Contents

# ?tbcon

Estimates the reciprocal of the condition number of a triangular band matrix.

## Syntax

Include Files
• mkl.h
Description
The routine estimates the reciprocal of the condition number of a triangular band matrix
A
in either the 1-norm or infinity-norm:
κ
1
(
A
) =||
A
||
1
||
A
-1
||
1
=
κ
(
A
T
) =
κ
(
A
H
)
κ
(
A
) =||
A
||
||
A
-1
||
=
κ
1
(
A
T
) =
κ
1
(
A
H
) .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
norm
Must be
'1'
or
'O'
or
'I'
.
If
norm
=
'1'
or
'O'
, then the routine estimates the condition number of matrix
A
in 1-norm.
If
norm
=
'I'
, then the routine estimates the condition number of matrix
A
in infinity-norm.
uplo
Must be
'U'
or
'L'
. Indicates whether
A
is upper or lower triangular:
If
uplo
=
'U'
, the array
ap
stores the upper triangle of
A
in packed form.
If
uplo
=
'L'
, the array
ap
stores the lower triangle of
A
in packed form.
diag
Must be
'N'
or
'U'
.
If
diag
=
'N'
, then
A
is not a unit triangular matrix.
If
diag
=
'U'
, then
A
is unit triangular: diagonal elements are assumed to be 1 and not referenced in the array
ab
.
n
The order of the matrix
A
;
n
0.
kd
The number of superdiagonals or subdiagonals in the matrix
A
;
kd
0.
ab
The array
ab
of size max(1,
ldab
*
n
)
contains the band matrix
A
.
ldab
The leading dimension of the array
ab
. (
ldab
kd
+1).
Output Parameters
rcond
An estimate of the reciprocal of the condition number. The routine sets
rcond
=0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytime
rcond
is small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
had an illegal value.
Application Notes
The computed
rcond
is never less than
r
(the reciprocal of the true condition number) and in practice is nearly always less than 10
r
. A call to this routine involves solving a number of systems of linear equations
A
*
x
=
b
; the number is usually 4 or 5 and never more than 11. Each solution requires approximately
2*
n
(
kd
+ 1)
floating-point operations for real flavors and
8*
n
(
kd
+ 1)
operations for complex flavors.

#### Product and Performance Information

1

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Notice revision #20110804