Arguments

DL

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

D

(input) REAL or COMPLEX array, shape $(:)$ with $size({\bf D}) = n$.
The diagonal of $A$.

DU

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

B

(input/output) 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 $X$.

DLF

Optional (input or output) REAL or COMPLEX array, shape $(:)$ with size(DLF)$= n-1$.
If FACT = 'F' then ${\bf DLF}$ is an input argument that contains the multipliers that define the matrix $L$ from the $LU$ factorization of $A$.
If FACT = 'N' then DLF is an output argument that contains the multipliers that define the matrix $L$ from the $LU$ factorization of $A$.

DF

Optional (input or output) REAL or COMPLEX array, shape $(:)$ with size(DF)$= n$.
If FACT = 'F' then DF is an input argument that contains the diagonal of the matrix $U$.
If FACT = 'N' then DF is an output argument that contains the diagonal of the matrix $U$.

DUF

Optional (input or output) REAL or COMPLEX array, shape $(:)$ with size(DUF) $= n-1$.
If FACT = 'F' then DUF is an input argument that contains the first superdiagonal of $U$.
If FACT = 'N' then DUF is an output argument that contains the first superdiagonal of $U$.

DU2

Optional (input or output) REAL or COMPLEX array, shape $(:)$ with $size({\bf DU2}) = n-2$.
If FACT = 'F', then DU2 is an input argument that contains the second superdiagonal of $U$.
If FACT = 'N', then DU2 is an output argument that contains the second superdiagonal of $U$.

IPIV

Optional (input or output) INTEGER array, shape $(:)$ with $size({\bf IPIV})=n$.
If FACT = 'F' then IPIV is an input argument that contains the pivot indices from the $L\,U$ factorization of $A$.
If FACT = 'N', then IPIV is an output argument that contains the pivot indices from the $LU$ factorization of $A$; row i of the matrix was interchanged with row ${\bf IPIV}_i$. ${\bf IPIV}_i$ will always be either $i$ or $i+1$; ${\bf IPIV}_i = i$ indicates a row interchange was not required.

FACT

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


Default value: 'N'.

TRANS

Optional (input) CHARACTER(LEN=1).
Specifies the form of the system of equations:


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 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 matrix $A$. If 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].