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MQL5 リファレンス行列とベクトルのメソッドOpenBLASLeast SquaresLeastSquaresGaussMarkov2 

LeastSquaresGaussMarkov2

Solves a general Gauss-Markov linear model (GLM) problem

 minimize || y ||_2   subject to   d = A*x + B*y
             x

where A is an n-by-m matrix, B is an n-by-p matrix, and d is a given n-vector. It is assumed that m <= n <= m+p, and rank(A) = m and rank( A B) = n.

Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by

 A = Q*(R),   B = Q*T*Z.
       (0)

In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem

 minimize || inv(B)*(d-A*x) ||_2
             x

where inv(B) denotes the inverse of B. LAPACK function GGGLM.

 

Computing for type matrix<double>

bool  matrix::LeastSquaresGaussMarkov2(
  matrix&           B,           // second matrix B
  matrix&           D,           // right hand side matrix D
  matrix&             X,           // solution matrix X
  matrix&             Y           // solution matrix Y
  );
 
bool  matrix::LeastSquaresGaussMarkov2(
  matrix&           B,           // second matrix B
  vector&           D,           // right hand side vector D
  vector&             X,           // solution vector X
  vector&             Y           // solution vector Y
  );

Computing for type matrix<float>

bool  matrixf::LeastSquaresGaussMarkov2(
  matrixf&         B,           // second matrix B
  matrixf&         D,           // right hand side matrix D
  matrixf&           X,           // solution matrix X
  matrixf&           Y           // solution matrix Y
  );
 
bool  matrixf::LeastSquaresGaussMarkov2(
  matrixf&         B,           // second matrix B
  vectorf&           D,           // right hand side vector D
  vectorf&           X,           // solution vector X
  vectorf&           Y           // solution vector Y
  );

Computing for type matrix<complex>

bool  matrixc::LeastSquaresGaussMarkov2(
  matrixc&         B,           // second matrix B
  matrixc&         D,           // right hand side matrix D
  matrixc&           X,           // solution matrix X
  matrixc&           Y           // solution matrix Y
  );
 
bool  matrixc::LeastSquaresGaussMarkov2(
  matrixc&         B,           // second matrix B
  vectorc&         D,           // right hand side vector D
  vectorc&           X,           // solution vector X
  vectorc&           Y           // solution vector Y
  );

Computing for type matrix<complexf>

bool  matrixcf::LeastSquaresGaussMarkov2(
  matrixcf&         B,           // second matrix B
  matrixcf&         D,           // right hand side matrix D
  matrixcf&           X,           // solution matrix X
  matrixcf&           Y           // solution matrix Y
  );
 
bool  matrixcf::LeastSquaresGaussMarkov2(
  matrixcf&         B,           // second matrix B
  vectorcf&         D,           // right hand side vector D
  vectorcf&           X,           // solution vector X
  vectorcf&           Y           // solution vector Y
  );

Parameters

B

[in]  Second matrix B of the GLM problem.

D

[in]  Matrix D whose column is the right-hand side for the system of equations, matix D must contain only one column. Vector D contains one column of right-hand side.

X

[out]  Matrix or vector X with solutions of GLM problem.

Y

[out]  Matrix or vector Y with solutions of GLM problem.

 

Return Value

Return true if successful, otherwise false in case of an error.

Note

Output vector X has size m, and output vector Y has size p. For matrix overloads, X has m rows and Y has p rows, with the same number of columns as D.