Arguments

D

(input) REAL array, shape $(:)$ with $size({\bf D}) = n$, where $n$ is the order of $A$.
The diagonal of $A$.

E

(input) REAL or COMPLEX array, shape $(:)$ with $size({\bf E}) = n-1$.
The subdiagonal of $A$.

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 $X$.

DF

Optional (input or output) REAL array, shape $(:)$ with the same size as D.
If FACT = 'F', then DF is an input argument that contains the diagonal of $D$ from the $L D L^H$ factorization of $A$.
If ${\bf FACT} =$ 'N', then DF is an output argument that contains the diagonal of $D$ from the $L D L^H$ factorization of $A$.

EF

Optional (input or output) REAL or COMPLEX array, shape $(:)$ with the same size as E.
If FACT = 'F', then EF is an input argument that contains the subdiagonal of $L$ from the $L D L^H$ factorization of $A$.
If FACT = 'N', then EF is an output argument that contains the subdiagonal of $L$ from the $L D L^H$ factorization of $A$.

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 $X_j$.

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 matrix $A$. 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].