- AB
- (
*input/output*)**REAL**or**COMPLEX**rectangular array, shape with and , where and are, respectively, the numbers of subdiagonals and superdiagonals in the band of , and is the order of .

On entry, the matrix or its equilibration in band storage. The diagonals of are stored in rows to of**AB**, so that the column of is stored in the column of**AB**as follows:

The remaining elements in need not be set.

If 'F' and 'N' then has been equilibrated by the scaling factors in and/or during the previous call to**LA_GBSVX**.

On exit, if 'E', 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 . - KL
*Optional*(*input*)**INTEGER**.

The number of subdiagonals in the band of ().

The number of superdiagonals in the band is given by .

Default value: .- AFB
*Optional*(*input*or*output*)**REAL**or**COMPLEX**rectangular array, shape with and

If = 'F' then**AFB**is an*input*argument that contains the details of the factorization of (the equilibrated) returned by a previous call to**LA_GBSVX**.

If 'F' then is an*output*argument that contains the details of the factorization of (the equilibrated) . is an upper triangular band matrix with diagonals. These are stored in the first rows of . The multipliers that arise during the factorization are stored in the remaining rows.- IPIV
*Optional*(*input*or*output*)**INTEGER**array, shape with .

If = 'F' then is an*input*argument that contains the pivot indices from the factorization of (the equilibrated) , returned by a previous call to**LA_GBSVX**.

If 'F' then is an*output*argument that contains the pivot indices from the factorization of (the equilibrated) .- FACT
*Optional*(*input*)**CHARACTER(LEN=1)**.

Specifies whether the factored form of the matrix is supplied on entry, and, if not, whether the matrix should be equilibrated before it is factored.

Default value: 'N'.- TRANS
*Optional*(*input*)**CHARACTER(LEN=1)**.

Specifies the form of the system of equations:

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'.- R
*Optional*(*input*or*output*)**REAL**array, shape with .

The row scale factors for .**R**is an*input*argument if**FACT**= 'F' and 'R' or 'B'.**R**is an*output*argument if**FACT**= 'E' and 'R' or 'B'.- C
*Optional*(*input*or*output*)**REAL**array, shape with .

The column scale factors for .

**C**is an*input*argument if**FACT**= 'F' and 'C' or 'B'.

**C**is an*output*argument if**FACT**= 'E' and 'C' or 'B'.- FERR
*Optional*(*output*)**REAL**array of shape , with , or**REAL**scalar.

The estimated forward error bound for each solution vector (the -th 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**RCOND**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**RCOND**is less than the machine precision, the matrix is singular to working precision. This condition is indicated by a return code of**INFO**.- RPVGRW
*Optional*(*output*)**REAL**.

The reciprocal pivot growth factor . If**RPVGRW**is much less than , then the stability of the factorization of the (equilibrated) matrix could be poor. This also means that the solution , condition estimator**RCOND**, and forward error bound could be unreliable. If the factorization fails with , then**RPVGRW**contains the reciprocal pivot growth factor for the leading**INFO**columns of .- INFO
*Optional*(*output*)**INTEGER**

If is not present and an error occurs, then the program is terminated with an error message.

**References**: [1] and [17,9,20,21].