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## Arguments

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].

Next: Example (from Program LA_GBSVX_EXAMPLE) Up: General Linear Systems Previous: Description   Contents   Index
Susan Blackford 2001-08-19