Linear Algebra Functions
[Modules]

All linear algebra functions which operate on the matrix as a whole. More...

Functions
ml_matrix &	ml_matrix::transpose ()
	Transposes the matrix.
ml_matrix &	ml_matrix::inv ()
	Finds the inverse of the matrix. Principally used for matrix division.
ml_matrix	ml_matrix::invp (const ml_matrix &n, int k) const
	Returns the product form of the matrix inverse.
ml_matrix &	ml_matrix::mpow (int n)
	Returns a matrix raised to a power.
ml_matrix	ml_matrix::diag () const
	Creates a diagonal matrix from a row or column matrix, or creates a row matrix from a diagonal matrix.
double	ml_matrix::trace () const
	Returns the trace of the matrix.
ml_matrix	ml_matrix::mag () const
	Returns a row matrix containing the magnitudes of each column of the matrix.
double	ml_matrix::vmag () const
	Returns the magnitude of a column or row matrix.
ml_matrix &	ml_matrix::cross (const ml_matrix &n)
	Crosses the matrix with the given matrix.
double	ml_matrix::dot (const ml_matrix &n) const
	Takes the dot product of two column vectors.
ml_matrix	ml_matrix::skew_symm () const
	Creates a skew symmetric matrix from a vector of three numbers.
ml_matrix &	ml_matrix::unit ()
	Makes each column into a row vector.
ml_matrix &	ml_matrix::sign ()
	Changes all positive elements into 1, all negative elements into -1.
ml_matrix &	ml_matrix::vunit ()
	Unitize a vector matrix by dividing by its vector magnitude.
double	ml_matrix::norm () const
	Returns the normal of the matrix (largest singular value).
ml_matrix &	ml_matrix::solve_ax_eq_b (const ml_matrix &a)
	Solve the general system of linear equations AX=B.
ml_matrix &	ml_matrix::row_mult (int row, double fac)
ml_matrix	transpose (const ml_matrix &m)
	Transposes the matrix.
ml_matrix	inv (const ml_matrix &m)
	Finds the inverse of the matrix. Principally used for matrix division.
ml_matrix	mpow (const ml_matrix &m, int n)
	Raises the matrix m to the power n.
ml_matrix	cross (const ml_matrix &m, const ml_matrix &y)
	Crosses the two matrices.
ml_matrix	unit (const ml_matrix &m)
	Makes each column into a row vector.
ml_matrix	sign (const ml_matrix &m)
	Changes all positive elements into 1, all negative elements into -1.
ml_matrix	svd (ml_matrix &u, ml_matrix &v, const ml_matrix &a)
	Returns the singular value decomposition of the third matrix.
ml_matrix	vunit (const ml_matrix &m)
	Converts the matrix into a unit vector.
ml_matrix	solve_ax_eq_b (const ml_matrix &a, const ml_matrix &b)
	Solve AX=B.
bool	simplex (ml_matrix &x, ml_matrix c, ml_matrix a, ml_matrix b, double max_val)
	Uses the simplex method to minimize the cost when solving the problem au = b and the cost is cu.
void	simplex2 (ml_matrix a, ml_matrix c, ml_matrix &x, ml_int_array &s, ml_int_array &g, ml_int_array &gu, ml_matrix &b_inv, double max_val)
	Computes the solution to the simplex problem with an optional maximum constraint.

---

Detailed Description

---

Function Documentation

ml_matrix & ml_matrix::transpose (   )  [inherited]

Transposes the matrix. Returns: Returns a transposed matrix

ml_matrix & ml_matrix::inv (   )  [inherited]

Finds the inverse of the matrix. Principally used for matrix division. This function can return an error matrix of ml_non_invertible_matrix if the matrix is empty, non-square, or otherwise non-invertible. Returns: Returns the inverse of the matrix.

ml_matrix ml_matrix::invp (  const ml_matrix &  v, int  k )  const [inherited]

Returns the product form of the matrix inverse. This function can return an error matrix of type ml_bad_index if the specified column is out of range. Parameters: v  The matrix to be used in the computation. k  The column index of v.

ml_matrix & ml_matrix::mpow (  int  n  )  [inherited]

Returns a matrix raised to a power. Parameters: n  The power to raise the matrix to Returns: Returns the matrix raised to the power n

ml_matrix ml_matrix::diag (   )  const [inherited]

Creates a diagonal matrix from a row or column matrix, or creates a row matrix from a 2-dimensional matrix's diagonal. Returns: Returns a new matrix.

double ml_matrix::trace (   )  const [inherited]

Calculates the trace of the matrix. A trace of a matrix is the summation of the diagonal. Returns: Returns the trace of the matrix.

ml_matrix ml_matrix::mag (   )  const [inherited]

Calculates the magnitudes of each column of the matrix. Returns: Returns a new row matrix containing the magnitudes of each column of the matrix.

double ml_matrix::vmag (   )  const [inherited]

Calculates the scalar magnitude of a column or row matrix. Returns: Returns the scalar magnitude of a column or row matrix.

ml_matrix & ml_matrix::cross (  const ml_matrix &  m  )  [inherited]

Crosses the matrix with matrix m. Parameters: m  The second matrix. Returns: Returns m cross n.

double ml_matrix::dot (  const ml_matrix &  v  )  const [inherited]

Takes the dot product of this matrix and the given matrix.

ml_matrix ml_matrix::skew_symm (   )  const [inherited]

Creates a skew symmetric matrix, the matrix form of the cross product, from a vector of three numbers. Returns: Returns a new matrix equal to the skew symmetric of the matrix.

ml_matrix & ml_matrix::unit (   )  [inherited]

Makes each column into a row vector.

ml_matrix & ml_matrix::sign (   )  [inherited]

Changes all positive elements into 1, all negative elements into -1.

ml_matrix & ml_matrix::vunit (   )  [inherited]

Unitize a vector matrix by dividing by its vector magnitude. Returns: Returns the unit vector of the matrix.

double ml_matrix::norm (   )  const [inherited]

Returns the normal of the matrix (largest singular value).

ml_matrix & ml_matrix::solve_ax_eq_b (  const ml_matrix &  a  )  [inherited]

Attempt to solve the generalize system of linear equations AX = B. This matrix is used as B, and on return will be X if a solution was found. This function can return an error matrix of type ml_size_mismatch if a is not a square matrix, or if the number of rows in a does not match the number of columns in this matrix. Parameters: a  The A matrix to use in the calculation. Must be square and have the same number of rows as this matrix. Returns: Returns itself, to be used in later calculations.

ml_matrix& ml_matrix::row_mult (  int  row, double  fac )  [inline, inherited]

Multiplies an entire row by the given factor Parameters: row  The row to be multiplied. fac  The factor in the multiplication. Returns: The matrix.

ml_matrix transpose (  const ml_matrix &  a  )

Creates a new matrix equal to the transpose of the specified matrix. Returns: Returns a transposed matrix.

ml_matrix inv (  const ml_matrix &  m  )

Creates a new matrix equal to the inverse of the specified matrix. Returns: Returns the inverse of the matrix.

ml_matrix mpow (  const ml_matrix &  m, int  n )

Creates a new matrix equal to the specified matrix raised to the power n. Parameters: m  A square matrix. n  The integer power. Returns: Returns the resulting matrix.

ml_matrix cross (  const ml_matrix &  m, const ml_matrix &  n )

Crosses the matrix m with matrix n. Parameters: m  The first matrix. n  The second matrix. Returns: Returns a new matrix equal to m cross n.

ml_matrix unit (  const ml_matrix &  m  )

Makes each column into a row vector.

ml_matrix sign (  const ml_matrix &  m  )

Changes all positive elements into 1, all negative elements into -1. Parameters: m  The matrix to be used in the calculation. Returns: Returns a new matrix equal to the sign of the original matrix.

ml_matrix svd (  ml_matrix &  U, ml_matrix &  V, const ml_matrix &  A )

Singular value decomposition, of the form A = U*S*V'. From "Computer Methods for Mathematical Computations," G. E. Forsythe, C. B. Moler, M. A. Malcolm, Prentice-Hall 1977, pp.201-235. The algorithms first reduces the input matrix to bidiagonal form. Then it iteratively reduces the superdiagonal elements to a negligible size, based on machine accuracy. Parameters: U  A matrix for storing the unitary matrix U. V  A matrix for storing the unitary matrix V. A  The matrix to be decomposed. Returns: Returns a diagonal matrix with the singular values.

ml_matrix vunit (  const ml_matrix &  m  )

Unitize a vector matrix by dividing by its vector magnitude. Parameters: m  A one-dimensional matrix. Returns: Returns the unit vector of m.

ml_matrix solve_ax_eq_b (  const ml_matrix &  a, const ml_matrix &  b )

Attempt to solve the generalize system of linear equations AX = B. Parameters: a  The A matrix to use in the calculation. Must be a square matrix. b  The B matrix to be used in the calculation. Must have the same number of rows as A. Returns: The solution matrix X.

bool simplex (  ml_matrix &  x, ml_matrix  c, ml_matrix  a, ml_matrix  b, double  max_val )

Uses the simplex method to minimize the cost when solving the problem au = b and the cost is cu. Parameters: x  The solution matrix will be stored in this variable. c  Cost vector a  Constraint matrix b  Right-hand-side, an mx1 column matrix. max_val  Maximum constraint on x Returns: Returns true if a feasible solution is found, false if not.

void simplex2 (  ml_matrix  a, ml_matrix  c, ml_matrix &  x, ml_int_array &  s, ml_int_array &  g, ml_int_array &  gU, ml_matrix &  BInv, double  max_val )

Computes the solution to the simplex problem with an optional maximum constraint. Parameters: a  Constraint matrix c  Cost vector x  State vector s  Indices to the constraint matrix g  Index to non-basic columns of the constraint matrix gU  Index to non-basic columns of the constraint matrix that are at their upper bound BInv  Inverse of basic columns max_val  Maximum constraint on x*