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 | 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: | ||
:{|class="keinrahmen" | |||
|<code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code> | |||
|... uses functions DGESV and DGELS; | |||
|arguments ''A'', ''B'' and result ''X'' are real | |||
|- | |||
|<code>cleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code> | |||
|... uses functions ZGESV and ZGELS; | |||
|arguments ''A'', ''B'' and result ''X'' are complex | |||
|} | |||
:;<var>A</var>: left side MxN matrix ''x'' | :;<var>A</var>: left side MxN matrix ''x'' | ||
:;<var>B</var>: right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions) | :;<var>B</var>: right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions) | ||
| Line 15: | Line 24: | ||
:The function DGESV (ZGESV) solves a linear equation system. | :The function DGESV (ZGESV) solves a linear equation system. | ||
::*<code>''A''[M x M] * ''X''[M x NRHS] = ''B''[M x NRHS]</code> | ::*<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 | :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). | ||
::*<code>'''M | ::*<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> | ::*<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 | :A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org]. | ||
;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column. | ;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column. | ||
;See also: [[../rpolyreg|rpolyreg]], [[../complex arithmetic|complex arithmetic]], [[../svd|svd]] | |||
[[../#Functions|<function list>]] | |||
Latest revision as of 19:08, 21 April 2011
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
