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Arguments

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:  and [17,9,20,21].

Subsections     Next: Example (from Program LA_PBSVX_EXAMPLE) Up: Symmetric/Hermitian Positive Definite Linear Previous: Description   Contents   Index
Susan Blackford 2001-08-19