Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?tpcon

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

Syntax

lapack_int LAPACKE_stpcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const float*
ap
,
float*
rcond
);
lapack_int LAPACKE_dtpcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const double*
ap
,
double*
rcond
);
lapack_int LAPACKE_ctpcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_float*
ap
,
float*
rcond
);
lapack_int LAPACKE_ztpcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_double*
ap
,
double*
rcond
);
Include Files
  • mkl.h
Description
The routine estimates the reciprocal of the condition number of a packed triangular 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
ap
.
n
The order of the matrix
A
;
n
0.
ap
The array
ap
contains the packed matrix
A
. The dimension of
ap
must be at least max(1,
n
(
n
+1)/2).
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
n
2
floating-point operations for real flavors and
4
n
2
operations for complex flavors.

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 reserved 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