| solve {base} | R Documentation |
Solve a System of Equations
Description
This generic function solves the equation a %*% x = b for x,
where b can be either a vector or a matrix.
Usage
solve(a, b, ...)
## Default S3 method:
solve(a, b, tol, LINPACK = FALSE, ...)
Arguments
a |
a square numeric or complex matrix containing the coefficients of the linear system. Logical matrices are coerced to numeric. |
b |
a numeric or complex vector or matrix giving the right-hand
side(s) of the linear system. If missing, |
tol |
the tolerance for detecting linear dependencies in the
columns of |
LINPACK |
logical. Defunct and an error. |
... |
further arguments passed to or from other methods. |
Details
a or b can be complex, but this uses double complex
arithmetic which might not be available on all platforms.
The row and column names of the result are taken from the column names
of a and of b respectively. If b is missing the
column names of the result are the row names of a. No check is
made that the column names of a match the row names of b.
For back-compatibility a can be a (real) QR decomposition,
although qr.solve should be called in that case.
qr.solve can handle non-square systems.
Unsuccessful results from the underlying LAPACK code will result in an error giving a positive error code: these can only be interpreted by detailed study of the FORTRAN code.
What happens if a and/or b contain missing, NaN
or infinite values is platform-dependent, including on the version of
LAPACK is in use.
tol is a tolerance for the (estimated 1-norm)
‘reciprocal condition number’: the check is skipped if
tol <= 0.
For historical reasons, the default method accepts a as an
object of class "qr" (with a warning) and passes it on to
solve.qr.
Source
The default method is an interface to the LAPACK routines DGESV
and ZGESV.
LAPACK is from https://netlib.org/lapack/.
References
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammerling S, McKenney A, Sorensen D (1999). LAPACK Users' Guide, series Software, Environments, and Tools, Third edition. Society for Industrial and Applied Mathematics, Philadelphia, PA. ISBN 9780898714470. doi:10.1137/1.9781611971811. https://netlib.org/lapack/lug/lapack_lug.html.
Becker RA, Chambers JM, Wilks AR (1988). The New S Language. Chapman and Hall/CRC, London.
See Also
solve.qr for the qr method,
chol2inv for inverting from the Cholesky factor
backsolve, qr.solve.
Examples
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, `+`) }
h8 <- hilbert(8); h8
sh8 <- solve(h8)
round(sh8 %*% h8, 3)
A <- hilbert(4)
A[] <- as.complex(A)
## might not be supported on all platforms
try(solve(A))