Field Detail

• VERBOSE_EXCEPTIONS

  public static boolean VERBOSE_EXCEPTIONS

  Generating the text in certain exceptions is not a trivial task if you expect those exceptions to be called millions of times.

Constructor Detail

• Equations

  public Equations()

Method Detail

• toString

  public static String toString(double[][] d)

• toString

  public static String toString(double[] d)

• toString

  public static String toString(BigDecimal[][] d)

• toString

  public static String toString(BigDecimal[] d)

• solve

  public static void solve(double[][] coefficients)

  Given a matrix of variable coefficients for a linear system of equations, this will solve for each variable.

  For example, if you have the three equations:
  2x + y + z = 1
  6x + 2y + z = -1
  -2x + 2y + z = 7

  You can call:
double[][] coeffs = { { 2, 1, 1, 1},
{ 6, 2, 1, -1},
{ -2, 2, 1, 7} };
Equations.solve(coeffs,true);

  Then this method will simplify the matrix to:
{ { 1, 0, 0, -1},
{ 0, 1, 0, 2},
{ 0, 0, 1, 1} }

  This indicates that:
  1*x+0*y+0*z = -1
  0*x+1*y+0*z = 2
  0*x+0*y+1*z = 1

  This method uses Gaussian Elimination and back substitution.

  Note that due to the limits of double-precision, some safeguards were built-in that may round values less than .00000001 to zero. If you need better precision, you may have to copy and paste the algorithm in this code and use a more precise number format.

  Parameters:

  coefficients - the matrix of coefficients. It must be N x (N+1) units in size.

  Throws:

  IllegalArgumentException - if it is impossible to solve for each variable. In this case an exception is thrown, and no guarantee is made regarding the final state of the coefficients matrix.

  Also an exception may be thrown if the matrix is not correctly sized.

• solve

  public static void solve(BigDecimal[][] coefficients)

  Given a matrix of variable coefficients for a linear system of equations, this will solve for each variable.

  For example, if you have the three equations:
  2x + y + z = 1
  6x + 2y + z = -1
  -2x + 2y + z = 7

  You can call:
double[][] coeffs = { { 2, 1, 1, 1},
{ 6, 2, 1, -1},
{ -2, 2, 1, 7} };
Equations.solve(coeffs,true);

  Then this method will simplify the matrix to:
{ { 1, 0, 0, -1},
{ 0, 1, 0, 2},
{ 0, 0, 1, 1} }

  This indicates that:
  1*x+0*y+0*z = -1
  0*x+1*y+0*z = 2
  0*x+0*y+1*z = 1

  This method uses Gaussian Elimination and back substitution.

  Note that due to the limits of double-precision, some safeguards were built-in that may round values less than .00000001 to zero. If you need better precision, you may have to copy and paste the algorithm in this code and use a more precise number format.

  Parameters:

  coefficients - the matrix of coefficients. It must be N x (N+1) units in size.

  Throws:

  IllegalArgumentException - if it is impossible to solve for each variable. In this case an exception is thrown, and no guarantee is made regarding the final state of the coefficients matrix.

  Also an exception may be thrown if the matrix is not correctly sized.

• solve

  public static void solve(double[][] coefficients,
                           boolean sort)

  Given a matrix of variable coefficients for a linear system of equations, this will solve for each variable.

  For example, if you have the three equations:
  2x + y + z = 1
  6x + 2y + z = -1
  -2x + 2y + z = 7

  You can call:
double[][] coeffs = { { 2, 1, 1, 1},
{ 6, 2, 1, -1},
{ -2, 2, 1, 7} };
Equations.solve(coeffs,true);

  Then this method will simplify the matrix to:
{ { 1, 0, 0, -1},
{ 0, 1, 0, 2},
{ 0, 0, 1, 1} }

  This indicates that:
  1*x+0*y+0*z = -1
  0*x+1*y+0*z = 2
  0*x+0*y+1*z = 1

  This method uses Gaussian Elimination and back substitution.

  Note that due to the limits of double-precision, some safeguards were built-in that may round values less than .00000001 to zero. If you need better precision, you may have to copy and paste the algorithm in this code and use a more precise number format.

  Parameters:

  coefficients - the matrix of coefficients. It must be N x (N+1) units in size.

  sort - If this is true, then you're guaranteed for your final solution to be sorted such that the 1's form a diagonal line from [0,0] to [N,N]. If this is false, then the solution may not form a diagonal line of 1's.

  (If there are no zeroes in the matrix, the diagonal line will be there by default, but if zeroes are present then some rows may have to be skipped and the normal order is disrupted.)

  The sort is performed by calling Arrays.sort().

  Throws:

  IllegalArgumentException - if it is impossible to solve for each variable. In this case an exception is thrown, and no guarantee is made regarding the final state of the coefficients matrix.

  Also an exception may be thrown if the matrix is not correctly sized.

• solve

  public static void solve(BigDecimal[][] coefficients,
                           boolean sort)

  Given a matrix of variable coefficients for a linear system of equations, this will solve for each variable.

  For example, if you have the three equations:
  2x + y + z = 1
  6x + 2y + z = -1
  -2x + 2y + z = 7

  You can call:
double[][] coeffs = { { 2, 1, 1, 1},
{ 6, 2, 1, -1},
{ -2, 2, 1, 7} };
Equations.solve(coeffs,true);

  Then this method will simplify the matrix to:
{ { 1, 0, 0, -1},
{ 0, 1, 0, 2},
{ 0, 0, 1, 1} }

  This indicates that:
  1*x+0*y+0*z = -1
  0*x+1*y+0*z = 2
  0*x+0*y+1*z = 1

  This method uses Gaussian Elimination and back substitution.

  Note that due to the limits of double-precision, some safeguards were built-in that may round values less than .00000001 to zero. If you need better precision, you may have to copy and paste the algorithm in this code and use a more precise number format.

  Parameters:

  coefficients - the matrix of coefficients. It must be N x (N+1) units in size.

  sort - If this is true, then you're guaranteed for your final solution to be sorted such that the 1's form a diagonal line from [0,0] to [N,N]. If this is false, then the solution may not form a diagonal line of 1's.

  (If there are no zeroes in the matrix, the diagonal line will be there by default, but if zeroes are present then some rows may have to be skipped and the normal order is disrupted.)

  The sort is performed by calling Arrays.sort().

  Throws:

  IllegalArgumentException - if it is impossible to solve for each variable. In this case an exception is thrown, and no guarantee is made regarding the final state of the coefficients matrix.

  Also an exception may be thrown if the matrix is not correctly sized.