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. and ten others (1999)
*LAPACK Users' Guide*. Third Edition. SIAM.

Available on-line at
https://netlib.org/lapack/lug/lapack_lug.html.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

### 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))
```

*base*version 4.4.1 Index]