Contents

# ?hecon

Estimates the reciprocal of the condition number of a Hermitian matrix.

## Syntax

Include Files
• mkl.h
Description
The routine estimates the reciprocal of the condition number of a Hermitian matrix
A
:
κ
1
(
A
) = ||
A
||
1
||
A
-1
||
1
(since
A
is Hermitian,
κ
(
A
) =
κ
1
(
A
)
).
Before calling this routine:
• compute
anorm
(either ||
A
||
1
=max
j
Σ
i
|
a
i
j
| or ||
A
||
=max
i
Σ
j
|
a
i
j
|)
• call
?hetrf
to compute the factorization of
A
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular factor
U
of the factorization
A
=
U*D*U
H
.
If
uplo
=
'L'
, the array
a
stores the lower triangular factor
L
of the factorization
A
=
L*D*L
H
.
n
The order of matrix
A
;
n
0.
a
The array
a
of size max(1,
lda
*
n
)
contains the factored matrix
A
, as returned by
?hetrf
.
lda
a
;
lda
max(1,
n
)
.
ipiv
Array, size at least
max(1,
n
)
.
The array
ipiv
, as returned by
?hetrf
.
anorm
The norm of the
original
matrix
A
(see
Description
)
.
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
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 5 and never more than 11. Each solution requires approximately
8
n
2
floating-point operations.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserverd for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804