ssolve | R Documentation |

Covariance matrices of variables with very different orders of magnitude can have very large ratios between their greatest and their least eigenvalues, causing them to appear to the algorithms to be near-singular when they are actually very much SPD. These functions first scale the matrix's rows and/or columns by its diagonal elements and then undo the scaling on the result.

```
ssolve(a, b, ..., snnd = TRUE)
sginv(X, ..., snnd = TRUE)
ginv_eigen(X, tol = sqrt(.Machine$double.eps), ...)
xTAx_seigen(x, A, tol = sqrt(.Machine$double.eps), ...)
srcond(x, ..., snnd = TRUE)
snearPD(x, ...)
xTAx_ssolve(x, A, ...)
xTAx_qrssolve(x, A, tol = 1e-07, ...)
sandwich_ssolve(A, B, ...)
```

`snnd` |
assume that the matrix is symmetric non-negative definite (SNND). This typically entails scaling that converts covariance to correlation and use of eigendecomposition rather than singular-value decomposition. If it's "obvious" that the matrix is not SSND (e.g., negative diagonal elements), an error is raised. |

`x` , `a` , `b` , `X` , `A` , `B` , `tol` , `...` |
corresponding arguments of the wrapped functions. |

`ginv_eigen()`

reimplements `MASS::ginv()`

but using
eigendecomposition rather than SVD; this means that it is only
suitable for symmetric matrices, but that detection of negative
eigenvalues is more robust.

`ssolve()`

, `sginv()`

, `sginv_eigen()`

, and `snearPD()`

wrap
`solve()`

, `MASS::ginv()`

, `ginv_eigen()`

, and `Matrix::nearPD()`

,
respectively. `srcond()`

returns the reciprocal condition number of
`rcond()`

net of the above scaling. `xTAx_ssolve()`

,
`xTAx_qrssolve()`

, `xTAx_seigen()`

, and `sandwich_ssolve()`

wrap
the corresponding statnet.common functions.

```
x <- rnorm(2, sd=c(1,1e12))
x <- c(x, sum(x))
A <- matrix(c(1, 0, 1,
0, 1e24, 1e24,
1, 1e24, 1e24), 3, 3)
stopifnot(all.equal(
xTAx_qrssolve(x,A),
structure(drop(x%*%sginv(A)%*%x), rank = 2L, nullity = 1L)
))
x <- rnorm(2, sd=c(1,1e12))
x <- c(x, rnorm(1, sd=1e12))
A <- matrix(c(1, 0, 1,
0, 1e24, 1e24,
1, 1e24, 1e24), 3, 3)
stopifnot(try(xTAx_qrssolve(x,A), silent=TRUE) ==
"Error in xTAx_qrssolve(x, A) : x is not in the span of A\n")
```

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