- LeastSquaresSolution
- LeastSquaresSolutionDC
- LeastSquaresSolutionSVD
- LeastSquaresSolutionWY
- LeastSquaresSolutionsQRPivot
- LeastSquaresSolutionQRTallSkinny
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(
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Computing for type matrix<float>
bool matrixf::LeastSquaresSolution(
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Computing for type matrix<complex>
bool matrixc::LeastSquaresSolution(
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Computing for type matrix<complexf>
bool matrixcf::LeastSquaresSolution(
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Parameters
trans
[in] ENUM_EQUATIONS_FORM enumeration value which specifies the form of the system of equations.
B
[in] Matrix B whose columns are the right-hand sides for the systems of equations. Vector B contains one column of right-hand side.
X
[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.