Arguments

A

(input/output) REAL or COMPLEX square array, shape $(:,:)$.
On entry, the matrix $A$ or its equilibration:
If UPLO = 'U', then the upper triangular part of A contains the upper triangular part of (the equilibrated) $A$, and the strictly lower triangular part of A is not referenced.
If UPLO = 'L', then the lower triangular part of A contains the lower triangular part of (the equilibrated) $A$, and the strictly upper triangular part of A is not referenced.
If FACT = 'F' and EQUED = 'Y', then $A$ has been equilibrated by the scaling factors in S during a previous call to LA_POSVX.
On exit, if ${\bf FACT} =$ 'E', then the equilibrated version of $A$ is stored in A; otherwise, ${\bf A}$ is unchanged.

B

(input/output) REAL or COMPLEX array, shape $(:,:)$ with $size({\bf B},1) = size({\bf A},1)$ or shape $(:)$ with $size({\bf B})=size({\bf A},1)$.
On entry, the matrix $B$.
On exit, the scaled version of $B$ if the system has been equilibrated; otherwise, ${\bf B}$ is unchanged.

X

(output) REAL or COMPLEX array, shape $(:,:)$ with $size({\bf X},1) = size({\bf A},1)$ and $size({\bf X},2) = size({\bf B},2)$, or shape $(:)$ with $size({\bf X}) = size({\bf A},1)$.
The solution matrix $X$.

UPLO

Optional (input) CHARACTER(LEN=1).


Default value: 'U'.

AF

Optional (input or output) REAL or COMPLEX array, shape $(:,:)$ with the same size as A.
If FACT $=$ 'F' then AF is an input argument that contains the factor $U$ or $L$ from the Cholesky factorization of (the equilibrated) $A$, in the same storage format as $A$, returned by a previous call to LA_POSVX
If FACT $\neq$ 'F' then AF is an output argument that contains the factor $U$ or $L$ from the Cholesky factorization of (the equilibrated) $A$ in the same storage format as $A$.

FACT

Optional (input) CHARACTER(LEN=1).
Specifies whether the factored form of the matrix $A$ is supplied on entry, and, if not, whether $A$ should be equilibrated before it is factored.


Default value: 'N'.

EQUED

Optional (input or output) CHARACTER(LEN=1).
Specifies the form of equilibration that was done.
${\bf EQUED}$ is an input argument if ${\bf FACT} =$ 'F', otherwise it is an output argument:


Default value: 'N'.

S

Optional (input or output) REAL array, shape $(:)$ with $size(S) = size({\bf A},1)$.
The scaling factors for $A$.
S is an input argument if FACT = 'F' and EQUED = 'Y'.
S is an output argument if FACT = 'E' and EQUED = 'Y'.

FERR

Optional (output) REAL array of shape $(:)$, with $size({\bf FERR})=size({\bf X},2)$, or REAL scalar.
The estimated forward error bound for each solution vector $X_j$ (the $j^{th}$ column of the solution matrix $X$). If $XTRUE$ is the true solution corresponding to $X_j$, ${\bf FERR}_j$ is an estimated upper bound for the magnitude of the largest element in ($X_j - XTRUE)$ divided by the magnitude of the largest element in $X_j$. The estimate is as reliable as the estimate for ${\bf RCOND}$, and is almost always a slight overestimate of the true error.

BERR

Optional (output) REAL array of shape $(:)$, with $size({\bf BERR})=size({\bf X},2)$, or REAL scalar.
The componentwise relative backward error of each solution vector $X_j$ (i.e., the smallest relative change in any element of $A$ or $B$ that makes $X_j$ an exact solution).

RCOND

Optional (output) REAL
The estimate of the reciprocal condition number of (the equilibrated) $A$. If ${\bf RCOND}$ is less than the machine precision, the matrix is singular to working precision. This condition is indicated by a return code of ${\bf INFO} > 0$.

INFO

Optional (output) INTEGER


If INFO is not present and an error occurs, then the program is terminated with an error message.

References: [1] and [17,9,20,21].