Arguments

AP

(input) REAL or COMPLEX array, shape $(:)$ with $size(AP) = n(n+1)/2$, where $n$ is the order of $A$.
On entry, the upper or lower triangle of matrix $A$ in packed storage. The elements are stored columnwise as follows:

$$\begin{array}{c\vert c\vert c} A_{i,j} & i,j & {\bf UPLO} ... ... \leq i \leq n \end{array} & \mbox{ 'L'} \\ \hline \end{array}$$

B

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

X

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

UPLO

Optional (input) CHARACTER(LEN=1).


Default value: 'U'.

AFP

Optional (input or output) REAL or COMPLEX array, shape $(:,:)$ with the same size as AP.
If FACT = 'F', then AFP 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_SPSVX or LA_HPSVX and stored as a packed triangular matrix in the same storage format as $A$.
If FACT = 'N', then AFP 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 $A$, stored as a packed triangular matrix in the same storage format as $A$.

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 and on exit contains details of the interchanges and the block structure of $D$ (as described above).

FACT

Optional (input) CHARACTER(LEN=1).
Specifies whether the factored form of $A$ 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].