- AB
- (
*input/output*)**REAL**or**COMPLEX**array, shape with and , where is the number of superdiagonals or subdiagonals and is the order of .

On entry, the upper (if**UPLO**= 'U') or lower (if**UPLO**= 'L') triangle of matrix , or its equilibration, in band storage. The diagonals of are stored in the rows of**AB**so that the column of is stored in the column of**AB**as follows:

On exit, if 'E', then the equilibrated version of is stored in**AB**; otherwise, is unchanged. - B
- (
*input/output*)**REAL**or**COMPLEX**array, shape with or shape with .

On entry, the matrix .

On exit, the scaled version of if the system has been equilibrated; otherwise, is unchanged. - X
- (
*output*)**REAL**or**COMPLEX**array, shape with and , or shape with .

The solution matrix . - UPLO
*Optional*(*input*)**CHARACTER(LEN=1)**.

Default value: 'U'.- AFB
*Optional*(*input*or*output*)**REAL**or**COMPLEX**array, shape with the same size as**AB**.

If**FACT**'F' then**AFB**is an*input*argument that contains the factor or from the Cholesky factorization of (the equilibrated) , in the same storage format as , returned by a previous call to**LA_PBSVX**.

If**FACT**'F' then**AFB**is an*output*argument that contains the factor or from the Cholesky factorization of (the equilibrated) in the same storage format as .- FACT
*Optional*(*input*)**CHARACTER(LEN=1)**.

Specifies whether the factored form of the matrix is supplied on entry, and if not, whether 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.

is an*input*argument if 'F', otherwise it is an*output*argument

Default value: 'N'.- S
*Optional*(*input or output)***REAL**array, shape with .

The scaling factors for .**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 , or**REAL**scalar.

The estimated forward error bound for each solution vector (the column of the solution matrix ). If is the true solution corresponding to , is an estimated upper bound for the magnitude of the largest element in ( divided by the magnitude of the largest element in . The estimate is as reliable as the estimate for , and is almost always a slight overestimate of the true error.- BERR
*Optional*(*output*)**REAL**array of shape , with , or**REAL**scalar.

The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any element of or that makes an exact solution).- RCOND
*Optional*(*output)***REAL**

The estimate of the reciprocal condition number of (the equilibrated) . If is less than the machine precision, the matrix is singular to working precision. This condition is indicated by a return code of .- 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].