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

LeastSquaresSolution

Solves overdetermined or underdetermined real / complex linear systems involving an m-by-n matrix A, or its transpose / conjugate-transpose, using a QR or LQ factorization of A. It is assumed that A has full rank.

The following options are provided:

1. If trans = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||.

2. If trans = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.

3. If trans = 'T' and m >= n: find the minimum norm solution of an underdetermined system A**T * X = B.

4. If trans = 'T' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**T * X ||.

LAPACK function GELS.

Computing for type matrix<double>

bool matrix::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
matrix& B, // right hand side matrix B
matrix& X, // solution matrix X
matrix& residuals // matrix with residual sums of squares
);

bool matrix::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
vector& B, // right hand side vector B
vector& X, // solution vector X
vector& residuals // vector with residual sums of squares
);

Computing for type matrix<float>

bool matrixf::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
matrixf& B, // right hand side matrix B
matrixf& X, // solution matrix X
matrixf& residuals // matrix with residual sums of squares
);

bool matrixf::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
vectorf& B, // right hand side vector B
vectorf& X, // solution vector X
vectorf& residuals // vector with residual sums of squares
);

Computing for type matrix<complex>

bool matrixc::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
matrixc& B, // right hand side matrix B
matrixc& X, // solution matrix X
matrixc& residuals // matrix with residual sums of squares
);

bool matrixc::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
vectorc& B, // right hand side vector B
vectorc& X, // solution vector X
vectorc& residuals // vector with residual sums of squares
);

Computing for type matrix<complexf>

bool matrixcf::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
matrixcf& B, // right hand side matrix B
matrixcf& X, // solution matrix X
matrixcf& residuals // matrix with residual sums of squares
);

bool matrixcf::LeastSquaresSolution(
ENUM_EQUATIONS_FORM trans, // form of the system of equations
vectorcf& B, // right hand side vector B
vectorcf& X, // solution vector X
vectorcf& residuals // vector with residual sums of squares
);

Parameters

trans

[in] ENUM_EQUATIONS_FORM enumeration value which specifies the form of the system of equations.

[in] Matrix B whose columns are the right-hand sides for the systems of equations. Vector B contains one column of right-hand side.

[out] Matrix or vector X with solutions of linear least squares problem.

residuals

[out] Matrix or vector with the residual sum of squares for the solution in each column, given by the sum of squares of modulus of elements in that column. If trans='N' and m<=n or trans!='N' and m>=n, then residuals matrix (vector) is empty.

Return Value

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

Note

If trans='N'. Matrix B must be of size m-by-nrhs, where nrhs is number of right-hand side vectors, matrix X is of size n-by-nrhs. If m>=n, matrix X contains nrhs least squares solution vectors. If m<n, matrix X contains nrhs minimum norm solution vectors.

If trans!='N'. Matrix B must be of size n-by-nrhs, matrix X is of size m-by-nrhs. If m>=n, matrix X contains nrhs minimum norm solution vectors. If m<n, matrix X contains nrhs least squares solution vectors.

ENUM_EQUATIONS_FORM

An enumeration defining which form of the equations' system calculated.

ID	Description
EQUATIONSFORM_N	'N': the linear system involves A (No transpose)
EQUATIONSFORM_T	'T': the linear system involves A**T (Transpose)
EQUATIONSFORM_C	'C': the linear system involves A**H (Conjugate transpose)

In case of real matrices the value EQUATIONSFORM_C assumed as Transpose.

In case of complex matrices the value EQUATIONSFORM_T assumed as Conjugate transpose.

Least Squares

LeastSquaresSolutionDC