Arguments

A

(input) REAL or COMPLEX square array, shape $(:,:)$.
The symmetric or Hermitian matrix $A$.
If UPLO = 'U', the upper triangular part of A contains the upper triangular part of the matrix $A$, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the lower triangular part of A contains the lower triangular part of the matrix $A$, and the strictly upper triangular part of A is not referenced.

B

(input) REAL or COMPLEX array, shape $(:,:)$ with $size({\bf B},1) = size({\bf A},1)$ or shape $(:)$ with $size({\bf B})=size({\bf A},1)$.
The matrix $B$.

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 block diagonal matrix $D$ and the multipliers used to obtain the factor $L$ or $U$ from the factorization of $A$, returned by a previous call to LA_SYSVX or LA_HESVX.
If FACT = 'N', then AF is an output argument that contains the block diagonal matrix $D$ and the multipliers used to obtain the factor $L$ or $U$ from the factorization of $A$.

IPIV

Optional (input or output) INTEGER array, shape $(:)$ with $size({\bf IPIV})=size({\bf A},1)$.
If FACT = 'F', then ${\bf IPIV}$ is an input argument that contains details of the row and column interchanges and the block structure of $D$.


If FACT = 'N', then IPIV is an output argument that contains details of the row and column interchanges and the block structure of $D$; as described above.

FACT

Optional (input) CHARACTER(LEN=1).
Specifies whether the factored form of the matrix $A$ has been supplied on entry.


Default value: 'N'.

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 $A$. 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

(output) INTEGER


If ${\bf INFO}$ is not present and an error occurs, then the program is terminated with an error message.

References: [1] and [17,9,20,21].