## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?la_gbrcond

Estimates the Skeel condition number for a general banded matrix.

## Syntax

Include Files
• mkl.fi
Description
The function estimates the Skeel condition number of
op(
A
) * op2(
C
)
where
the
cmode
parameter determines
op2
as follows:
cmode
Value
op2(C)
1
C
0
I
-1
inv(
C
)
The Skeel condition number
cond(
A
) = norminf(|inv(
A
)||
A
|)
is computed by computing scaling factors
R
such that
diag(
R
)*
A
*op2(
C
)
is row equilibrated and by computing the standard infinity-norm condition number.
Input Parameters
trans
CHARACTER*1
. Must be
'N'
or
'T'
or
'C'
.
Specifies the form of the system of equations:
If
trans
=
'N'
, the system has the form
A*X
=
B
.
If
trans
=
'T'
, the system has the form
A
T
*
X
=
B
.
If
trans
=
'C'
, the system has the form
A
H
*
X
=
B
.
n
INTEGER
. The number of linear equations, that is, the order of the matrix
A
;
n
0.
kl
INTEGER
. The number of subdiagonals within the band of
A
;
kl
0.
ku
INTEGER
. The number of superdiagonals within the band of
A
;
ku
0.
ab
,
afb
, ,
REAL
for
sla_gbrcond
DOUBLE PRECISION
for
dla_gbrcond
Arrays:
ab
(
ldab
,*) contains the original band matrix
A
stored in rows from 1 to
kl
+
ku
+ 1. The
j
-th column of
A
is stored in the
j
-th column of the array
ab
as follows:
ab
(
ku
+1+
i
-
j
,
j
) = A(
i
,
j
)
for
max(1,
j
-
ku
)
i
min(
n
,
j
+
kl
)
afb
(
ldafb
,*) contains details of the LU factorization of the band matrix
A
, as returned by
?gbtrf
.
U
is stored as an upper triangular band matrix with
kl
+
ku
superdiagonals in rows 1 to
kl
+
ku
+1
, and the multipliers used during the factorization are stored in rows
kl
+
ku
+2
to
2*
kl
+
ku
+1
.
c
,
DIMENSION