*e16*e152;
A[2 + 10*4]=e06*e27*e07+e23*e05*e08+e23*e04*e07+e03*e05*e28+e03*e25*e08+e03*e04*e27+e03*e24*e07+e20*e02*e08+e20*e01*e07+e00*e02*e28+e00*e22*e08+e00*e01*e27+e00*e21*e07+e00*e20*e06-e06*e25*e05-e06*e24*e04-e06*e21*e01-e06*e22*e02+e06*e28*e08-0.5*e26*e042-0.5*e26*e052-0.5*e26*e012-0.5*e26*e022+0.5*e26*e082+0.5*e26*e072+1.5*e26*e062+0.5*e002*e26+e03*e23*e06+0.5*e032*e26;
A[2 + 10*5]=e13*e05*e28+e00*e12*e28+e13*e25*e08+e13*e04*e27+e13*e24*e07+e13*e23*e06+e03*e14*e27+e03*e24*e17+e03*e15*e28+e03*e25*e18+e03*e13*e26+e03*e23*e16+e20*e02*e18+e20*e12*e08+e20*e01*e17+e20*e11*e07+e00*e21*e17+e10*e02*e28+e10*e22*e08+e10*e01*e27+e10*e21*e07+e10*e20*e06+e00*e11*e27-e26*e15*e05-e26*e14*e04-e26*e11*e01-e26*e12*e02-e16*e25*e05-e16*e24*e04-e16*e21*e01-e16*e22*e02-e06*e24*e14-e06*e22*e12-e06*e21*e11-e06*e25*e15+e00*e20*e16+e00*e22*e18+e00*e10*e26+e26*e18*e08+e26*e17*e07+e16*e28*e08+e16*e27*e07+e06*e27*e17+e06*e28*e18+3*e06*e26*e16+e23*e05*e18+e23*e15*e08+e23*e04*e17+e23*e14*e07;
A[2 + 10*6]=e10*e22*e18+0.5*e26*e182+0.5*e26*e172+e16*e28*e18+e16*e27*e17-e16*e25*e15-e16*e21*e11-e16*e22*e12+1.5*e26*e162+e13*e15*e28+e13*e24*e17+e13*e14*e27+e23*e15*e18+e23*e14*e17+e10*e12*e28+e10*e21*e17+e10*e11*e27+e20*e12*e18+e20*e11*e17+e13*e23*e16+e13*e25*e18+e10*e20*e16+0.5*e102*e26-0.5*e26*e122-0.5*e26*e142-0.5*e26*e152-e16*e24*e14-0.5*e26*e112+0.5*e132*e26;
A[2 + 10*7]=-0.5*e06*e212-0.5*e06*e252-0.5*e06*e242+0.5*e06*e272+0.5*e06*e282-0.5*e06*e222+e20*e02*e28+e03*e23*e26+e03*e24*e27+e03*e25*e28+e23*e24*e07+e23*e04*e27+e23*e25*e08+e23*e05*e28+e26*e28*e08-e26*e22*e02-e26*e21*e01-e26*e24*e04-e26*e25*e05+e26*e27*e07+e00*e20*e26+e00*e21*e27+e00*e22*e28+e20*e21*e07+e20*e01*e27+e20*e22*e08+0.5*e202*e06+0.5*e232*e06+1.5*e06*e262;
A[2 + 10*8]=-e26*e24*e14-0.5*e16*e212-0.5*e16*e252-0.5*e16*e242-e26*e25*e15-0.5*e16*e222-e26*e21*e11+e26*e28*e18+e26*e27*e17-e26*e22*e12+e23*e15*e28+e23*e24*e17+e23*e14*e27+0.5*e232*e16+1.5*e16*e262+0.5*e16*e272+0.5*e16*e282+e10*e20*e26+e10*e21*e27+e10*e22*e28+e20*e22*e18+e20*e12*e28+e20*e21*e17+e20*e11*e27+e13*e23*e26+e13*e24*e27+e13*e25*e28+e23*e25*e18+0.5*e202*e16;
A[2 + 10*9]=0.5*e202*e26+e20*e21*e27+e20*e22*e28+0.5*e232*e26+e23*e24*e27+e23*e25*e28+0.5*e263+0.5*e26*e272+0.5*e26*e282-0.5*e26*e222-0.5*e26*e212-0.5*e26*e252-0.5*e26*e242;
A[2 + 10*10]=e03*e34*e07+0.5*e032*e36+1.5*e36*e062+e03*e33*e06+e00*e31*e07+e00*e01*e37+e00*e32*e08+e00*e02*e38+e30*e01*e07+e30*e02*e08+e03*e04*e37+e03*e35*e08+e03*e05*e38+0.5*e002*e36-0.5*e36*e022-0.5*e36*e042-0.5*e36*e052+0.5*e36*e072+0.5*e36*e082-0.5*e36*e012+e33*e04*e07+e33*e05*e08+e06*e37*e07+e06*e38*e08-e06*e32*e02-e06*e31*e01-e06*e34*e04-e06*e35*e05+e00*e30*e06;
A[2 + 10*11]=e13*e33*e06+e13*e34*e07+e13*e04*e37+e13*e35*e08+e13*e05*e38+e33*e14*e07+e33*e04*e17+e33*e15*e08+e33*e05*e18+3*e06*e36*e16+e06*e38*e18+e06*e37*e17+e16*e37*e07+e16*e38*e08+e36*e17*e07+e36*e18*e08-e06*e35*e15-e06*e31*e11-e06*e32*e12+e00*e31*e17+e00*e11*e37+e10*e30*e06+e10*e31*e07+e10*e01*e37+e10*e32*e08+e10*e02*e38+e30*e11*e07+e30*e01*e17+e30*e12*e08+e30*e02*e18+e03*e33*e16+e03*e13*e36+e03*e35*e18+e03*e15*e38+e03*e34*e17+e03*e14*e37+e00*e30*e16+e00*e12*e38-e06*e34*e14-e16*e32*e02-e16*e31*e01-e16*e34*e04-e16*e35*e05-e36*e12*e02-e36*e11*e01-e36*e14*e04-e36*e15*e05+e00*e10*e36+e00*e32*e18;
A[2 + 10*12]=0.5*e36*e182+0.5*e36*e172-0.5*e36*e112-0.5*e36*e122-0.5*e36*e142-0.5*e36*e152+0.5*e102*e36+0.5*e132*e36+1.5*e36*e162+e10*e30*e16+e10*e32*e18+e10*e12*e38+e10*e31*e17+e10*e11*e37+e30*e12*e18+e30*e11*e17+e13*e33*e16+e13*e35*e18+e13*e15*e38+e13*e34*e17+e13*e14*e37+e33*e15*e18+e33*e14*e17+e16*e38*e18+e16*e37*e17-e16*e35*e15-e16*e31*e11-e16*e32*e12-e16*e34*e14;
A[2 + 10*13]=e00*e20*e36+e00*e31*e27+e00*e21*e37+e00*e32*e28+e00*e22*e38+e20*e30*e06+e20*e31*e07+e20*e01*e37+e20*e32*e08+e20*e02*e38+e30*e21*e07+e30*e01*e27+e30*e22*e08+e30*e02*e28+e03*e33*e26+e03*e23*e36+e03*e34*e27+e03*e24*e37+e03*e35*e28-e26*e31*e01-e26*e35*e05-e36*e22*e02-e36*e21*e01-e36*e24*e04-e36*e25*e05-e26*e34*e04+e03*e25*e38+e23*e34*e07+e23*e04*e37+e23*e35*e08+e23*e05*e38+e33*e24*e07+e33*e04*e27+e33*e25*e08+e33*e05*e28+3*e06*e36*e26+e06*e37*e27+e06*e38*e28+e26*e37*e07+e26*e38*e08+e36*e27*e07+e36*e28*e08-e06*e32*e22-e06*e31*e21-e06*e35*e25-e06*e34*e24-e26*e32*e02+e00*e30*e26+e23*e33*e06;
A[2 + 10*14]=e10*e30*e26+e10*e20*e36+e10*e31*e27+e10*e21*e37+e10*e32*e28+e10*e22*e38+e20*e30*e16+e20*e32*e18+e20*e12*e38+e20*e31*e17+e20*e11*e37+e30*e22*e18+e30*e12*e28+e30*e21*e17+e30*e11*e27+e13*e33*e26+e13*e23*e36+e13*e34*e27+e13*e24*e37+e13*e35*e28+e13*e25*e38+e23*e33*e16+e23*e35*e18+e23*e15*e38+e23*e34*e17+e23*e14*e37+e33*e25*e18+e33*e15*e28+e33*e24*e17+e33*e14*e27+3*e16*e36*e26+e16*e37*e27+e16*e38*e28+e26*e38*e18+e26*e37*e17+e36*e28*e18+e36*e27*e17-e16*e32*e22-e16*e31*e21-e16*e35*e25-e16*e34*e24-e26*e35*e15-e26*e31*e11-e26*e32*e12-e26*e34*e14-e36*e25*e15-e36*e21*e11-e36*e22*e12-e36*e24*e14;
A[2 + 10*15]=e33*e25*e28+e20*e30*e26+e20*e32*e28+e20*e31*e27+e20*e21*e37+e20*e22*e38+e30*e21*e27+e30*e22*e28+e23*e33*e26+e23*e34*e27+e23*e24*e37+e23*e35*e28+e23*e25*e38+e33*e24*e27+e26*e37*e27+e26*e38*e28-e26*e32*e22-e26*e31*e21-e26*e35*e25-e26*e34*e24+0.5*e202*e36+0.5*e232*e36+1.5*e36*e262+0.5*e36*e272+0.5*e36*e282-0.5*e36*e222-0.5*e36*e212-0.5*e36*e252-0.5*e36*e242;
A[2 + 10*16]=e00*e30*e36+e00*e32*e38+e00*e31*e37+e30*e31*e07+e30*e01*e37+e30*e32*e08+e30*e02*e38+e03*e33*e36-0.5*e06*e342+e03*e35*e38+e33*e34*e07+e33*e04*e37+e33*e35*e08+e33*e05*e38+e36*e37*e07+e36*e38*e08-e36*e32*e02-e36*e31*e01-e36*e34*e04-e36*e35*e05+e03*e34*e37+0.5*e302*e06+0.5*e332*e06+1.5*e06*e362+0.5*e06*e382+0.5*e06*e372-0.5*e06*e352-0.5*e06*e312-0.5*e06*e322;
A[2 + 10*17]=-e36*e35*e15+e10*e30*e36+0.5*e302*e16+0.5*e332*e16+1.5*e16*e362+0.5*e16*e382+0.5*e16*e372-0.5*e16*e352-0.5*e16*e312-0.5*e16*e322-0.5*e16*e342+e10*e32*e38+e10*e31*e37+e30*e32*e18+e30*e12*e38+e30*e31*e17+e30*e11*e37+e13*e33*e36+e13*e35*e38+e13*e34*e37+e33*e35*e18+e33*e15*e38+e33*e34*e17+e33*e14*e37+e36*e38*e18+e36*e37*e17-e36*e31*e11-e36*e32*e12-e36*e34*e14;
A[2 + 10*18]=-e36*e35*e25+e30*e32*e28+0.5*e302*e26+0.5*e332*e26+1.5*e26*e362+0.5*e26*e382+0.5*e26*e372-0.5*e26*e352-0.5*e26*e312-0.5*e26*e322-0.5*e26*e342+e20*e30*e36+e20*e32*e38+e20*e31*e37+e30*e31*e27+e30*e21*e37+e30*e22*e38+e23*e33*e36+e23*e35*e38+e23*e34*e37+e33*e34*e27+e33*e24*e37+e33*e35*e28+e33*e25*e38+e36*e37*e27+e36*e38*e28-e36*e32*e22-e36*e31*e21-e36*e34*e24;
A[2 + 10*19]=0.5*e302*e36+e30*e32*e38+e30*e31*e37+0.5*e332*e36+e33*e35*e38+e33*e34*e37+0.5*e363+0.5*e36*e382+0.5*e36*e372-0.5*e36*e352-0.5*e36*e312-0.5*e36*e322-0.5*e36*e342;
A[3 + 10*0]=0.5*e01*e002+0.5*e013+0.5*e01*e022+e04*e00*e03+0.5*e01*e042+e04*e02*e05+e07*e00*e06+0.5*e01*e072+e07*e02*e08-0.5*e01*e032-0.5*e01*e052-0.5*e01*e062-0.5*e01*e082;
A[3 + 10*1]=1.5*e11*e012+0.5*e11*e002+0.5*e11*e022+0.5*e11*e042+0.5*e11*e072-0.5*e11*e032-0.5*e11*e052-0.5*e11*e062-0.5*e11*e082+e01*e10*e00+e01*e12*e02+e04*e10*e03+e04*e00*e13+e04*e01*e14+e04*e12*e05+e04*e02*e15+e14*e00*e03+e14*e02*e05+e07*e10*e06+e07*e00*e16+e07*e01*e17+e07*e12*e08+e07*e02*e18+e17*e00*e06+e17*e02*e08-e01*e13*e03-e01*e16*e06-e01*e15*e05-e01*e18*e08;
A[3 + 10*2]=e17*e02*e18+e14*e10*e03+e11*e12*e02-e11*e18*e08+0.5*e01*e102+0.5*e01*e122+1.5*e01*e112+0.5*e01*e142+0.5*e01*e172-0.5*e01*e132-0.5*e01*e152-0.5*e01*e162-0.5*e01*e182+e11*e10*e00+e04*e10*e13+e04*e12*e15+e04*e11*e14+e14*e00*e13+e14*e12*e05+e14*e02*e15+e07*e10*e16+e07*e12*e18+e07*e11*e17+e17*e10*e06+e17*e00*e16+e17*e12*e08-e11*e13*e03-e11*e16*e06-e11*e15*e05;
A[3 + 10*3]=0.5*e11*e102+0.5*e11*e122+0.5*e113+e14*e10*e13+e14*e12*e15+0.5*e11*e142+e17*e10*e16+e17*e12*e18+0.5*e11*e172-0.5*e11*e132-0.5*e11*e152-0.5*e11*e162-0.5*e11*e182;
A[3 + 10*4]=-e01*e25*e05-e01*e26*e06-e01*e23*e03+e27*e02*e08+e27*e00*e06+e07*e02*e28+e07*e22*e08+e07*e01*e27+e07*e00*e26+e24*e02*e05+e24*e00*e03+e04*e02*e25+e04*e22*e05+e04*e01*e24+e04*e00*e23+e04*e20*e03+e01*e22*e02+e01*e20*e00-e01*e28*e08+e07*e20*e06+0.5*e21*e072+0.5*e21*e042+0.5*e21*e022+0.5*e21*e002+1.5*e21*e012-0.5*e21*e082-0.5*e21*e052-0.5*e21*e062-0.5*e21*e032;
A[3 + 10*5]=e11*e20*e00+e07*e20*e16+3*e01*e21*e11+e01*e22*e12-e21*e18*e08-e21*e15*e05-e21*e16*e06-e21*e13*e03-e11*e28*e08-e11*e25*e05-e11*e26*e06-e11*e23*e03-e01*e28*e18-e01*e23*e13-e01*e25*e15-e01*e26*e16+e27*e02*e18+e27*e12*e08+e27*e00*e16+e27*e10*e06+e17*e02*e28+e17*e22*e08+e17*e01*e27+e17*e00*e26+e17*e20*e06+e07*e11*e27+e07*e21*e17+e07*e12*e28+e07*e22*e18+e07*e10*e26+e24*e02*e15+e24*e12*e05+e24*e00*e13+e24*e10*e03+e14*e02*e25+e14*e22*e05+e14*e01*e24+e14*e00*e23+e14*e20*e03+e04*e11*e24+e04*e21*e14+e04*e12*e25+e04*e22*e15+e21*e12*e02+e04*e20*e13+e01*e20*e10+e11*e22*e02+e21*e10*e00+e04*e10*e23;
A[3 + 10*6]=1.5*e21*e112+0.5*e21*e102+0.5*e21*e122+e11*e20*e10+e11*e22*e12+e14*e10*e23+e14*e22*e15+e14*e12*e25-0.5*e21*e162-0.5*e21*e152-0.5*e21*e132-0.5*e21*e182+e27*e12*e18-e11*e26*e16-e11*e25*e15-e11*e23*e13-e11*e28*e18+e17*e20*e16+e17*e10*e26+e17*e22*e18+e17*e12*e28+e17*e11*e27+e27*e10*e16+0.5*e21*e172+e14*e11*e24+e24*e10*e13+e24*e12*e15+0.5*e21*e142+e14*e20*e13;
A[3 + 10*7]=-0.5*e01*e262-0.5*e01*e282-0.5*e01*e252-0.5*e01*e232+0.5*e01*e272+e27*e22*e08+e27*e02*e28-e21*e23*e03-e21*e26*e06-e21*e25*e05-e21*e28*e08+e04*e22*e25+e24*e20*e03+e24*e00*e23+e24*e22*e05+e24*e02*e25+e07*e20*e26+e07*e21*e27+e07*e22*e28+e27*e20*e06+e27*e00*e26+e21*e20*e00+e21*e22*e02+e04*e20*e23+e04*e21*e24+0.5*e01*e222+0.5*e01*e242+1.5*e01*e212+0.5*e01*e202;
A[3 + 10*8]=-0.5*e11*e282-0.5*e11*e252-e21*e26*e16+e27*e12*e28-e21*e25*e15-e21*e23*e13-e21*e28*e18+e17*e20*e26+e17*e21*e27+e17*e22*e28+e27*e20*e16+e27*e10*e26+e27*e22*e18+0.5*e11*e242+0.5*e11*e272-0.5*e11*e232-0.5*e11*e262+0.5*e11*e202+1.5*e11*e212+0.5*e11*e222+e21*e20*e10+e14*e20*e23+e14*e21*e24+e14*e22*e25+e24*e20*e13+e24*e10*e23+e24*e22*e15+e24*e12*e25+e21*e22*e12;
A[3 + 10*9]=0.5*e21*e202+0.5*e213+0.5*e21*e222+e24*e20*e23+0.5*e21*e242+e24*e22*e25+e27*e20*e26+0.5*e21*e272+e27*e22*e28-0.5*e21*e232-0.5*e21*e262-0.5*e21*e282-0.5*e21*e252;
A[3 + 10*10]=-0.5*e31*e032-0.5*e31*e052-0.5*e31*e062-0.5*e31*e082+e07*e30*e06+e07*e00*e36+e07*e01*e37+e07*e32*e08+e07*e02*e38+e37*e00*e06+e37*e02*e08-e01*e33*e03-e01*e36*e06-e01*e35*e05-e01*e38*e08+0.5*e31*e072+e04*e30*e03+e04*e00*e33+e04*e01*e34+e04*e32*e05+e04*e02*e35+e34*e00*e03+e34*e02*e05+0.5*e31*e002+0.5*e31*e022+0.5*e31*e042+e01*e30*e00+e01*e32*e02+1.5*e31*e012;
A[3 + 10*11]=e34*e12*e05+e34*e02*e15+e07*e10*e36+e07*e32*e18+e07*e12*e38+e07*e31*e17+e07*e11*e37+e17*e30*e06+e17*e00*e36+e17*e01*e37+e17*e32*e08+e17*e02*e38+e37*e10*e06+e37*e00*e16+e37*e12*e08+e37*e02*e18-e01*e36*e16-e01*e35*e15-e01*e33*e13-e01*e38*e18-e11*e33*e03-e11*e36*e06-e11*e35*e05+e01*e30*e10+e01*e32*e12+3*e01*e31*e11+e11*e30*e00+e11*e32*e02+e31*e10*e00+e31*e12*e02+e04*e30*e13+e04*e10*e33+e04*e32*e15+e04*e12*e35+e04*e31*e14+e04*e11*e34+e14*e30*e03+e14*e00*e33+e14*e01*e34+e14*e32*e05+e14*e02*e35+e34*e10*e03+e34*e00*e13+e07*e30*e16-e11*e38*e08-e31*e13*e03-e31*e16*e06-e31*e15*e05-e31*e18*e08;
A[3 + 10*12]=-e11*e33*e13-e11*e38*e18+0.5*e31*e142+0.5*e31*e172-0.5*e31*e162-0.5*e31*e152-0.5*e31*e132-0.5*e31*e182+0.5*e31*e122+0.5*e31*e102+e11*e30*e10+e11*e32*e12+e14*e30*e13+e14*e10*e33+e14*e32*e15+e14*e12*e35+e14*e11*e34+e34*e10*e13+e34*e12*e15+e17*e30*e16+e17*e10*e36+e17*e32*e18+e17*e12*e38+e17*e11*e37+e37*e10*e16+e37*e12*e18-e11*e36*e16-e11*e35*e15+1.5*e31*e112;
A[3 + 10*13]=-e21*e35*e05+e07*e32*e28+e01*e30*e20-e21*e33*e03-e21*e36*e06-e21*e38*e08-e31*e23*e03-e31*e26*e06-e31*e25*e05-e31*e28*e08+3*e01*e31*e21+e01*e32*e22+e21*e30*e00+e21*e32*e02+e31*e20*e00+e31*e22*e02+e04*e30*e23+e04*e20*e33+e04*e31*e24+e04*e21*e34+e04*e32*e25+e04*e22*e35+e24*e30*e03+e24*e00*e33+e24*e01*e34+e24*e32*e05+e24*e02*e35+e34*e20*e03+e34*e00*e23+e34*e22*e05+e34*e02*e25+e07*e30*e26+e07*e20*e36+e07*e31*e27+e07*e21*e37+e07*e22*e38+e27*e30*e06+e27*e00*e36+e27*e01*e37+e27*e32*e08+e27*e02*e38+e37*e00*e26+e37*e22*e08+e37*e02*e28-e01*e33*e23-e01*e36*e26-e01*e38*e28-e01*e35*e25+e37*e20*e06;
A[3 + 10*14]=e11*e32*e22+e34*e12*e25+e11*e30*e20+3*e11*e31*e21+e21*e30*e10+e21*e32*e12+e34*e10*e23+e34*e22*e15+e17*e30*e26+e17*e20*e36+e17*e31*e27+e17*e21*e37+e17*e32*e28+e17*e22*e38+e27*e30*e16+e27*e10*e36+e27*e32*e18+e27*e12*e38+e27*e11*e37+e37*e20*e16+e37*e10*e26+e37*e22*e18+e37*e12*e28-e11*e33*e23-e11*e36*e26-e11*e38*e28-e11*e35*e25-e21*e36*e16-e21*e35*e15-e21*e33*e13-e21*e38*e18-e31*e26*e16-e31*e25*e15-e31*e23*e13-e31*e28*e18+e31*e20*e10+e31*e22*e12+e14*e30*e23+e14*e20*e33+e14*e31*e24+e14*e21*e34+e14*e32*e25+e14*e22*e35+e24*e30*e13+e24*e10*e33+e24*e32*e15+e24*e12*e35+e24*e11*e34+e34*e20*e13;
A[3 + 10*15]=-e21*e36*e26+e37*e22*e28-e21*e33*e23-e21*e38*e28-e21*e35*e25+0.5*e31*e222+0.5*e31*e242+0.5*e31*e272-0.5*e31*e232-0.5*e31*e262-0.5*e31*e282-0.5*e31*e252+e21*e30*e20+e21*e32*e22+e24*e30*e23+e24*e20*e33+e24*e21*e34+e24*e32*e25+e24*e22*e35+e34*e20*e23+e34*e22*e25+e27*e30*e26+e27*e20*e36+e27*e21*e37+e27*e32*e28+e27*e22*e38+e37*e20*e26+1.5*e31*e212+0.5*e31*e202;
A[3 + 10*16]=e04*e32*e35+0.5*e01*e372-0.5*e01*e352-0.5*e01*e362-0.5*e01*e332-0.5*e01*e382+e04*e31*e34+e34*e30*e03+e34*e00*e33+e34*e32*e05+e34*e02*e35+e07*e30*e36+e07*e32*e38+e07*e31*e37+e37*e30*e06+e37*e00*e36+e37*e32*e08+e04*e30*e33+e37*e02*e38-e31*e33*e03-e31*e36*e06-e31*e35*e05-e31*e38*e08+0.5*e01*e302+0.5*e01*e322+1.5*e01*e312+0.5*e01*e342+e31*e30*e00+e31*e32*e02;
A[3 + 10*17]=e31*e32*e12+e14*e30*e33+e14*e32*e35+e14*e31*e34+e34*e30*e13+e34*e10*e33+e34*e32*e15+e34*e12*e35+e17*e30*e36+e17*e32*e38+e17*e31*e37+e37*e30*e16+e37*e10*e36+e37*e32*e18+e37*e12*e38-e31*e36*e16-e31*e35*e15+0.5*e11*e302+0.5*e11*e322+1.5*e11*e312-e31*e33*e13-e31*e38*e18+0.5*e11*e342+0.5*e11*e372+e31*e30*e10-0.5*e11*e352-0.5*e11*e362-0.5*e11*e332-0.5*e11*e382;
A[3 + 10*18]=e34*e32*e25+0.5*e21*e342+0.5*e21*e372-0.5*e21*e352-0.5*e21*e362-0.5*e21*e332-0.5*e21*e382+0.5*e21*e302+0.5*e21*e322+1.5*e21*e312+e31*e30*e20+e31*e32*e22+e24*e30*e33+e24*e32*e35+e24*e31*e34+e34*e30*e23+e34*e20*e33+e34*e22*e35+e27*e30*e36+e27*e32*e38+e27*e31*e37+e37*e30*e26+e37*e20*e36+e37*e32*e28+e37*e22*e38-e31*e33*e23-e31*e36*e26-e31*e38*e28-e31*e35*e25;
A[3 + 10*19]=0.5*e31*e302+0.5*e31*e322+0.5*e313+e34*e30*e33+e34*e32*e35+0.5*e31*e342+e37*e30*e36+e37*e32*e38+0.5*e31*e372-0.5*e31*e352-0.5*e31*e362-0.5*e31*e332-0.5*e31*e382;
A[4 + 10*0]=e01*e00*e03+0.5*e012*e04+e01*e02*e05+0.5*e04*e032+0.5*e043+0.5*e04*e052+e07*e03*e06+0.5*e04*e072+e07*e05*e08-0.5*e04*e002-0.5*e04*e022-0.5*e04*e062-0.5*e04*e082;
A[4 + 10*1]=e07*e13*e06+e01*e10*e03-0.5*e14*e002-0.5*e14*e022-0.5*e14*e062-0.5*e14*e082+e01*e00*e13+e01*e11*e04+e01*e12*e05+e01*e02*e15+e11*e00*e03+e11*e02*e05+e04*e13*e03+e04*e15*e05+e07*e03*e16+e07*e04*e17+e07*e15*e08+e07*e05*e18+e17*e03*e06+e17*e05*e08-e04*e10*e00-e04*e12*e02-e04*e16*e06-e04*e18*e08+0.5*e012*e14+1.5*e14*e042+0.5*e14*e032+0.5*e14*e052+0.5*e14*e072;
A[4 + 10*2]=e11*e10*e03+0.5*e112*e04+0.5*e04*e132+0.5*e04*e152+1.5*e04*e142+0.5*e04*e172-0.5*e04*e102-0.5*e04*e162-0.5*e04*e122-0.5*e04*e182+e01*e10*e13+e01*e12*e15+e01*e11*e14+e11*e00*e13+e11*e12*e05+e11*e02*e15+e14*e13*e03+e14*e15*e05+e07*e13*e16+e07*e15*e18+e07*e14*e17+e17*e13*e06+e17*e03*e16+e17*e15*e08+e17*e05*e18-e14*e10*e00-e14*e12*e02-e14*e16*e06-e14*e18*e08;
A[4 + 10*3]=e11*e10*e13+e11*e12*e15+0.5*e112*e14+0.5*e14*e132+0.5*e14*e152+0.5*e143+e17*e13*e16+e17*e15*e18+0.5*e14*e172-0.5*e14*e102-0.5*e14*e162-0.5*e14*e122-0.5*e14*e182;
A[4 + 10*4]=-e04*e28*e08-e04*e26*e06-e04*e22*e02-e04*e20*e00+e27*e05*e08+e27*e03*e06+e07*e05*e28+e07*e25*e08+e07*e04*e27+e07*e03*e26+e07*e23*e06+e04*e25*e05+e04*e23*e03+e21*e02*e05+e21*e00*e03+e01*e02*e25+e01*e22*e05+e01*e21*e04+e01*e00*e23+e01*e20*e03+0.5*e012*e24+0.5*e24*e072+0.5*e24*e052+0.5*e24*e032+1.5*e24*e042-0.5*e24*e022-0.5*e24*e002-0.5*e24*e082-0.5*e24*e062;
A[4 + 10*5]=e11*e02*e25+e11*e22*e05+e11*e21*e04-e24*e18*e08-e24*e16*e06-e24*e12*e02-e14*e28*e08-e14*e26*e06-e14*e22*e02-e14*e20*e00-e04*e28*e18-e04*e22*e12-e04*e26*e16-e04*e20*e10+e27*e05*e18+e27*e15*e08+e27*e03*e16+e27*e13*e06+e17*e05*e28+e17*e25*e08+e17*e04*e27+e17*e03*e26+e17*e23*e06+e07*e14*e27+e07*e24*e17+e07*e15*e28+e07*e25*e18+e07*e13*e26+e07*e23*e16+e24*e15*e05+e24*e13*e03+e14*e25*e05+e14*e23*e03+3*e04*e24*e14+e04*e25*e15+e04*e23*e13+e21*e02*e15+e21*e12*e05+e21*e00*e13+e21*e10*e03-e24*e10*e00+e01*e20*e13+e01*e10*e23+e01*e22*e15+e01*e12*e25+e01*e11*e24+e11*e20*e03+e11*e00*e23+e01*e21*e14;
A[4 + 10*6]=e11*e12*e25-0.5*e24*e182-0.5*e24*e102-0.5*e24*e162-0.5*e24*e122+e27*e13*e16+e27*e15*e18-e14*e20*e10-e14*e26*e16-e14*e22*e12-e14*e28*e18+e17*e15*e28+e17*e14*e27+1.5*e24*e142+0.5*e24*e132+0.5*e24*e152+0.5*e112*e24+0.5*e24*e172+e11*e21*e14+e11*e22*e15+e11*e10*e23+e11*e20*e13+e21*e10*e13+e21*e12*e15+e17*e13*e26+e17*e23*e16+e14*e25*e15+e14*e23*e13+e17*e25*e18;
A[4 + 10*7]=e27*e03*e26+e27*e25*e08+e27*e05*e28-e24*e20*e00-e24*e22*e02-e24*e26*e06-e24*e28*e08+0.5*e04*e232+1.5*e04*e242+0.5*e04*e252+0.5*e04*e272-0.5*e04*e202-0.5*e04*e222-0.5*e04*e262-0.5*e04*e282+e24*e23*e03+e24*e25*e05+e07*e23*e26+e07*e24*e27+e07*e25*e28+e27*e23*e06+e21*e20*e03+e21*e00*e23+e21*e22*e05+e21*e02*e25+0.5*e212*e04+e01*e20*e23+e01*e21*e24+e01*e22*e25;
A[4 + 10*8]=-e24*e22*e12-e24*e28*e18+0.5*e14*e272-0.5*e14*e202-0.5*e14*e222-0.5*e14*e262-0.5*e14*e282+e17*e23*e26+e17*e24*e27+e17*e25*e28+e27*e23*e16+e27*e13*e26+e27*e25*e18+e27*e15*e28-e24*e20*e10-e24*e26*e16+0.5*e14*e232+1.5*e14*e242+0.5*e14*e252+e21*e10*e23+e21*e22*e15+e21*e12*e25+e24*e23*e13+e24*e25*e15+e21*e20*e13+0.5*e212*e14+e11*e20*e23+e11*e22*e25+e11*e21*e24;
A[4 + 10*9]=e21*e20*e23+0.5*e212*e24+e21*e22*e25+0.5*e24*e232+0.5*e243+0.5*e24*e252+e27*e23*e26+0.5*e24*e272+e27*e25*e28-0.5*e24*e202-0.5*e24*e222-0.5*e24*e262-0.5*e24*e282;
A[4 + 10*10]=-e04*e38*e08-e04*e32*e02-e04*e36*e06-0.5*e34*e002-0.5*e34*e022-0.5*e34*e062-0.5*e34*e082+e37*e03*e06+e37*e05*e08-e04*e30*e00+0.5*e34*e032+0.5*e34*e052+0.5*e34*e072+1.5*e34*e042+e01*e30*e03+e01*e00*e33+e01*e31*e04+e01*e32*e05+e01*e02*e35+e31*e00*e03+e31*e02*e05+e04*e33*e03+e04*e35*e05+e07*e03*e36+e07*e04*e37+e07*e35*e08+e07*e05*e38+0.5*e012*e34+e07*e33*e06;
A[4 + 10*11]=e07*e13*e36+e01*e12*e35-e04*e30*e10+e17*e04*e37+e17*e35*e08+e17*e05*e38+e37*e13*e06+e37*e03*e16+e37*e15*e08+e37*e05*e18-e04*e36*e16+e17*e33*e06+e04*e33*e13+e04*e35*e15+3*e04*e34*e14+e14*e33*e03+e14*e35*e05+e34*e13*e03+e34*e15*e05+e07*e33*e16+e07*e35*e18+e07*e15*e38+e07*e34*e17+e07*e14*e37+e17*e03*e36+e31*e10*e03+e01*e30*e13+e01*e10*e33+e01*e32*e15+e01*e31*e14+e01*e11*e34+e11*e30*e03+e11*e00*e33+e11*e31*e04+e11*e32*e05+e11*e02*e35+e31*e00*e13+e31*e12*e05+e31*e02*e15-e34*e12*e02-e34*e16*e06-e34*e18*e08-e14*e32*e02-e14*e36*e06-e14*e38*e08-e34*e10*e00-e04*e32*e12-e04*e38*e18-e14*e30*e00;
A[4 + 10*12]=e11*e32*e15-0.5*e34*e102-0.5*e34*e162-0.5*e34*e122-0.5*e34*e182+e37*e13*e16+0.5*e112*e34+1.5*e34*e142+0.5*e34*e132+0.5*e34*e152+0.5*e34*e172+e11*e30*e13+e11*e10*e33+e11*e12*e35+e11*e31*e14+e31*e10*e13+e31*e12*e15+e14*e33*e13+e14*e35*e15+e17*e33*e16+e17*e13*e36+e17*e35*e18+e17*e15*e38+e17*e14*e37+e37*e15*e18-e14*e30*e10-e14*e36*e16-e14*e32*e12-e14*e38*e18;
A[4 + 10*13]=e01*e22*e35-e04*e30*e20-e04*e32*e22+e01*e31*e24+e01*e21*e34+e01*e32*e25+e21*e30*e03+e21*e00*e33+e21*e31*e04+e21*e32*e05+e21*e02*e35+e31*e20*e03+e31*e00*e23+e31*e22*e05+e31*e02*e25+e04*e33*e23+3*e04*e34*e24+e04*e35*e25+e24*e33*e03+e37*e05*e28-e04*e36*e26-e04*e38*e28-e24*e30*e00-e24*e32*e02-e24*e36*e06-e24*e38*e08+e24*e35*e05+e34*e23*e03+e34*e25*e05+e07*e33*e26+e07*e23*e36+e07*e34*e27+e07*e24*e37+e07*e35*e28+e07*e25*e38+e27*e33*e06+e27*e03*e36+e27*e04*e37+e27*e35*e08+e27*e05*e38+e37*e23*e06+e37*e03*e26+e37*e25*e08-e34*e20*e00-e34*e22*e02-e34*e26*e06-e34*e28*e08+e01*e30*e23+e01*e20*e33;
A[4 + 10*14]=e21*e10*e33+e11*e30*e23+e11*e20*e33+e11*e31*e24+e11*e21*e34+e11*e32*e25+e11*e22*e35+e21*e30*e13+e21*e32*e15+e21*e12*e35+e21*e31*e14+e31*e20*e13+e31*e10*e23+e31*e22*e15+e31*e12*e25+e14*e33*e23+3*e14*e34*e24+e14*e35*e25+e24*e33*e13+e24*e35*e15+e34*e23*e13+e34*e25*e15+e17*e33*e26+e17*e23*e36+e17*e34*e27+e17*e24*e37+e17*e35*e28+e17*e25*e38+e27*e33*e16+e27*e13*e36+e27*e35*e18+e27*e15*e38+e27*e14*e37+e37*e23*e16+e37*e13*e26+e37*e25*e18+e37*e15*e28-e34*e28*e18-e34*e22*e12-e14*e32*e22-e14*e36*e26-e14*e38*e28-e24*e30*e10-e24*e36*e16-e24*e32*e12-e24*e38*e18-e34*e20*e10-e34*e26*e16-e14*e30*e20;
A[4 + 10*15]=-0.5*e34*e202-0.5*e34*e222-0.5*e34*e262-0.5*e34*e282+e37*e25*e28-e24*e32*e22-e24*e36*e26-e24*e38*e28-e24*e30*e20+0.5*e212*e34+1.5*e34*e242+0.5*e34*e232+0.5*e34*e252+0.5*e34*e272+e21*e30*e23+e21*e20*e33+e21*e31*e24+e21*e32*e25+e21*e22*e35+e31*e20*e23+e31*e22*e25+e24*e33*e23+e24*e35*e25+e27*e33*e26+e27*e23*e36+e27*e24*e37+e27*e35*e28+e27*e25*e38+e37*e23*e26;
A[4 + 10*16]=e37*e33*e06+e01*e30*e33+e01*e31*e34+e31*e30*e03+e31*e02*e35+e34*e33*e03+e34*e35*e05+e07*e33*e36+e07*e35*e38+e07*e34*e37+e37*e03*e36+e37*e35*e08+e37*e05*e38-e34*e32*e02-e34*e36*e06-e34*e38*e08+e31*e32*e05+e31*e00*e33+0.5*e312*e04+0.5*e04*e332+0.5*e04*e352+1.5*e04*e342+0.5*e04*e372+e01*e32*e35-0.5*e04*e302-0.5*e04*e322-0.5*e04*e362-0.5*e04*e382-e34*e30*e00;
A[4 + 10*17]=0.5*e14*e372-0.5*e14*e302-0.5*e14*e322-0.5*e14*e362-0.5*e14*e382+0.5*e312*e14+0.5*e14*e332+0.5*e14*e352+1.5*e14*e342+e11*e30*e33+e11*e32*e35+e11*e31*e34+e31*e30*e13+e31*e10*e33+e31*e32*e15+e31*e12*e35+e34*e33*e13+e34*e35*e15+e17*e33*e36+e17*e35*e38+e17*e34*e37+e37*e33*e16+e37*e13*e36+e37*e35*e18+e37*e15*e38-e34*e30*e10-e34*e36*e16-e34*e32*e12-e34*e38*e18;
A[4 + 10*18]=-e34*e32*e22-e34*e36*e26-e34*e38*e28+0.5*e24*e332+0.5*e24*e352+1.5*e24*e342+0.5*e24*e372-0.5*e24*e302-0.5*e24*e322-0.5*e24*e362-0.5*e24*e382+e21*e30*e33+0.5*e312*e24+e21*e32*e35+e21*e31*e34+e31*e30*e23+e31*e20*e33+e31*e32*e25+e31*e22*e35+e34*e33*e23+e34*e35*e25+e27*e33*e36+e27*e35*e38+e27*e34*e37+e37*e33*e26+e37*e23*e36+e37*e35*e28+e37*e25*e38-e34*e30*e20;
A[4 + 10*19]=e31*e30*e33+e31*e32*e35+0.5*e312*e34+0.5*e34*e332+0.5*e34*e352+0.5*e343+e37*e33*e36+e37*e35*e38+0.5*e34*e372-0.5*e34*e302-0.5*e34*e322-0.5*e34*e362-0.5*e34*e382;
A[5 + 10*0]=e01*e00*e06+0.5*e012*e07+e01*e02*e08+e04*e03*e06+0.5*e042*e07+e04*e05*e08+0.5*e07*e062+0.5*e073+0.5*e07*e082-0.5*e07*e002-0.5*e07*e022-0.5*e07*e032-0.5*e07*e052;
A[5 + 10*1]=e04*e13*e06+0.5*e042*e17+1.5*e17*e072+0.5*e17*e062+0.5*e17*e082-0.5*e17*e002-0.5*e17*e022-0.5*e17*e032-0.5*e17*e052+e01*e10*e06+e07*e16*e06+e07*e18*e08-e07*e10*e00-e07*e12*e02-e07*e13*e03-e07*e15*e05+e01*e00*e16+e01*e11*e07+e01*e12*e08+e01*e02*e18+e11*e00*e06+e11*e02*e08+e04*e03*e16+e04*e14*e07+e04*e15*e08+e04*e05*e18+e14*e03*e06+e14*e05*e08+0.5*e012*e17;
A[5 + 10*2]=-e17*e10*e00+0.5*e112*e07+0.5*e142*e07+0.5*e07*e162+0.5*e07*e182+1.5*e07*e172-0.5*e07*e102-0.5*e07*e152-0.5*e07*e132-0.5*e07*e122+e01*e10*e16+e01*e12*e18+e01*e11*e17+e11*e10*e06+e11*e00*e16+e11*e12*e08+e11*e02*e18+e04*e13*e16+e04*e15*e18+e04*e14*e17+e14*e13*e06+e14*e03*e16+e14*e15*e08+e14*e05*e18+e17*e16*e06+e17*e18*e08-e17*e12*e02-e17*e13*e03-e17*e15*e05;
A[5 + 10*3]=e11*e10*e16+e11*e12*e18+0.5*e112*e17+e14*e13*e16+e14*e15*e18+0.5*e142*e17+0.5*e17*e162+0.5*e17*e182+0.5*e173-0.5*e17*e102-0.5*e17*e152-0.5*e17*e132-0.5*e17*e122;
A[5 + 10*4]=e01*e22*e08+e07*e28*e08-e07*e20*e00-e07*e23*e03-e07*e22*e02-e07*e25*e05+0.5*e012*e27+0.5*e042*e27+1.5*e27*e072+0.5*e27*e062+0.5*e27*e082-0.5*e27*e002-0.5*e27*e022-0.5*e27*e032-0.5*e27*e052+e07*e26*e06+e01*e20*e06+e01*e00*e26+e01*e21*e07+e01*e02*e28+e21*e00*e06+e21*e02*e08+e04*e23*e06+e04*e03*e26+e04*e24*e07+e04*e25*e08+e04*e05*e28+e24*e03*e06+e24*e05*e08;
A[5 + 10*5]=e14*e24*e07+e14*e03*e26+e14*e23*e06+e04*e14*e27+e04*e24*e17+e04*e15*e28+e04*e25*e18+e04*e13*e26+e04*e23*e16+e21*e02*e18+e21*e12*e08-e27*e15*e05-e27*e13*e03-e27*e12*e02-e27*e10*e00-e17*e25*e05-e17*e23*e03-e17*e22*e02-e17*e20*e00-e07*e22*e12-e07*e23*e13-e07*e25*e15-e07*e20*e10+e27*e18*e08+e27*e16*e06+e17*e28*e08+e17*e26*e06+3*e07*e27*e17+e07*e28*e18+e07*e26*e16+e24*e05*e18+e24*e15*e08+e24*e03*e16+e24*e13*e06+e14*e05*e28+e14*e25*e08+e01*e12*e28+e01*e20*e16+e01*e10*e26+e01*e22*e18+e01*e21*e17+e11*e20*e06+e01*e11*e27+e21*e00*e16+e21*e10*e06+e11*e21*e07+e11*e22*e08+e11*e02*e28+e11*e00*e26;
A[5 + 10*6]=-0.5*e27*e102-0.5*e27*e152-0.5*e27*e132-0.5*e27*e122+0.5*e142*e27+1.5*e27*e172+0.5*e27*e162+0.5*e27*e182+0.5*e112*e27+e11*e22*e18+e11*e10*e26+e11*e20*e16-e17*e22*e12-e17*e23*e13-e17*e25*e15-e17*e20*e10+e17*e28*e18+e17*e26*e16+e24*e15*e18+e24*e13*e16+e14*e24*e17+e14*e15*e28+e14*e25*e18+e14*e13*e26+e14*e23*e16+e21*e12*e18+e21*e10*e16+e11*e21*e17+e11*e12*e28;
A[5 + 10*7]=-0.5*e07*e252+e27*e26*e06+e27*e28*e08-e27*e20*e00-e27*e22*e02-e27*e23*e03-e27*e25*e05+1.5*e07*e272+0.5*e07*e282+e01*e22*e28+e21*e20*e06+e21*e00*e26+e21*e22*e08+e21*e02*e28+e04*e23*e26+e04*e24*e27+e04*e25*e28+e24*e23*e06+e24*e03*e26+e24*e25*e08+e24*e05*e28+0.5*e212*e07+0.5*e242*e07+0.5*e07*e262+e01*e20*e26+e01*e21*e27-0.5*e07*e202-0.5*e07*e232-0.5*e07*e222;
A[5 + 10*8]=-e27*e25*e15-e27*e23*e13-e27*e22*e12-0.5*e17*e252-0.5*e17*e202-0.5*e17*e222-0.5*e17*e232+0.5*e17*e262+1.5*e17*e272+0.5*e17*e282+e24*e23*e16+e24*e13*e26+e24*e25*e18+e24*e15*e28+e27*e26*e16+e27*e28*e18-e27*e20*e10+e14*e24*e27+e14*e25*e28+0.5*e212*e17+0.5*e242*e17+e11*e20*e26+e11*e21*e27+e11*e22*e28+e21*e20*e16+e21*e10*e26+e21*e22*e18+e21*e12*e28+e14*e23*e26;
A[5 + 10*9]=e21*e20*e26+0.5*e212*e27+e21*e22*e28+e24*e23*e26+0.5*e242*e27+e24*e25*e28+0.5*e27*e262+0.5*e273+0.5*e27*e282-0.5*e27*e202-0.5*e27*e222-0.5*e27*e232-0.5*e27*e252;
A[5 + 10*10]=e04*e05*e38+e01*e30*e06-0.5*e37*e002-0.5*e37*e022-0.5*e37*e032-0.5*e37*e052-e07*e32*e02-e07*e35*e05-e07*e33*e03+e07*e36*e06+e07*e38*e08-e07*e30*e00+1.5*e37*e072+0.5*e37*e062+0.5*e37*e082+e01*e02*e38+e31*e00*e06+e31*e02*e08+e04*e33*e06+e04*e03*e36+e04*e34*e07+e04*e35*e08+e34*e03*e06+e34*e05*e08+0.5*e012*e37+0.5*e042*e37+e01*e00*e36+e01*e31*e07+e01*e32*e08;
A[5 + 10*11]=e14*e33*e06+e11*e30*e06+e11*e00*e36+e11*e31*e07+e31*e10*e06+e11*e32*e08+e11*e02*e38+e31*e00*e16+e31*e12*e08+e31*e02*e18+e04*e33*e16+e04*e13*e36+e04*e35*e18+e04*e15*e38+e01*e10*e36+e01*e32*e18+e01*e12*e38+e01*e31*e17+e01*e11*e37+e01*e30*e16-e17*e35*e05-e37*e10*e00-e37*e12*e02-e37*e13*e03-e37*e15*e05+e37*e18*e08-e07*e30*e10-e07*e35*e15-e07*e33*e13-e07*e32*e12-e17*e30*e00-e17*e32*e02-e17*e33*e03+e07*e38*e18+3*e07*e37*e17+e17*e36*e06+e17*e38*e08+e37*e16*e06+e04*e34*e17+e04*e14*e37+e14*e03*e36+e14*e34*e07+e14*e35*e08+e14*e05*e38+e34*e13*e06+e34*e03*e16+e34*e15*e08+e34*e05*e18+e07*e36*e16;
A[5 + 10*12]=e11*e32*e18-0.5*e37*e102-0.5*e37*e152-0.5*e37*e132-0.5*e37*e122+0.5*e112*e37+0.5*e142*e37+1.5*e37*e172+0.5*e37*e162+0.5*e37*e182+e11*e10*e36+e11*e12*e38+e11*e31*e17+e31*e10*e16+e31*e12*e18+e14*e33*e16+e14*e13*e36+e14*e35*e18+e14*e15*e38+e14*e34*e17+e34*e13*e16+e34*e15*e18+e17*e36*e16+e17*e38*e18-e17*e30*e10-e17*e35*e15-e17*e33*e13-e17*e32*e12+e11*e30*e16;
A[5 + 10*13]=e01*e20*e36+e01*e31*e27+e01*e21*e37+e01*e32*e28+e01*e22*e38+e21*e30*e06+e21*e00*e36+e21*e31*e07+e21*e32*e08+e21*e02*e38+e01*e30*e26+e31*e20*e06+e31*e00*e26+e31*e22*e08+e31*e02*e28+e04*e33*e26+e04*e23*e36+e04*e34*e27+e04*e24*e37+e04*e35*e28+e04*e25*e38+e24*e33*e06+e24*e03*e36+e24*e34*e07+e24*e35*e08+e24*e05*e38+e34*e23*e06+e34*e03*e26+e34*e25*e08+e34*e05*e28+e07*e36*e26+3*e07*e37*e27+e07*e38*e28+e27*e36*e06+e27*e38*e08+e37*e26*e06+e37*e28*e08-e07*e30*e20-e07*e32*e22-e07*e33*e23-e07*e35*e25-e27*e30*e00-e27*e32*e02-e27*e33*e03-e27*e35*e05-e37*e20*e00-e37*e22*e02-e37*e23*e03-e37*e25*e05;
A[5 + 10*14]=e11*e30*e26+e11*e20*e36+e11*e31*e27+e11*e21*e37+e11*e32*e28+e11*e22*e38+e21*e10*e36+e21*e32*e18+e21*e12*e38+e21*e31*e17+e31*e20*e16+e31*e10*e26+e31*e22*e18+e31*e12*e28+e14*e33*e26+e14*e23*e36+e14*e34*e27+e14*e24*e37+e14*e35*e28+e14*e25*e38+e24*e33*e16+e24*e13*e36+e24*e35*e18+e24*e15*e38+e24*e34*e17+e34*e23*e16+e34*e13*e26+e34*e25*e18+e34*e15*e28+e17*e36*e26+3*e17*e37*e27+e17*e38*e28+e27*e36*e16+e27*e38*e18+e37*e26*e16+e37*e28*e18-e17*e30*e20-e17*e32*e22-e17*e33*e23-e17*e35*e25-e27*e30*e10-e27*e35*e15-e27*e33*e13-e27*e32*e12-e37*e20*e10-e37*e25*e15-e37*e23*e13-e37*e22*e12+e21*e30*e16;
A[5 + 10*15]=e21*e20*e36+e21*e31*e27+e21*e32*e28+e21*e22*e38+e31*e22*e28+e24*e33*e26+e24*e23*e36+e24*e34*e27+e24*e35*e28+e24*e25*e38+e34*e23*e26+e34*e25*e28+e27*e36*e26+e27*e38*e28-e27*e30*e20-e27*e32*e22-e27*e33*e23-e27*e35*e25+0.5*e242*e37+1.5*e37*e272+0.5*e37*e262+0.5*e37*e282+e31*e20*e26+e21*e30*e26+0.5*e212*e37-0.5*e37*e202-0.5*e37*e222-0.5*e37*e232-0.5*e37*e252;
A[5 + 10*16]=e01*e30*e36+e01*e32*e38+e01*e31*e37+e31*e30*e06+e31*e00*e36+e31*e32*e08+e31*e02*e38+e04*e33*e36+e04*e35*e38+e04*e34*e37+e34*e33*e06+e34*e03*e36+e34*e35*e08+e34*e05*e38+e37*e36*e06+e37*e38*e08-e37*e30*e00-e37*e32*e02-e37*e33*e03-e37*e35*e05+0.5*e312*e07+0.5*e342*e07+0.5*e07*e362+0.5*e07*e382+1.5*e07*e372-0.5*e07*e302-0.5*e07*e352-0.5*e07*e322-0.5*e07*e332;
A[5 + 10*17]=0.5*e312*e17+0.5*e342*e17+0.5*e17*e362+0.5*e17*e382+1.5*e17*e372-0.5*e17*e302-0.5*e17*e352-0.5*e17*e322-0.5*e17*e332-e37*e32*e12-e37*e33*e13+e11*e30*e36+e11*e32*e38+e11*e31*e37+e31*e30*e16+e31*e10*e36+e31*e32*e18+e31*e12*e38+e14*e33*e36+e14*e35*e38+e14*e34*e37+e34*e33*e16+e34*e13*e36+e34*e35*e18+e34*e15*e38+e37*e36*e16+e37*e38*e18-e37*e30*e10-e37*e35*e15;
A[5 + 10*18]=e21*e31*e37-0.5*e27*e332+e21*e30*e36+e21*e32*e38+e31*e30*e26+e31*e20*e36+e31*e32*e28+e31*e22*e38+e24*e33*e36+e24*e35*e38+e24*e34*e37+e34*e33*e26+e34*e23*e36+e34*e35*e28+e34*e25*e38+e37*e36*e26+e37*e38*e28-e37*e30*e20-e37*e32*e22-e37*e33*e23-e37*e35*e25+0.5*e312*e27+0.5*e342*e27+0.5*e27*e362+0.5*e27*e382+1.5*e27*e372-0.5*e27*e302-0.5*e27*e352-0.5*e27*e322;
A[5 + 10*19]=e31*e30*e36+e31*e32*e38+0.5*e312*e37+e34*e33*e36+e34*e35*e38+0.5*e342*e37+0.5*e37*e362+0.5*e37*e382+0.5*e373-0.5*e37*e302-0.5*e37*e352-0.5*e37*e322-0.5*e37*e332;
A[6 + 10*0]=0.5*e02*e002+0.5*e02*e012+0.5*e023+e05*e00*e03+e05*e01*e04+0.5*e02*e052+e08*e00*e06+e08*e01*e07+0.5*e02*e082-0.5*e02*e032-0.5*e02*e042-0.5*e02*e062-0.5*e02*e072;
A[6 + 10*1]=-0.5*e12*e042-0.5*e12*e062-0.5*e12*e072+0.5*e12*e082-0.5*e12*e032+1.5*e12*e022+0.5*e12*e002+0.5*e12*e012+0.5*e12*e052+e02*e10*e00+e02*e11*e01+e05*e10*e03+e05*e00*e13+e05*e11*e04+e05*e01*e14+e05*e02*e15+e15*e00*e03+e15*e01*e04+e08*e10*e06+e08*e00*e16+e08*e11*e07+e08*e01*e17+e08*e02*e18+e18*e00*e06+e18*e01*e07-e02*e13*e03-e02*e14*e04-e02*e16*e06-e02*e17*e07;
A[6 + 10*2]=0.5*e02*e102+1.5*e02*e122+0.5*e02*e112+0.5*e02*e152+0.5*e02*e182-0.5*e02*e162-0.5*e02*e172-0.5*e02*e132-0.5*e02*e142+e12*e10*e00+e12*e11*e01+e05*e10*e13+e05*e12*e15+e05*e11*e14+e15*e10*e03+e15*e00*e13+e15*e11*e04+e15*e01*e14+e08*e10*e16+e08*e12*e18+e08*e11*e17+e18*e10*e06+e18*e00*e16+e18*e11*e07+e18*e01*e17-e12*e13*e03-e12*e14*e04-e12*e16*e06-e12*e17*e07;
A[6 + 10*3]=0.5*e12*e102+0.5*e123+0.5*e12*e112+e15*e10*e13+0.5*e12*e152+e15*e11*e14+e18*e10*e16+0.5*e12*e182+e18*e11*e17-0.5*e12*e162-0.5*e12*e172-0.5*e12*e132-0.5*e12*e142;
A[6 + 10*4]=-0.5*e22*e032-0.5*e22*e042-0.5*e22*e062-0.5*e22*e072+0.5*e22*e082+1.5*e22*e022+0.5*e22*e002+0.5*e22*e012+0.5*e22*e052+e02*e20*e00+e02*e21*e01+e05*e20*e03+e05*e00*e23+e05*e21*e04+e05*e01*e24+e05*e02*e25+e25*e00*e03+e25*e01*e04+e08*e20*e06+e08*e00*e26+e08*e21*e07+e08*e01*e27+e08*e02*e28+e28*e00*e06+e28*e01*e07-e02*e27*e07-e02*e23*e03-e02*e24*e04-e02*e26*e06;
A[6 + 10*5]=-e22*e17*e07-e22*e16*e06-e22*e14*e04-e22*e13*e03-e12*e26*e06-e12*e24*e04-e12*e23*e03-e12*e27*e07-e02*e24*e14-e02*e23*e13-e02*e27*e17-e02*e26*e16+e28*e01*e17+e28*e11*e07+e28*e00*e16+e28*e10*e06+e18*e02*e28+e18*e01*e27+e18*e21*e07+e18*e00*e26+e18*e20*e06+e08*e11*e27+e08*e21*e17+e08*e12*e28+e08*e22*e18+e08*e10*e26+e25*e01*e14+e25*e11*e04+e25*e00*e13+e25*e10*e03+e15*e01*e24+e02*e21*e11+e12*e21*e01+e15*e02*e25+e15*e21*e04+e05*e22*e15+e05*e11*e24+e15*e20*e03+e15*e00*e23+e05*e10*e23+e05*e12*e25+e05*e21*e14+e22*e10*e00+e22*e11*e01+e02*e20*e10+3*e02*e22*e12+e12*e20*e00+e08*e20*e16+e05*e20*e13;
A[6 + 10*6]=-e12*e24*e14-e12*e23*e13-e12*e27*e17-e12*e26*e16+e28*e11*e17+e28*e10*e16+e18*e11*e27+e18*e21*e17+e18*e12*e28+e18*e10*e26+e18*e20*e16+e25*e11*e14+e25*e10*e13+e15*e11*e24+e15*e21*e14+e15*e12*e25+e15*e10*e23+e15*e20*e13+e12*e21*e11+0.5*e22*e182+0.5*e22*e152+1.5*e22*e122+0.5*e22*e102+e12*e20*e10+0.5*e22*e112-0.5*e22*e172-0.5*e22*e132-0.5*e22*e142-0.5*e22*e162;
A[6 + 10*7]=0.5*e02*e282+e28*e01*e27-e22*e27*e07-e22*e23*e03-e22*e24*e04-e22*e26*e06+0.5*e02*e252+e05*e20*e23+e05*e22*e25+e25*e20*e03+e25*e00*e23+e25*e21*e04+e25*e01*e24+e08*e20*e26+e08*e21*e27+e08*e22*e28+e28*e20*e06+e28*e00*e26+e28*e21*e07+e05*e21*e24+0.5*e02*e202+0.5*e02*e212+1.5*e02*e222+e22*e20*e00+e22*e21*e01-0.5*e02*e272-0.5*e02*e242-0.5*e02*e232-0.5*e02*e262;
A[6 + 10*8]=-e22*e27*e17-e22*e23*e13-e22*e24*e14-0.5*e12*e232-0.5*e12*e262-0.5*e12*e242-0.5*e12*e272+0.5*e12*e282+e18*e21*e27+e28*e20*e16+e28*e10*e26+e28*e21*e17+e28*e11*e27-e22*e26*e16+e18*e22*e28+0.5*e12*e252+0.5*e12*e202+0.5*e12*e212+1.5*e12*e222+e22*e20*e10+e15*e20*e23+e15*e21*e24+e15*e22*e25+e25*e20*e13+e25*e10*e23+e25*e21*e14+e25*e11*e24+e18*e20*e26+e22*e21*e11;
A[6 + 10*9]=0.5*e22*e202+0.5*e22*e212+0.5*e223+e25*e20*e23+e25*e21*e24+0.5*e22*e252+e28*e20*e26+e28*e21*e27+0.5*e22*e282-0.5*e22*e232-0.5*e22*e262-0.5*e22*e242-0.5*e22*e272;
A[6 + 10*10]=e08*e31*e07-0.5*e32*e032-e02*e33*e03-e02*e34*e04-e02*e36*e06-0.5*e32*e042-0.5*e32*e062-0.5*e32*e072+e38*e01*e07+e38*e00*e06-e02*e37*e07+e05*e31*e04+e05*e01*e34+e05*e02*e35+e35*e01*e04+e35*e00*e03+e08*e30*e06+e08*e00*e36+e08*e01*e37+e08*e02*e38+0.5*e32*e052+e02*e30*e00+e02*e31*e01+e05*e30*e03+e05*e00*e33+1.5*e32*e022+0.5*e32*e012+0.5*e32*e002+0.5*e32*e082;
A[6 + 10*11]=e05*e32*e15+e32*e11*e01+e38*e10*e06+e08*e12*e38-e32*e14*e04-e32*e16*e06-e32*e17*e07-e12*e36*e06-e32*e13*e03-e02*e34*e14-e12*e37*e07-e12*e33*e03-e12*e34*e04-e02*e37*e17-e02*e33*e13+e38*e01*e17-e02*e36*e16+e18*e01*e37+e18*e02*e38+e38*e00*e16+e38*e11*e07+e08*e30*e16+e08*e10*e36+e08*e32*e18+e08*e31*e17+e08*e11*e37+e18*e30*e06+e18*e00*e36+e18*e31*e07+e35*e10*e03+e35*e00*e13+e35*e11*e04+e35*e01*e14+e15*e02*e35+e05*e10*e33+e05*e12*e35+e05*e31*e14+e05*e11*e34+e15*e30*e03+e15*e00*e33+e15*e31*e04+e15*e01*e34+e05*e30*e13+e02*e30*e10+e02*e31*e11+3*e02*e32*e12+e12*e30*e00+e12*e31*e01+e32*e10*e00;
A[6 + 10*12]=0.5*e32*e102+0.5*e32*e112+e12*e30*e10+1.5*e32*e122+e12*e31*e11+e15*e30*e13+e15*e10*e33+e15*e12*e35+e15*e31*e14+e15*e11*e34+e35*e10*e13-0.5*e32*e162-0.5*e32*e172-0.5*e32*e132-0.5*e32*e142-e12*e37*e17-e12*e33*e13-e12*e34*e14+0.5*e32*e182+0.5*e32*e152+e35*e11*e14+e18*e30*e16+e18*e10*e36+e18*e12*e38+e18*e31*e17+e18*e11*e37+e38*e10*e16+e38*e11*e17-e12*e36*e16;
A[6 + 10*13]=3*e02*e32*e22+e05*e31*e24+e08*e22*e38+e02*e31*e21+e22*e30*e00+e22*e31*e01+e32*e20*e00+e32*e21*e01+e05*e30*e23+e05*e20*e33+e05*e21*e34-e22*e37*e07-e22*e33*e03-e22*e34*e04-e22*e36*e06-e32*e27*e07-e32*e23*e03-e32*e24*e04-e32*e26*e06+e05*e32*e25+e25*e30*e03+e25*e00*e33+e25*e31*e04+e25*e01*e34+e25*e02*e35+e35*e20*e03+e35*e00*e23+e35*e21*e04+e35*e01*e24+e08*e30*e26+e08*e20*e36+e08*e31*e27+e08*e21*e37+e08*e32*e28+e28*e30*e06+e28*e00*e36+e28*e31*e07+e28*e01*e37+e28*e02*e38+e38*e20*e06+e38*e00*e26+e38*e21*e07+e38*e01*e27-e02*e33*e23-e02*e36*e26-e02*e34*e24-e02*e37*e27+e05*e22*e35+e02*e30*e20;
A[6 + 10*14]=e18*e22*e38+e12*e31*e21+3*e12*e32*e22+e22*e30*e10+e22*e31*e11+e32*e20*e10+e32*e21*e11+e15*e30*e23+e15*e20*e33+e15*e31*e24+e15*e21*e34+e15*e32*e25+e15*e22*e35+e25*e30*e13+e25*e10*e33+e25*e12*e35+e25*e31*e14+e25*e11*e34+e35*e20*e13+e35*e10*e23+e35*e21*e14+e35*e11*e24+e18*e30*e26+e18*e20*e36+e18*e31*e27+e18*e21*e37+e18*e32*e28+e28*e30*e16+e28*e10*e36+e28*e12*e38+e28*e31*e17+e28*e11*e37+e38*e20*e16+e38*e10*e26+e12*e30*e20-e22*e37*e17-e22*e33*e13-e22*e34*e14-e32*e26*e16-e32*e27*e17-e32*e23*e13-e32*e24*e14-e22*e36*e16+e38*e21*e17+e38*e11*e27-e12*e33*e23-e12*e36*e26-e12*e34*e24-e12*e37*e27;
A[6 + 10*15]=e25*e30*e23+e22*e30*e20+e22*e31*e21+e25*e20*e33+e25*e31*e24+e25*e21*e34+e25*e22*e35+e35*e20*e23+e35*e21*e24+e28*e30*e26+e28*e20*e36+e28*e31*e27+e28*e21*e37+e28*e22*e38+e38*e20*e26+e38*e21*e27-e22*e33*e23-e22*e36*e26-e22*e34*e24-e22*e37*e27+0.5*e32*e212+0.5*e32*e252+1.5*e32*e222+0.5*e32*e202+0.5*e32*e282-0.5*e32*e232-0.5*e32*e262-0.5*e32*e242-0.5*e32*e272;
A[6 + 10*16]=0.5*e02*e302+1.5*e02*e322+0.5*e02*e312+0.5*e02*e352+0.5*e02*e382-0.5*e02*e342-0.5*e02*e362-0.5*e02*e332-0.5*e02*e372+e38*e30*e06+e32*e30*e00+e32*e31*e01+e05*e30*e33+e05*e32*e35+e05*e31*e34+e35*e30*e03+e35*e00*e33+e35*e31*e04+e35*e01*e34+e08*e30*e36+e08*e32*e38+e08*e31*e37+e38*e00*e36+e38*e31*e07+e38*e01*e37-e32*e37*e07-e32*e33*e03-e32*e34*e04-e32*e36*e06;
A[6 + 10*17]=e32*e30*e10+e32*e31*e11+e15*e30*e33+e15*e32*e35+e15*e31*e34+e35*e30*e13+e35*e10*e33+e35*e31*e14+e35*e11*e34+e18*e30*e36+e18*e32*e38+e18*e31*e37+e38*e30*e16+e38*e10*e36+e38*e31*e17+e38*e11*e37-e32*e36*e16-e32*e37*e17-e32*e33*e13-e32*e34*e14+0.5*e12*e382-0.5*e12*e342-0.5*e12*e362-0.5*e12*e332-0.5*e12*e372+0.5*e12*e352+1.5*e12*e322+0.5*e12*e312+0.5*e12*e302;
A[6 + 10*18]=0.5*e22*e302+0.5*e22*e312+0.5*e22*e352+0.5*e22*e382-0.5*e22*e342-0.5*e22*e362-0.5*e22*e332-0.5*e22*e372+1.5*e22*e322+e32*e30*e20+e32*e31*e21+e25*e30*e33+e25*e32*e35+e25*e31*e34+e35*e30*e23+e35*e20*e33+e35*e31*e24+e35*e21*e34+e28*e30*e36+e28*e32*e38+e28*e31*e37+e38*e30*e26+e38*e20*e36+e38*e31*e27+e38*e21*e37-e32*e33*e23-e32*e36*e26-e32*e34*e24-e32*e37*e27;
A[6 + 10*19]=0.5*e32*e302+0.5*e323+0.5*e32*e312+e35*e30*e33+0.5*e32*e352+e35*e31*e34+e38*e30*e36+0.5*e32*e382+e38*e31*e37-0.5*e32*e342-0.5*e32*e362-0.5*e32*e332-0.5*e32*e372;
A[7 + 10*0]=e02*e01*e04+e02*e00*e03+0.5*e022*e05+0.5*e05*e032+0.5*e05*e042+0.5*e053+e08*e03*e06+e08*e04*e07+0.5*e05*e082-0.5*e05*e002-0.5*e05*e062-0.5*e05*e012-0.5*e05*e072;
A[7 + 10*1]=e08*e13*e06+e02*e10*e03+e02*e00*e13+e02*e11*e04+e02*e01*e14+e02*e12*e05+e12*e01*e04+e12*e00*e03+e05*e13*e03+e05*e14*e04+e08*e03*e16+e08*e14*e07+e08*e04*e17+e08*e05*e18+e18*e03*e06+e18*e04*e07-e05*e10*e00-e05*e11*e01-e05*e16*e06-e05*e17*e07+0.5*e022*e15+1.5*e15*e052+0.5*e15*e032+0.5*e15*e042+0.5*e15*e082-0.5*e15*e002-0.5*e15*e062-0.5*e15*e012-0.5*e15*e072;
A[7 + 10*2]=0.5*e122*e05+0.5*e05*e132+1.5*e05*e152+0.5*e05*e142+0.5*e05*e182-0.5*e05*e102-0.5*e05*e162-0.5*e05*e112-0.5*e05*e172+e02*e10*e13+e02*e12*e15+e02*e11*e14+e12*e10*e03+e12*e00*e13+e12*e11*e04+e12*e01*e14+e15*e13*e03+e15*e14*e04+e08*e13*e16+e08*e15*e18+e08*e14*e17+e18*e13*e06+e18*e03*e16+e18*e14*e07+e18*e04*e17-e15*e11*e01-e15*e16*e06-e15*e17*e07-e15*e10*e00;
A[7 + 10*3]=e12*e10*e13+0.5*e122*e15+e12*e11*e14+0.5*e15*e132+0.5*e153+0.5*e15*e142+e18*e13*e16+0.5*e15*e182+e18*e14*e17-0.5*e15*e102-0.5*e15*e162-0.5*e15*e112-0.5*e15*e172;
A[7 + 10*4]=0.5*e25*e082-0.5*e25*e002-0.5*e25*e062-0.5*e25*e012-0.5*e25*e072+e02*e20*e03+e02*e00*e23+e02*e21*e04+e02*e01*e24+e02*e22*e05+e22*e01*e04+e22*e00*e03+e05*e23*e03+e05*e24*e04+e08*e23*e06+e08*e03*e26+e08*e24*e07+e08*e04*e27+e08*e05*e28+e28*e03*e06+e28*e04*e07-e05*e20*e00-e05*e27*e07-e05*e21*e01-e05*e26*e06+0.5*e022*e25+1.5*e25*e052+0.5*e25*e032+0.5*e25*e042;
A[7 + 10*5]=-e25*e17*e07-e25*e16*e06-e25*e11*e01-e25*e10*e00-e15*e26*e06-e15*e21*e01-e15*e27*e07-e15*e20*e00-e05*e27*e17-e05*e21*e11-e05*e26*e16-e05*e20*e10+e28*e04*e17+e28*e14*e07+e28*e03*e16+e28*e13*e06+e18*e05*e28+e18*e04*e27+e18*e24*e07+e18*e03*e26+e18*e23*e06+e08*e14*e27+e08*e24*e17+e08*e15*e28+e08*e25*e18+e08*e13*e26+e08*e23*e16+e25*e14*e04+e25*e13*e03+e15*e24*e04+e15*e23*e03+e05*e24*e14+3*e05*e25*e15+e05*e23*e13+e22*e01*e14+e22*e11*e04+e22*e00*e13+e22*e10*e03+e12*e22*e05+e12*e01*e24+e12*e21*e04+e12*e00*e23+e12*e20*e03+e02*e11*e24+e02*e21*e14+e02*e12*e25+e02*e22*e15+e02*e10*e23+e02*e20*e13;
A[7 + 10*6]=-e15*e27*e17-e15*e21*e11-e15*e26*e16+e28*e14*e17+e28*e13*e16+e18*e14*e27+e18*e24*e17+e18*e15*e28+e18*e13*e26+e15*e24*e14+e15*e23*e13+e22*e11*e14+e22*e10*e13+e12*e11*e24+e12*e21*e14+e12*e22*e15+e12*e10*e23+e18*e23*e16+0.5*e25*e142+0.5*e25*e182+1.5*e25*e152+0.5*e25*e132+0.5*e122*e25+e12*e20*e13-0.5*e25*e172-0.5*e25*e162-0.5*e25*e112-0.5*e25*e102-e15*e20*e10;
A[7 + 10*7]=e28*e24*e07-0.5*e05*e272-0.5*e05*e262-0.5*e05*e212+0.5*e05*e282-0.5*e05*e202+e28*e23*e06+e08*e23*e26+e08*e25*e28+e08*e24*e27+e28*e03*e26+e28*e04*e27-e25*e27*e07-e25*e21*e01-e25*e26*e06+e02*e20*e23+e02*e22*e25+e02*e21*e24+e22*e20*e03+e22*e00*e23+e22*e21*e04+e22*e01*e24+e25*e23*e03+e25*e24*e04+0.5*e222*e05+0.5*e05*e232+1.5*e05*e252+0.5*e05*e242-e25*e20*e00;
A[7 + 10*8]=-0.5*e15*e202-0.5*e15*e262-0.5*e15*e212-0.5*e15*e272+e18*e23*e26+e18*e25*e28+e18*e24*e27+e28*e23*e16+e28*e13*e26+e28*e24*e17+e28*e14*e27-e25*e20*e10-e25*e26*e16-e25*e21*e11-e25*e27*e17+0.5*e15*e282+0.5*e15*e232+1.5*e15*e252+0.5*e15*e242+0.5*e222*e15+e12*e21*e24+e22*e20*e13+e22*e10*e23+e22*e21*e14+e22*e11*e24+e25*e23*e13+e25*e24*e14+e12*e20*e23+e12*e22*e25;
A[7 + 10*9]=e22*e20*e23+0.5*e222*e25+e22*e21*e24+0.5*e25*e232+0.5*e253+0.5*e25*e242+e28*e23*e26+0.5*e25*e282+e28*e24*e27-0.5*e25*e202-0.5*e25*e262-0.5*e25*e212-0.5*e25*e272;
A[7 + 10*10]=-0.5*e35*e062-0.5*e35*e012-0.5*e35*e072-e05*e30*e00-e05*e31*e01-e05*e36*e06-e05*e37*e07-0.5*e35*e002+0.5*e35*e082+e05*e34*e04+e08*e33*e06+e08*e03*e36+e08*e34*e07+e08*e04*e37+e08*e05*e38+e38*e04*e07+e38*e03*e06+0.5*e022*e35+1.5*e35*e052+0.5*e35*e042+0.5*e35*e032+e02*e30*e03+e02*e00*e33+e02*e31*e04+e02*e01*e34+e02*e32*e05+e32*e01*e04+e32*e00*e03+e05*e33*e03;
A[7 + 10*11]=e08*e33*e16-e35*e16*e06-e35*e17*e07-e15*e30*e00-e15*e37*e07-e15*e31*e01-e15*e36*e06-e35*e10*e00-e35*e11*e01-e05*e37*e17-e05*e31*e11+e38*e04*e17-e05*e30*e10-e05*e36*e16+e18*e33*e06+e18*e03*e36+e18*e34*e07+e18*e04*e37+e18*e05*e38+e38*e13*e06+e38*e03*e16+e38*e14*e07+e35*e14*e04+e08*e13*e36+e08*e35*e18+e08*e15*e38+e08*e34*e17+e08*e14*e37+e35*e13*e03+e05*e33*e13+3*e05*e35*e15+e05*e34*e14+e15*e33*e03+e15*e34*e04+e12*e01*e34+e12*e32*e05+e32*e10*e03+e32*e00*e13+e32*e11*e04+e32*e01*e14+e12*e30*e03+e02*e30*e13+e02*e32*e15+e02*e10*e33+e02*e12*e35+e12*e00*e33+e02*e31*e14+e02*e11*e34+e12*e31*e04;
A[7 + 10*12]=-0.5*e35*e162-0.5*e35*e172-e15*e36*e16-e15*e31*e11-e15*e37*e17-0.5*e35*e102-0.5*e35*e112-e15*e30*e10+e18*e13*e36+e18*e15*e38+e18*e34*e17+e18*e14*e37+e38*e13*e16+e38*e14*e17+e18*e33*e16+1.5*e35*e152+0.5*e35*e132+0.5*e35*e142+0.5*e35*e182+0.5*e122*e35+e32*e10*e13+e32*e11*e14+e15*e33*e13+e15*e34*e14+e12*e10*e33+e12*e32*e15+e12*e31*e14+e12*e11*e34+e12*e30*e13;
A[7 + 10*13]=e05*e33*e23+3*e05*e35*e25+e05*e34*e24+e25*e33*e03+e25*e34*e04+e35*e23*e03+e35*e24*e04+e08*e33*e26+e08*e23*e36+e08*e35*e28+e02*e20*e33+e02*e32*e25+e02*e22*e35+e02*e31*e24+e02*e21*e34+e22*e30*e03+e22*e00*e33+e22*e31*e04+e22*e01*e34+e22*e32*e05+e32*e20*e03+e32*e00*e23+e32*e21*e04+e32*e01*e24+e02*e30*e23-e35*e27*e07-e35*e21*e01-e35*e26*e06+e08*e25*e38+e08*e34*e27+e08*e24*e37+e28*e33*e06+e28*e03*e36+e28*e34*e07+e28*e04*e37+e28*e05*e38+e38*e23*e06+e38*e03*e26+e38*e24*e07+e38*e04*e27-e05*e30*e20-e05*e36*e26-e05*e31*e21-e05*e37*e27-e25*e30*e00-e25*e37*e07-e25*e31*e01-e25*e36*e06-e35*e20*e00;
A[7 + 10*14]=e12*e21*e34+e18*e25*e38+e12*e30*e23+e12*e20*e33+e12*e32*e25+e12*e22*e35+e12*e31*e24+e22*e30*e13+e22*e10*e33+e22*e32*e15+e22*e31*e14+e22*e11*e34+e32*e20*e13+e32*e10*e23+e32*e21*e14-e25*e30*e10-e25*e36*e16-e25*e31*e11-e25*e37*e17-e35*e20*e10-e35*e26*e16-e35*e21*e11-e35*e27*e17+e15*e33*e23+3*e15*e35*e25+e15*e34*e24+e25*e33*e13+e25*e34*e14+e35*e23*e13+e35*e24*e14+e18*e33*e26+e18*e23*e36+e18*e35*e28+e18*e34*e27+e18*e24*e37+e28*e33*e16+e28*e13*e36+e28*e15*e38+e28*e34*e17+e28*e14*e37+e38*e23*e16+e38*e13*e26+e38*e24*e17+e38*e14*e27-e15*e30*e20-e15*e36*e26-e15*e31*e21-e15*e37*e27+e32*e11*e24;
A[7 + 10*15]=-0.5*e35*e202-0.5*e35*e262-0.5*e35*e212-0.5*e35*e272+e25*e34*e24+e28*e23*e36+e28*e25*e38+e28*e34*e27+e28*e24*e37+e38*e23*e26+e38*e24*e27-e25*e30*e20-e25*e36*e26-e25*e31*e21-e25*e37*e27+e25*e33*e23+0.5*e222*e35+1.5*e35*e252+0.5*e35*e232+0.5*e35*e242+0.5*e35*e282+e22*e30*e23+e22*e20*e33+e22*e32*e25+e22*e31*e24+e22*e21*e34+e32*e20*e23+e32*e21*e24+e28*e33*e26;
A[7 + 10*16]=-e35*e30*e00-e35*e31*e01-e35*e36*e06-e35*e37*e07+0.5*e322*e05+0.5*e05*e332+0.5*e05*e342+1.5*e05*e352+0.5*e05*e382-0.5*e05*e302-0.5*e05*e362-0.5*e05*e312-0.5*e05*e372+e02*e30*e33+e02*e31*e34+e02*e32*e35+e32*e30*e03+e32*e00*e33+e32*e31*e04+e32*e01*e34+e35*e33*e03+e35*e34*e04+e08*e33*e36+e08*e34*e37+e08*e35*e38+e38*e33*e06+e38*e03*e36+e38*e34*e07+e38*e04*e37;
A[7 + 10*17]=-e35*e30*e10+e12*e32*e35-0.5*e15*e362-0.5*e15*e312-0.5*e15*e372-e35*e36*e16+0.5*e322*e15+0.5*e15*e332+0.5*e15*e342+1.5*e15*e352+0.5*e15*e382-0.5*e15*e302+e12*e30*e33+e12*e31*e34+e32*e30*e13+e32*e10*e33+e32*e31*e14+e32*e11*e34+e35*e33*e13+e35*e34*e14+e18*e33*e36+e18*e34*e37+e18*e35*e38+e38*e33*e16+e38*e13*e36+e38*e34*e17+e38*e14*e37-e35*e31*e11-e35*e37*e17;
A[7 + 10*18]=-0.5*e25*e302-0.5*e25*e362-0.5*e25*e312-0.5*e25*e372+0.5*e322*e25+0.5*e25*e332+0.5*e25*e342+1.5*e25*e352+0.5*e25*e382+e22*e30*e33+e22*e31*e34+e22*e32*e35+e32*e30*e23+e32*e20*e33+e32*e31*e24+e32*e21*e34+e35*e33*e23+e35*e34*e24+e28*e33*e36+e28*e34*e37+e28*e35*e38+e38*e33*e26+e38*e23*e36+e38*e34*e27+e38*e24*e37-e35*e30*e20-e35*e36*e26-e35*e31*e21-e35*e37*e27;
A[7 + 10*19]=e32*e30*e33+e32*e31*e34+0.5*e322*e35+0.5*e35*e332+0.5*e35*e342+0.5*e353+e38*e33*e36+e38*e34*e37+0.5*e35*e382-0.5*e35*e302-0.5*e35*e362-0.5*e35*e312-0.5*e35*e372;
A[8 + 10*0]=e02*e00*e06+e02*e01*e07+0.5*e022*e08+e05*e04*e07+e05*e03*e06+0.5*e052*e08+0.5*e08*e062+0.5*e08*e072+0.5*e083-0.5*e08*e042-0.5*e08*e002-0.5*e08*e012-0.5*e08*e032;
A[8 + 10*1]=e02*e10*e06+e02*e00*e16+e02*e11*e07+e02*e01*e17+e02*e12*e08+e12*e00*e06+e12*e01*e07+e05*e13*e06+e05*e03*e16+e05*e14*e07+e05*e04*e17+e05*e15*e08+e15*e04*e07+e15*e03*e06+e08*e16*e06+e08*e17*e07-e08*e10*e00-e08*e11*e01-e08*e13*e03-e08*e14*e04+0.5*e022*e18+0.5*e052*e18+1.5*e18*e082+0.5*e18*e062+0.5*e18*e072-0.5*e18*e042-0.5*e18*e002-0.5*e18*e012-0.5*e18*e032;
A[8 + 10*2]=e12*e01*e17+0.5*e152*e08+0.5*e08*e162+1.5*e08*e182+0.5*e08*e172-0.5*e08*e102-0.5*e08*e112-0.5*e08*e132-0.5*e08*e142+e05*e13*e16+e05*e14*e17+e05*e15*e18+e15*e13*e06+e15*e03*e16+e15*e14*e07+e15*e04*e17+e18*e16*e06+e18*e17*e07-e18*e10*e00-e18*e11*e01-e18*e13*e03-e18*e14*e04+0.5*e122*e08+e02*e10*e16+e02*e12*e18+e02*e11*e17+e12*e10*e06+e12*e00*e16+e12*e11*e07;
A[8 + 10*3]=e12*e10*e16+0.5*e122*e18+e12*e11*e17+e15*e13*e16+e15*e14*e17+0.5*e152*e18+0.5*e18*e162+0.5*e183+0.5*e18*e172-0.5*e18*e102-0.5*e18*e112-0.5*e18*e132-0.5*e18*e142;
A[8 + 10*4]=-e08*e20*e00+e08*e27*e07-e08*e21*e01-e08*e23*e03-e08*e24*e04+e02*e20*e06+e02*e00*e26+e02*e21*e07+e02*e01*e27+e02*e22*e08+e22*e00*e06+e22*e01*e07+e05*e23*e06+e05*e03*e26+e05*e24*e07+e05*e04*e27+e05*e25*e08+e25*e04*e07+e25*e03*e06+e08*e26*e06+0.5*e022*e28+0.5*e052*e28+1.5*e28*e082+0.5*e28*e062+0.5*e28*e072-0.5*e28*e042-0.5*e28*e002-0.5*e28*e012-0.5*e28*e032;
A[8 + 10*5]=e22*e10*e06+e22*e11*e07+e22*e01*e17+e05*e23*e16+e05*e13*e26+e05*e25*e18+e05*e15*e28+e05*e24*e17+e05*e14*e27+e15*e23*e06+e15*e03*e26+e15*e24*e07+e15*e04*e27+e15*e25*e08+e25*e13*e06+e25*e03*e16+e25*e14*e07+e25*e04*e17+e08*e26*e16+3*e08*e28*e18+e08*e27*e17+e18*e26*e06+e18*e27*e07+e22*e00*e16+e28*e16*e06+e28*e17*e07-e08*e20*e10-e08*e21*e11-e08*e23*e13-e08*e24*e14-e18*e20*e00-e18*e21*e01-e18*e23*e03-e18*e24*e04-e28*e10*e00-e28*e11*e01-e28*e13*e03-e28*e14*e04+e02*e20*e16+e02*e10*e26+e02*e22*e18+e02*e12*e28+e02*e21*e17+e02*e11*e27+e12*e20*e06+e12*e00*e26+e12*e21*e07+e12*e01*e27+e12*e22*e08;
A[8 + 10*6]=-e18*e24*e14-e18*e21*e11-e18*e23*e13-e18*e20*e10+e18*e27*e17+e18*e26*e16+e25*e14*e17+e25*e13*e16+e15*e25*e18+e15*e14*e27+e15*e24*e17+e15*e13*e26+e15*e23*e16+e22*e11*e17+e22*e10*e16+e12*e11*e27+e12*e21*e17+e12*e22*e18+e12*e10*e26+e12*e20*e16+0.5*e28*e162+0.5*e28*e172+1.5*e28*e182+0.5*e152*e28-0.5*e28*e142-0.5*e28*e112-0.5*e28*e132-0.5*e28*e102+0.5*e122*e28;
A[8 + 10*7]=-e28*e24*e04-e28*e21*e01-e28*e23*e03-e28*e20*e00+e28*e27*e07+e28*e26*e06+e25*e04*e27+e25*e24*e07+e25*e03*e26+e05*e24*e27+e05*e25*e28+e05*e23*e26+e22*e01*e27+e22*e21*e07+e22*e00*e26+e22*e20*e06+e02*e22*e28+e02*e20*e26+e02*e21*e27+0.5*e222*e08-0.5*e08*e242-0.5*e08*e212-0.5*e08*e232-0.5*e08*e202+0.5*e08*e262+0.5*e08*e272+1.5*e08*e282+0.5*e252*e08+e25*e23*e06;
A[8 + 10*8]=e25*e24*e17+e25*e14*e27+e28*e26*e16+e28*e27*e17-e28*e21*e11-e28*e24*e14+e12*e22*e28+e22*e10*e26+e22*e21*e17+e22*e11*e27+e15*e23*e26+e15*e25*e28+e15*e24*e27+e25*e23*e16+e25*e13*e26+e22*e20*e16+0.5*e222*e18+0.5*e252*e18+0.5*e18*e262+0.5*e18*e272+e12*e20*e26+e12*e21*e27-e28*e20*e10-0.5*e18*e232-0.5*e18*e242-e28*e23*e13-0.5*e18*e212+1.5*e18*e282-0.5*e18*e202;
A[8 + 10*9]=e22*e20*e26+e22*e21*e27+0.5*e222*e28+e25*e23*e26+0.5*e252*e28+e25*e24*e27+0.5*e28*e262+0.5*e28*e272+0.5*e283-0.5*e28*e202-0.5*e28*e212-0.5*e28*e232-0.5*e28*e242;
A[8 + 10*10]=-e08*e30*e00-0.5*e38*e042-0.5*e38*e002-0.5*e38*e012-0.5*e38*e032+1.5*e38*e082+0.5*e38*e062+0.5*e38*e072+e32*e01*e07+e05*e33*e06+e05*e03*e36+e05*e34*e07+e05*e04*e37+e05*e35*e08+e35*e04*e07+e35*e03*e06+e08*e36*e06+e08*e37*e07+0.5*e052*e38+e32*e00*e06+e02*e30*e06+e02*e00*e36+e02*e31*e07+e02*e01*e37+e02*e32*e08+0.5*e022*e38-e08*e33*e03-e08*e31*e01-e08*e34*e04;
A[8 + 10*11]=-e38*e11*e01-e38*e14*e04-e38*e10*e00-e38*e13*e03-e18*e30*e00-e18*e33*e03-e18*e31*e01-e18*e34*e04-e08*e30*e10-e08*e33*e13-e08*e31*e11-e08*e34*e14+3*e08*e38*e18+e08*e37*e17+e18*e36*e06+e18*e37*e07+e38*e16*e06+e38*e17*e07+e15*e35*e08+e35*e13*e06+e35*e03*e16+e35*e14*e07+e35*e04*e17+e08*e36*e16+e05*e35*e18+e05*e15*e38+e15*e33*e06+e15*e03*e36+e15*e34*e07+e15*e04*e37+e05*e14*e37+e12*e30*e06+e12*e31*e07+e12*e01*e37+e12*e00*e36+e12*e32*e08+e32*e10*e06+e32*e00*e16+e32*e11*e07+e32*e01*e17+e05*e33*e16+e05*e13*e36+e05*e34*e17+e02*e30*e16+e02*e10*e36+e02*e32*e18+e02*e12*e38+e02*e31*e17+e02*e11*e37;
A[8 + 10*12]=e12*e30*e16+e12*e10*e36+e12*e32*e18+e12*e31*e17+e12*e11*e37+e32*e10*e16+e32*e11*e17+e15*e33*e16+e15*e13*e36-0.5*e38*e102-0.5*e38*e112-0.5*e38*e132-0.5*e38*e142+0.5*e38*e162+0.5*e38*e172+e15*e34*e17+e15*e14*e37+e15*e35*e18+e35*e13*e16+e35*e14*e17+e18*e36*e16+e18*e37*e17-e18*e30*e10-e18*e33*e13-e18*e31*e11-e18*e34*e14+0.5*e122*e38+0.5*e152*e38+1.5*e38*e182;
A[8 + 10*13]=e22*e30*e06-e28*e34*e04+e05*e35*e28+e02*e22*e38+e22*e00*e36+e22*e31*e07+e22*e01*e37+e02*e32*e28+e02*e21*e37-e38*e20*e00-e28*e31*e01-e38*e23*e03-e38*e21*e01-e38*e24*e04-e28*e30*e00-e08*e30*e20-e08*e31*e21-e08*e33*e23-e08*e34*e24-e28*e33*e03+e35*e24*e07+e35*e04*e27+e08*e36*e26+e08*e37*e27+3*e08*e38*e28+e28*e36*e06+e28*e37*e07+e38*e26*e06+e38*e27*e07+e25*e04*e37+e25*e35*e08+e35*e23*e06+e35*e03*e26+e05*e23*e36+e05*e25*e38+e05*e34*e27+e05*e24*e37+e25*e33*e06+e25*e03*e36+e25*e34*e07+e05*e33*e26+e32*e21*e07+e32*e01*e27+e22*e32*e08+e32*e20*e06+e32*e00*e26+e02*e30*e26+e02*e20*e36+e02*e31*e27;
A[8 + 10*14]=e35*e13*e26-e38*e21*e11-e38*e24*e14+e35*e24*e17+e35*e14*e27+e18*e36*e26+e18*e37*e27+3*e18*e38*e28+e28*e36*e16+e28*e37*e17+e38*e26*e16+e38*e27*e17-e18*e30*e20-e18*e31*e21-e18*e33*e23-e18*e34*e24-e28*e30*e10-e28*e33*e13-e28*e31*e11-e28*e34*e14-e38*e20*e10-e38*e23*e13+e35*e23*e16+e12*e20*e36+e12*e30*e26+e12*e31*e27+e12*e21*e37+e12*e32*e28+e12*e22*e38+e22*e30*e16+e22*e10*e36+e22*e32*e18+e22*e31*e17+e22*e11*e37+e32*e20*e16+e32*e10*e26+e32*e21*e17+e32*e11*e27+e15*e33*e26+e15*e23*e36+e15*e35*e28+e15*e25*e38+e15*e34*e27+e15*e24*e37+e25*e33*e16+e25*e13*e36+e25*e34*e17+e25*e14*e37+e25*e35*e18;
A[8 + 10*15]=-e28*e30*e20+e22*e30*e26+e22*e20*e36+e22*e31*e27+e22*e21*e37+e22*e32*e28+e32*e20*e26+e32*e21*e27+e25*e33*e26+e25*e23*e36+e25*e35*e28+e25*e34*e27+e25*e24*e37+e35*e23*e26+e35*e24*e27+e28*e36*e26+e28*e37*e27-e28*e31*e21-e28*e33*e23-e28*e34*e24-0.5*e38*e242+0.5*e252*e38+1.5*e38*e282+0.5*e38*e262+0.5*e38*e272-0.5*e38*e202-0.5*e38*e212-0.5*e38*e232+0.5*e222*e38;
A[8 + 10*16]=-0.5*e08*e312-0.5*e08*e342+0.5*e352*e08+0.5*e08*e362+1.5*e08*e382+0.5*e08*e372-0.5*e08*e302-0.5*e08*e332+e02*e30*e36+e02*e32*e38+e02*e31*e37+e32*e30*e06+e32*e00*e36+e32*e31*e07+e32*e01*e37+e05*e33*e36+e05*e34*e37+e05*e35*e38+e35*e33*e06+e35*e03*e36+e35*e34*e07+e35*e04*e37+0.5*e322*e08+e38*e36*e06+e38*e37*e07-e38*e30*e00-e38*e33*e03-e38*e31*e01-e38*e34*e04;
A[8 + 10*17]=-e38*e30*e10+e38*e36*e16+e38*e37*e17-e38*e33*e13-e38*e31*e11-e38*e34*e14+0.5*e18*e362+e12*e30*e36+e12*e32*e38+e12*e31*e37+e32*e30*e16+e32*e10*e36+e32*e31*e17+e32*e11*e37+e15*e33*e36+e15*e34*e37+e15*e35*e38+e35*e33*e16+e35*e13*e36+e35*e34*e17+e35*e14*e37+0.5*e322*e18+0.5*e352*e18+1.5*e18*e382+0.5*e18*e372-0.5*e18*e302-0.5*e18*e332-0.5*e18*e312-0.5*e18*e342;
A[8 + 10*18]=-e38*e30*e20+e25*e35*e38+e22*e30*e36+e22*e32*e38+e22*e31*e37+e32*e30*e26+e32*e20*e36+e32*e31*e27+e32*e21*e37+e25*e33*e36+e25*e34*e37+e35*e33*e26+e35*e23*e36+e35*e34*e27+e35*e24*e37+e38*e36*e26+e38*e37*e27-e38*e31*e21-e38*e33*e23-e38*e34*e24-0.5*e28*e332-0.5*e28*e312-0.5*e28*e342+0.5*e322*e28+0.5*e352*e28+0.5*e28*e362+1.5*e28*e382+0.5*e28*e372-0.5*e28*e302;
A[8 + 10*19]=e32*e30*e36+0.5*e322*e38+e32*e31*e37+e35*e33*e36+e35*e34*e37+0.5*e352*e38+0.5*e38*e362+0.5*e383+0.5*e38*e372-0.5*e38*e302-0.5*e38*e332-0.5*e38*e312-0.5*e38*e342;
A[9 + 10*0]=e00*e04*e08-e00*e05*e07+e03*e02*e07-e03*e01*e08-e06*e02*e04+e06*e01*e05;
A[9 + 10*1]=e06*e01*e15-e16*e02*e04+e16*e01*e05+e03*e02*e17-e13*e01*e08+e06*e11*e05+e13*e02*e07+e00*e04*e18+e00*e14*e08-e00*e05*e17-e10*e05*e07-e00*e15*e07-e06*e12*e04-e06*e02*e14-e03*e01*e18-e03*e11*e08+e10*e04*e08+e03*e12*e07;
A[9 + 10*2]=-e13*e01*e18-e13*e11*e08+e13*e12*e07+e13*e02*e17+e03*e12*e17-e10*e15*e07+e10*e04*e18+e10*e14*e08-e10*e05*e17-e00*e15*e17+e00*e14*e18+e16*e01*e15+e06*e11*e15-e06*e12*e14-e16*e12*e04-e16*e02*e14+e16*e11*e05-e03*e11*e18;
A[9 + 10*3]=e10*e14*e18-e10*e15*e17-e13*e11*e18+e13*e12*e17+e16*e11*e15-e16*e12*e14;
A[9 + 10*4]=-e20*e05*e07+e03*e22*e07+e06*e21*e05+e06*e01*e25-e23*e01*e08+e23*e02*e07+e00*e24*e08-e00*e25*e07-e00*e05*e27+e00*e04*e28-e06*e22*e04-e06*e02*e24-e03*e21*e08-e03*e01*e28-e26*e02*e04+e26*e01*e05+e03*e02*e27+e20*e04*e08;
A[9 + 10*5]=e23*e12*e07-e26*e02*e14+e16*e21*e05-e23*e11*e08+e10*e24*e08-e20*e05*e17+e26*e11*e05+e26*e01*e15+e10*e04*e28+e00*e24*e18-e00*e15*e27+e03*e22*e17-e13*e01*e28+e23*e02*e17+e16*e01*e25+e20*e04*e18+e06*e11*e25+e13*e02*e27-e23*e01*e18-e20*e15*e07-e10*e25*e07+e13*e22*e07-e06*e22*e14-e26*e12*e04-e03*e11*e28-e03*e21*e18-e16*e22*e04-e16*e02*e24-e06*e12*e24+e06*e21*e15+e00*e14*e28-e00*e25*e17+e20*e14*e08-e13*e21*e08-e10*e05*e27+e03*e12*e27;
A[9 + 10*6]=-e13*e11*e28+e13*e12*e27+e13*e22*e17+e16*e11*e25+e10*e14*e28-e13*e21*e18-e23*e11*e18+e23*e12*e17+e20*e14*e18-e20*e15*e17+e26*e11*e15-e10*e15*e27-e10*e25*e17-e16*e22*e14-e16*e12*e24+e16*e21*e15-e26*e12*e14+e10*e24*e18;
A[9 + 10*7]=e26*e21*e05+e26*e01*e25+e20*e04*e28+e20*e24*e08-e20*e25*e07+e23*e22*e07+e03*e22*e27-e03*e21*e28-e26*e22*e04-e20*e05*e27-e00*e25*e27+e06*e21*e25-e06*e22*e24+e00*e24*e28-e26*e02*e24-e23*e21*e08-e23*e01*e28+e23*e02*e27;
A[9 + 10*8]=-e10*e25*e27+e10*e24*e28-e20*e15*e27-e20*e25*e17+e20*e14*e28+e20*e24*e18+e26*e11*e25+e23*e22*e17-e23*e11*e28+e23*e12*e27-e23*e21*e18-e13*e21*e28+e13*e22*e27-e26*e12*e24+e26*e21*e15-e16*e22*e24+e16*e21*e25-e26*e22*e14;
A[9 + 10*9]=-e20*e25*e27+e20*e24*e28-e23*e21*e28+e23*e22*e27-e26*e22*e24+e26*e21*e25;
A[9 + 10*10]=e03*e02*e37-e03*e31*e08-e03*e01*e38+e03*e32*e07-e00*e35*e07+e30*e04*e08+e06*e31*e05-e36*e02*e04+e36*e01*e05-e06*e32*e04-e06*e02*e34+e06*e01*e35+e00*e04*e38-e00*e05*e37+e33*e02*e07-e33*e01*e08-e30*e05*e07+e00*e34*e08;
A[9 + 10*11]=-e36*e12*e04+e30*e04*e18-e30*e15*e07-e36*e02*e14-e30*e05*e17+e30*e14*e08-e00*e35*e17-e00*e15*e37+e33*e02*e17-e06*e32*e14-e06*e12*e34-e16*e32*e04+e06*e31*e15+e06*e11*e35+e00*e34*e18-e10*e35*e07-e33*e11*e08-e33*e01*e18+e16*e01*e35-e16*e02*e34+e16*e31*e05-e03*e31*e18-e03*e11*e38+e03*e32*e17+e13*e02*e37-e13*e31*e08-e13*e01*e38+e10*e34*e08+e00*e14*e38+e36*e11*e05+e36*e01*e15+e03*e12*e37-e10*e05*e37+e10*e04*e38+e33*e12*e07+e13*e32*e07;
A[9 + 10*12]=-e36*e12*e14-e30*e15*e17+e13*e32*e17-e13*e31*e18-e33*e11*e18+e33*e12*e17+e10*e14*e38+e30*e14*e18-e13*e11*e38+e13*e12*e37-e10*e35*e17+e10*e34*e18-e16*e12*e34-e16*e32*e14+e16*e11*e35+e16*e31*e15+e36*e11*e15-e10*e15*e37;
A[9 + 10*13]=-e06*e22*e34-e06*e32*e24-e00*e25*e37-e00*e35*e27+e23*e02*e37+e00*e24*e38-e23*e01*e38-e03*e31*e28-e33*e01*e28+e03*e22*e37+e03*e32*e27+e33*e02*e27-e03*e21*e38-e26*e32*e04-e33*e21*e08+e36*e01*e25+e36*e21*e05-e20*e05*e37+e20*e04*e38+e30*e04*e28-e20*e35*e07+e33*e22*e07+e30*e24*e08-e30*e25*e07-e23*e31*e08+e23*e32*e07+e00*e34*e28+e06*e21*e35+e06*e31*e25-e36*e02*e24+e26*e01*e35-e36*e22*e04+e26*e31*e05-e26*e02*e34+e20*e34*e08-e30*e05*e27;
A[9 + 10*14]=e33*e22*e17+e33*e12*e27+e16*e21*e35-e16*e22*e34-e16*e32*e24+e23*e32*e17-e23*e11*e38-e23*e31*e18+e23*e12*e37-e13*e21*e38-e13*e31*e28+e13*e22*e37+e36*e21*e15-e36*e12*e24+e36*e11*e25-e26*e12*e34-e20*e35*e17+e20*e14*e38+e20*e34*e18+e30*e24*e18-e30*e15*e27-e30*e25*e17+e30*e14*e28-e33*e21*e18+e10*e34*e28+e10*e24*e38-e10*e35*e27-e10*e25*e37-e20*e15*e37-e26*e32*e14+e26*e11*e35+e26*e31*e15-e36*e22*e14+e13*e32*e27+e16*e31*e25-e33*e11*e28;
A[9 + 10*15]=-e20*e35*e27-e20*e25*e37+e20*e34*e28+e20*e24*e38+e30*e24*e28-e30*e25*e27+e23*e32*e27+e23*e22*e37-e23*e31*e28-e23*e21*e38+e33*e22*e27-e26*e22*e34-e26*e32*e24+e26*e21*e35+e26*e31*e25-e36*e22*e24+e36*e21*e25-e33*e21*e28;
A[9 + 10*16]=-e33*e01*e38-e03*e31*e38+e00*e34*e38+e33*e32*e07+e03*e32*e37+e06*e31*e35-e00*e35*e37-e36*e32*e04-e06*e32*e34-e36*e02*e34+e36*e01*e35+e36*e31*e05+e30*e04*e38+e30*e34*e08-e33*e31*e08+e33*e02*e37-e30*e05*e37-e30*e35*e07;
A[9 + 10*17]=-e33*e31*e18-e33*e11*e38+e10*e34*e38+e30*e14*e38-e10*e35*e37-e30*e15*e37-e13*e31*e38+e13*e32*e37-e30*e35*e17+e33*e12*e37+e30*e34*e18+e33*e32*e17+e16*e31*e35-e16*e32*e34-e36*e12*e34-e36*e32*e14+e36*e11*e35+e36*e31*e15;
A[9 + 10*18]=-e20*e35*e37+e20*e34*e38+e30*e24*e38-e30*e35*e27-e30*e25*e37+e30*e34*e28+e23*e32*e37-e23*e31*e38-e33*e21*e38-e33*e31*e28+e33*e22*e37+e33*e32*e27+e26*e31*e35-e26*e32*e34-e36*e22*e34-e36*e32*e24+e36*e21*e35+e36*e31*e25;
A[9 + 10*19]=-e33*e31*e38-e30*e35*e37+e36*e31*e35+e33*e32*e37+e30*e34*e38-e36*e32*e34;
}

363
modules/calib3d/test/test_fundam.cpp
Unescape View File

@ -1064,6 +1064,367 @@ void CV_FundamentalMatTest::prepare_to_validation( int test_case_idx )
f_prop2[1] = f[8];
f_prop2[2] = cv::determinant( F );
}
/******************************* find essential matrix ***********************************/
class CV_EssentialMatTest : public cvtest::ArrayTest
{
public:
CV_EssentialMatTest();
protected:
int read_params( CvFileStorage* fs );
void fill_array( int test_case_idx, int i, int j, Mat& arr );
int prepare_test_case( int test_case_idx );
void get_test_array_types_and_sizes( int test_case_idx, vector<vector<Size> >& sizes, vector<vector<int> >& types );
double get_success_error_level( int test_case_idx, int i, int j );
void run_func();
void prepare_to_validation( int );
double sampson_error(const double* f, double x1, double y1, double x2, double y2);
int method;
int img_size;
int cube_size;
int dims;
int e_result;
double min_f, max_f;
double sigma;
};
CV_EssentialMatTest::CV_EssentialMatTest()
{
// input arrays:
// 0, 1 - arrays of 2d points that are passed to %func%.
// Can have different data type, layout, be stored in homogeneous coordinates or not.
// 2 - array of 3d points that are projected to both view planes
// 3 - [R|t] matrix for the second view plane (for the first one it is [I|0]
// 4 - intrinsic matrix for both camera
test_array[INPUT].push_back(NULL);
test_array[INPUT].push_back(NULL);
test_array[INPUT].push_back(NULL);
test_array[INPUT].push_back(NULL);
test_array[INPUT].push_back(NULL);
test_array[TEMP].push_back(NULL);
test_array[TEMP].push_back(NULL);
test_array[TEMP].push_back(NULL);
test_array[TEMP].push_back(NULL);
test_array[TEMP].push_back(NULL);
test_array[OUTPUT].push_back(NULL); // Essential Matrix singularity
test_array[OUTPUT].push_back(NULL); // Inliers mask
test_array[OUTPUT].push_back(NULL); // Translation error
test_array[OUTPUT].push_back(NULL); // Positive depth count
test_array[REF_OUTPUT].push_back(NULL);
test_array[REF_OUTPUT].push_back(NULL);
test_array[REF_OUTPUT].push_back(NULL);
test_array[REF_OUTPUT].push_back(NULL);
element_wise_relative_error = false;
method = 0;
img_size = 10;
cube_size = 10;
min_f = 1;
max_f = 3;
}
int CV_EssentialMatTest::read_params( CvFileStorage* fs )
{
int code = cvtest::ArrayTest::read_params( fs );
return code;
}
void CV_EssentialMatTest::get_test_array_types_and_sizes( int /*test_case_idx*/,
vector<vector<Size> >& sizes, vector<vector<int> >& types )
{
RNG& rng = ts->get_rng();
int pt_depth = cvtest::randInt(rng) % 2 == 0 ? CV_32F : CV_64F;
double pt_count_exp = cvtest::randReal(rng)*6 + 1;
int pt_count = MAX(5, cvRound(exp(pt_count_exp)));
dims = cvtest::randInt(rng) % 2 + 2;
dims = 2;
method = CV_LMEDS << (cvtest::randInt(rng) % 2);
types[INPUT][0] = CV_MAKETYPE(pt_depth, 1);
if( 0 && cvtest::randInt(rng) % 2 )
sizes[INPUT][0] = cvSize(pt_count, dims);
else
{
sizes[INPUT][0] = cvSize(dims, pt_count);
if( cvtest::randInt(rng) % 2 )
{
types[INPUT][0] = CV_MAKETYPE(pt_depth, dims);
if( cvtest::randInt(rng) % 2 )
sizes[INPUT][0] = cvSize(pt_count, 1);
else
sizes[INPUT][0] = cvSize(1, pt_count);
}
}
sizes[INPUT][1] = sizes[INPUT][0];
types[INPUT][1] = types[INPUT][0];
sizes[INPUT][2] = cvSize(pt_count, 1 );
types[INPUT][2] = CV_64FC3;
sizes[INPUT][3] = cvSize(4,3);
types[INPUT][3] = CV_64FC1;
sizes[INPUT][4] = cvSize(3,3);
types[INPUT][4] = CV_MAKETYPE(CV_64F, 1);
sizes[TEMP][0] = cvSize(3,3);
types[TEMP][0] = CV_64FC1;
sizes[TEMP][1] = cvSize(pt_count,1);
types[TEMP][1] = CV_8UC1;
sizes[TEMP][2] = cvSize(3,3);
types[TEMP][2] = CV_64FC1;
sizes[TEMP][3] = cvSize(3, 1);
types[TEMP][3] = CV_64FC1;
sizes[TEMP][4] = cvSize(pt_count,1);
types[TEMP][4] = CV_8UC1;
sizes[OUTPUT][0] = sizes[REF_OUTPUT][0] = cvSize(3,1);
types[OUTPUT][0] = types[REF_OUTPUT][0] = CV_64FC1;
sizes[OUTPUT][1] = sizes[REF_OUTPUT][1] = cvSize(pt_count,1);
types[OUTPUT][1] = types[REF_OUTPUT][1] = CV_8UC1;
sizes[OUTPUT][2] = sizes[REF_OUTPUT][2] = cvSize(1,1);
types[OUTPUT][2] = types[REF_OUTPUT][2] = CV_64FC1;
sizes[OUTPUT][3] = sizes[REF_OUTPUT][3] = cvSize(1,1);
types[OUTPUT][3] = types[REF_OUTPUT][3] = CV_8UC1;
}
double CV_EssentialMatTest::get_success_error_level( int /*test_case_idx*/, int /*i*/, int /*j*/ )
{
return 1e-2;
}
void CV_EssentialMatTest::fill_array( int test_case_idx, int i, int j, Mat& arr )
{
double t[12]={0};
RNG& rng = ts->get_rng();
if( i != INPUT )
{
cvtest::ArrayTest::fill_array( test_case_idx, i, j, arr );
return;
}
switch( j )
{
case 0:
case 1:
return; // fill them later in prepare_test_case
case 2:
{
double* p = arr.ptr<double>();
for( i = 0; i < arr.cols*3; i += 3 )
{
p[i] = cvtest::randReal(rng)*cube_size;
p[i+1] = cvtest::randReal(rng)*cube_size;
p[i+2] = cvtest::randReal(rng)*cube_size + cube_size;
}
}
break;
case 3:
{
double r[3];
Mat rot_vec( 3, 1, CV_64F, r );
Mat rot_mat( 3, 3, CV_64F, t, 4*sizeof(t[0]) );
r[0] = cvtest::randReal(rng)*CV_PI*2;
r[1] = cvtest::randReal(rng)*CV_PI*2;
r[2] = cvtest::randReal(rng)*CV_PI*2;
cvtest::Rodrigues( rot_vec, rot_mat );
t[3] = cvtest::randReal(rng)*cube_size;
t[7] = cvtest::randReal(rng)*cube_size;
t[11] = cvtest::randReal(rng)*cube_size;
Mat( 3, 4, CV_64F, t ).convertTo(arr, arr.type());
}
break;
case 4:
t[0] = t[4] = cvtest::randReal(rng)*(max_f - min_f) + min_f;
t[2] = (img_size*0.5 + cvtest::randReal(rng)*4. - 2.)*t[0];
t[5] = (img_size*0.5 + cvtest::randReal(rng)*4. - 2.)*t[4];
t[8] = 1.;
Mat( 3, 3, CV_64F, t ).convertTo( arr, arr.type() );
break;
}
}
int CV_EssentialMatTest::prepare_test_case( int test_case_idx )
{
int code = cvtest::ArrayTest::prepare_test_case( test_case_idx );
if( code > 0 )
{
const Mat& _3d = test_mat[INPUT][2];
RNG& rng = ts->get_rng();
double Idata[] = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 };
Mat I( 3, 4, CV_64F, Idata );
int k;
for( k = 0; k < 2; k++ )
{
const Mat& Rt = k == 0 ? I : test_mat[INPUT][3];
const Mat& A = test_mat[INPUT][4];
Mat& _2d = test_mat[INPUT][k];
test_projectPoints( _3d, Rt, A, _2d, &rng, sigma );
}
}
return code;
}
void CV_EssentialMatTest::run_func()
{
Mat _input0(test_mat[INPUT][0]), _input1(test_mat[INPUT][1]);
Mat K(test_mat[INPUT][4]);
double focal(K.at<double>(0, 0));
cv::Point2d pp(K.at<double>(0, 2), K.at<double>(1, 2));
RNG& rng = ts->get_rng();
Mat E, mask1(test_mat[TEMP][1]);
E = cv::findEssentialMat( _input0, _input1, focal, pp, method, 0.99, MAX(sigma*3, 0.0001), mask1 );
if (E.rows > 3)
{
int count = E.rows / 3;
int row = (cvtest::randInt(rng) % count) * 3;
E = E.rowRange(row, row + 3) * 1.0;
}
E.copyTo(test_mat[TEMP][0]);
Mat R, t, mask2;
recoverPose( E, _input0, _input1, R, t, focal, pp, mask2 );
R.copyTo(test_mat[TEMP][2]);
t.copyTo(test_mat[TEMP][3]);
mask2.copyTo(test_mat[TEMP][4]);
}
double CV_EssentialMatTest::sampson_error(const double * f, double x1, double y1, double x2, double y2)
{
double Fx1[3] = {
f[0] * x1 + f[1] * y1 + f[2],
f[3] * x1 + f[4] * y1 + f[5],
f[6] * x1 + f[7] * y1 + f[8]
};
double Ftx2[3] = {
f[0] * x2 + f[3] * y2 + f[6],
f[1] * x2 + f[4] * y2 + f[7],
f[2] * x2 + f[5] * y2 + f[8]
};
double x2tFx1 = Fx1[0] * x2 + Fx1[1] * y2 + Fx1[2];
double error = x2tFx1 * x2tFx1 / (Fx1[0] * Fx1[0] + Fx1[1] * Fx1[1] + Ftx2[0] * Ftx2[0] + Ftx2[1] * Ftx2[1]);
error = sqrt(error);
return error;
}
void CV_EssentialMatTest::prepare_to_validation( int test_case_idx )
{
const Mat& Rt0 = test_mat[INPUT][3];
const Mat& A = test_mat[INPUT][4];
double f0[9], f[9], e[9];
Mat F0(3, 3, CV_64FC1, f0), F(3, 3, CV_64F, f);
Mat E(3, 3, CV_64F, e);
Mat invA, R=Rt0.colRange(0, 3), T1, T2;
cv::invert(A, invA, CV_SVD);
double tx = Rt0.at<double>(0, 3);
double ty = Rt0.at<double>(1, 3);
double tz = Rt0.at<double>(2, 3);
double _t_x[] = { 0, -tz, ty, tz, 0, -tx, -ty, tx, 0 };
// F = (A2^-T)*[t]_x*R*(A1^-1)
cv::gemm( invA, Mat( 3, 3, CV_64F, _t_x ), 1, Mat(), 0, T1, CV_GEMM_A_T );
cv::gemm( R, invA, 1, Mat(), 0, T2 );
cv::gemm( T1, T2, 1, Mat(), 0, F0 );
F0 *= 1./f0[8];
uchar* status = test_mat[TEMP][1].data;
double err_level = get_success_error_level( test_case_idx, OUTPUT, 1 );
uchar* mtfm1 = test_mat[REF_OUTPUT][1].data;
uchar* mtfm2 = test_mat[OUTPUT][1].data;
double* e_prop1 = (double*)test_mat[REF_OUTPUT][0].data;
double* e_prop2 = (double*)test_mat[OUTPUT][0].data;
Mat E_prop2 = Mat(3, 1, CV_64F, e_prop2);
int i, pt_count = test_mat[INPUT][2].cols;
Mat p1( 1, pt_count, CV_64FC2 );
Mat p2( 1, pt_count, CV_64FC2 );
test_convertHomogeneous( test_mat[INPUT][0], p1 );
test_convertHomogeneous( test_mat[INPUT][1], p2 );
cvtest::convert(test_mat[TEMP][0], E, E.type());
cv::gemm( invA, E, 1, Mat(), 0, T1, CV_GEMM_A_T );
cv::gemm( T1, invA, 1, Mat(), 0, F );
for( i = 0; i < pt_count; i++ )
{
double x1 = p1.at<Point2d>(i).x;
double y1 = p1.at<Point2d>(i).y;
double x2 = p2.at<Point2d>(i).x;
double y2 = p2.at<Point2d>(i).y;
// double t0 = sampson_error(f0, x1, y1, x2, y2);
// double t = sampson_error(f, x1, y1, x2, y2);
double n1 = 1./sqrt(x1*x1 + y1*y1 + 1);
double n2 = 1./sqrt(x2*x2 + y2*y2 + 1);
double t0 = fabs(f0[0]*x2*x1 + f0[1]*x2*y1 + f0[2]*x2 +
f0[3]*y2*x1 + f0[4]*y2*y1 + f0[5]*y2 +
f0[6]*x1 + f0[7]*y1 + f0[8])*n1*n2;
double t = fabs(f[0]*x2*x1 + f[1]*x2*y1 + f[2]*x2 +
f[3]*y2*x1 + f[4]*y2*y1 + f[5]*y2 +
f[6]*x1 + f[7]*y1 + f[8])*n1*n2;
mtfm1[i] = 1;
mtfm2[i] = !status[i] || t0 > err_level || t < err_level;
}
e_prop1[0] = sqrt(0.5);
e_prop1[1] = sqrt(0.5);
e_prop1[2] = 0;
e_prop2[0] = 0;
e_prop2[1] = 0;
e_prop2[2] = 0;
SVD::compute(E, E_prop2);
double* pose_prop1 = (double*)test_mat[REF_OUTPUT][2].data;
double* pose_prop2 = (double*)test_mat[OUTPUT][2].data;
double terr1 = norm(Rt0.col(3) / norm(Rt0.col(3)) + test_mat[TEMP][3]);
double terr2 = norm(Rt0.col(3) / norm(Rt0.col(3)) - test_mat[TEMP][3]);
Mat rvec;
Rodrigues(Rt0.colRange(0, 3), rvec);
pose_prop1[0] = 0;
// No check for CV_LMeDS on translation. Since it
// involves with some degraded problem, when data is exact inliers.
pose_prop2[0] = method == CV_LMEDS || pt_count == 5 ? 0 : MIN(terr1, terr2);
// int inliers_count = countNonZero(test_mat[TEMP][1]);
// int good_count = countNonZero(test_mat[TEMP][4]);
test_mat[OUTPUT][3] = true; //good_count >= inliers_count / 2;
test_mat[REF_OUTPUT][3] = true;
}
/********************************** convert homogeneous *********************************/
@ -1359,6 +1720,6 @@ TEST(Calib3d_Rodrigues, accuracy) { CV_RodriguesTest test; test.safe_run(); }
TEST(Calib3d_FindFundamentalMat, accuracy) { CV_FundamentalMatTest test; test.safe_run(); }
TEST(Calib3d_ConvertHomogeneoous, accuracy) { CV_ConvertHomogeneousTest test; test.safe_run(); }
TEST(Calib3d_ComputeEpilines, accuracy) { CV_ComputeEpilinesTest test; test.safe_run(); }
TEST(Calib3d_FindEssentialMat, accuracy) { CV_EssentialMatTest test; test.safe_run(); }
/* End of file. */

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