Programmer Guide/Command Reference/EVAL/rleqs

These functions implements an interface for the LAPACK functions DGESV, ZGESV, DGELS and ZGELS.

Usage

rleqs(A, B {, alg})	... uses functions DGESV and DGELS;	arguments A, B and result X are real
cleqs(A, B {, alg})	... uses functions ZGESV and ZGELS;	arguments A, B and result X are complex

A

left side MxN matrix x

B

right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions)

alg

select a LAPACK algorithm to be used

alg=0	...	use DGESV if M=N and DGELS otherwise
alg=1	...	use always DGESV, M must be equal to N
alg=2	...	use always DGELS

Description

The function DGESV (ZGESV) solves a linear equation system.

• A[M x M] * X[M x NRHS] = B[M x NRHS]

The function DGELS (ZGELS) can be used to find the least squares solution of an overdetermined system (M>=N) or the minimum norm solution of an underdetermined system (M<N).

• M>=N: minimize || B[M x NRHS] - A[M x N] * X[M x NRHS] ||
• M<N: A[M x M] * X[M x NRHS] = B[M x NRHS]

A detailed description of the LAPACK functions can be found at www.netlib.org.

Result

The result X has the same type as the argument B and contains one solution per column.

See also

rpolyreg, complex arithmetic, svd

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