matrix3x3 Class Reference

Constructs the zero-matrix.

Constructs s times the unit matrix.

Constructs a matrix from row vectors.

Constructs a matrix from a 3x3-array of doubles.

The first index represents the row, the second index the column

Destructor.

Access function.

Writes the matrix into the 1-dimensional array m, row by row. The array must be able to hold 9 doubles, otherwise your program will segfault.

Returns:

a constant reference to an element of the matrix. row and column must be between 0 and 2. No check is done.

Returns:

a non-constant reference to an element of the matrix. row and column must be between 0 and 2. No check is done.

Calculates the inverse of a matrix.

This method checks if the absolute value of the determinant is smaller than 1e-6. If so, nothing is done and an exception is thrown. Otherwise, the inverse matrix is calculated and returned. *this is not changed.

Warning:

If the determinant is close to zero, but not == 0.0, this method may behave in unexpected ways and return almost random results; details may depend on your particular floating point implementation. The use of this method is therefore highly discouraged, unless you are certain that the determinant is in a reasonable range, away from 0.0 (Stefan Kebekus)

Calculates the transpose of a matrix.

Generates a matrix for a random rotation.

The axis of the rotation will be uniformly distributed on the unit sphere and the angle will be uniformly distributed in the interval 0..360 degrees.

Returns:

The determinant of the matrix

Referenced by OpenBabel::signed_volume().

Checks if a matrix is symmetric.

Returns:

False if there are indices i,j such that fabs(*this[i][j]-*this[j][i]) > 1e-6. Otherwise, it returns true.

Referenced by matrix3x3::findEigenvectorsIfSymmetric().

Checks if a matrix is orthogonal.

This method checks if a matrix is orthogonal, i.e. if all column vectors are normalized and are mutually orthogonal. A matrix is orthogonal if, and only if the transformation it describes is orthonormal. An orthonormal transformation is a transformation that preserves length and angle.

The check is performed using the method isUnitMatrix() to check if

        *this * transpose()

Returns:

if a matrix is diagonal

Referenced by matrix3x3::isUnitMatrix().

Returns:

if a matrix is the unit matrix

Access function.

Warning:

row or column are not in the range 0..2, zero is returned !

Deprecated:

use the constant operator() instead

Referenced by vector3::operator*=().

Access function.

Warning:

if row or column are not in the range 0..2, nothing will happen !

Deprecated:

use the non-constant operator() instead

Referenced by OBUnitCell::GetFractionalMatrix().

Access function.

Warning:

If column is not in the range 0..2, the vector remains unchanged and an exception is thrown.

Referenced by matrix3x3::PlaneReflection().

Access function.

Warning:

If column is not in the range 0..2, the vector remains unchanged and an exception is thrown.

Access function.

Warning:

If col is not in the range 0..2, an exception is thrown.

Access function.

Warning:

If row is not in the range 0..2, an exception is thrown.

Multiplies all entries of the matrix by a scalar c.

Divides all entries of the matrix by a scalar c.

Calculate a rotation matrix for rotation about the x, y, and z axes by the angles specified (in degrees).

Referenced by OBBuilder::Connect().

Calculates a matrix that represents reflection on a plane.

Replaces *this with a matrix that represents reflection on the plane through 0 which is given by the normal vector norm.

Warning:

If the vector norm has length zero, this method will generate the 0-matrix. If the length of the axis is close to zero, but not == 0.0, this method may behave in unexpected ways and return almost random results; details may depend on your particular floating point implementation. The use of this method is therefore highly discouraged, unless you are certain that the length is in a reasonable range, away from 0.0 (Stefan Kebekus)

Deprecated:

This method will probably replaced by a safer algorithm in the future.

Todo:

Replace this method with a more fool-proof version.

Parameters:

norm

specifies the normal to the plane

Calculates a rotation matrix, rotating around the specified axis by the specified angle (in degrees).

Replaces *this with a matrix that represents rotation about the axis by a an angle.

Warning:

If the vector axis has length zero, this method will generate the 0-matrix. If the length of the axis is close to zero, but not == 0.0, this method may behave in unexpected ways and return almost random results; details may depend on your particular floating point implementation. The use of this method is therefore highly discouraged, unless you are certain that the length is in a reasonable range, away from 0.0 (Stefan Kebekus)

Deprecated:

This method will probably replaced by a safer algorithm in the future.

Todo:

Replace this method with a more fool-proof version.

Parameters:

	v	specifies the axis of the rotation
	angle	angle in degrees (0..360)

Referenced by OBMol::Align(), OBAtom::GetNewBondVector(), matrix3x3::randomRotation(), and OBAtom::SetHybAndGeom().

Calculate an orthogonalisation matrix for a unit cell specified by the parameters alpha, beta, gamma, a, b, c where alpha, beta, and gamma are the cell angles (in degrees) and a, b, and c are the cell vector lengths Used by OBUnitCell

Referenced by OBUnitCell::GetOrthoMatrix().

Find the eigenvalues and -vectors of a symmetric matrix.

This method employs the static method matrix3x3::jacobi(...) to find the eigenvalues and eigenvectors of a symmetric matrix. On entry it is checked if the matrix really is symmetric: if isSymmetric() returns 'false', an OBError is thrown.

Note:

The jacobi algorithm is should work great for all symmetric 3x3 matrices. If you need to find the eigenvectors of a non-symmetric matrix, you might want to resort to the sophisticated routines of LAPACK.

Parameters:

eigenvals

a reference to a vector3 where the eigenvalues will be stored. The eigenvalues are ordered so that eigenvals[0] <= eigenvals[1] <= eigenvals[2].

Returns:

an orthogonal matrix whose ith column is an eigenvector for the eigenvalue eigenvals[i]. Here 'orthogonal' means that all eigenvectors have length one and are mutually orthogonal. The ith eigenvector can thus be conveniently accessed by the GetColumn() method, as in the following example.

    // Calculate eigenvectors and -values
    vector3 eigenvals;
    matrix3x3 eigenmatrix = somematrix.findEigenvectorsIfSymmetric(eigenvals);
  
    // Print the 2nd eigenvector
    cout << eigenmatrix.GetColumn(1) << endl;

With these conventions, a matrix is diagonalized in the following way:

    // Diagonalize the matrix
    matrix3x3 diagonalMatrix = eigenmatrix.inverse() * somematrix * eigenmatrix;

Eigenvalue calculation.

This static function computes the eigenvalues and eigenvectors of a SYMMETRIC nxn matrix. This method is used internally by OpenBabel, but may be useful as a general eigenvalue finder.

The algorithm uses Jacobi transformations. It is described e.g. in Wilkinson, Reinsch "Handbook for automatic computation, Volume II: Linear Algebra", part II, contribution II/1. The implementation is also similar to the implementation in this book. This method is adequate to solve the eigenproblem for small matrices, of size perhaps up to 10x10. For bigger problems, you might want to resort to the sophisticated routines of LAPACK.

Note:

If you plan to find the eigenvalues of a symmetric 3x3 matrix, you will probably prefer to use the more convenient method findEigenvectorsIfSymmetric()

Parameters:

	n	the size of the matrix that should be diagonalized
	a	array of size n^2 which holds the symmetric matrix whose eigenvectors are to be computed. The convention is that the entry in row r and column c is addressed as a[n*r+c] where, of course, 0 <= r < n and 0 <= c < n. There is no check that the matrix is actually symmetric. If it is not, the behaviour of this function is undefined. On return, the matrix is overwritten with junk.
	d	pointer to a field of at least n doubles which will be overwritten. On return of this function, the entries d[0]..d[n-1] will contain the eigenvalues of the matrix.
	v	an array of size n^2 where the eigenvectors will be stored. On return, the columns of this matrix will contain the eigenvectors. The eigenvectors are normalized and mutually orthogonal.

Referenced by OBForceField::DistanceGeometry(), matrix3x3::findEigenvectorsIfSymmetric(), and OpenBabel::qtrfit().

Matrix-vector multiplication.

Calculates the product m*v of the matrix m and the column vector represented by v

Matrix-matrix multiplication.

Output a text representation of a matrix.

Print a text representation of the matrix in the standardized form: [ a, b, c ]
[ d, e, f ]
[ g, h, i ]
where the letters represent the appropriate entries in the matrix. Uses the standard output format for the individual entries, separated by ", " for each column, and [ ] indicating each row.