Programmer Guide/Command Reference/EVAL/rleqs: Difference between revisions
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{{DISPLAYTITLE:rleqs, cleqs}} | {{DISPLAYTITLE:rleqs, cleqs}} | ||
These functions implements an interface for the LAPACK functions DGESV, ZGESV, DGELS and ZGELS. | These functions implements an interface for the [[http://www.netlib.org/lapack|LAPACK]] functions DGESV, ZGESV, DGELS and ZGELS. | ||
;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>: | ;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>: | ||
:;<var>A</var>: left side MxN matrix ''x'' | :;<var>A</var>: left side MxN matrix ''x'' | ||
:;<var>B</var>: right side vector or | :;<var>B</var>: right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions) | ||
:;<var>alg</var>: select a LAPACK algorithm to be used | :;<var>alg</var>: select a LAPACK algorithm to be used | ||
:::{|class="keinrahmen" | :::{|class="keinrahmen" | ||
| Line 12: | Line 12: | ||
|''alg''='''2''' ||... || use always DGELS | |''alg''='''2''' ||... || use always DGELS | ||
|} | |} | ||
;Description: ... | ;Description: | ||
;Result: | :The function DGESV (ZGESV) solves a linear equation system. | ||
::*<code>''A''[M x M] * ''X''[M x NRHS] = ''B''[M x NRHS]</code> | |||
:The function DGELS (ZGELS) can be used to find the least solution of an overdetermined system (M>=N) or the minimum norm solution of an underdetermined system (M<N). | |||
::*<code>'''M>=N:''' minimize || ''B[M x NRHS] - ''A''[M x N] * ''X''[M x NRHS] ||</code> | |||
::*<code>'''M<N:''' ''A''[M x M] * ''X''[M x NRHS] = ''B''[M x NRHS]</code> | |||
:A detailed description of the functions can be found here: [[http://www.netlib.org/lapack]] | |||
;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column. | |||
Revision as of 07:08, 13 April 2011
These functions implements an interface for the [[1]] functions DGESV, ZGESV, DGELS and ZGELS.
- Usage
rleqs(A, B {, alg}):- 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 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 functions can be found here: [[2]]
- Result
- The result X has the same type as the argument B and contains one solution per column.
- Notes
-
- The function
cleqs(A, B {, alg})has the same arguments and result asrleqs, but the vectors/matrices A, B and X are complex. rleqscalls the LAPACK functions DGESV and DGELS, whilecleqscalls ZGESV and ZGELS
- The function
- See also
- rpolyreg
