Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?trcon

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

Syntax

lapack_int LAPACKE_strcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float*
rcond
);
lapack_int LAPACKE_dtrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double*
rcond
);
lapack_int LAPACKE_ctrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float*
rcond
);
lapack_int LAPACKE_ztrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_double*
a
,
lapack_int
lda
,
double*
rcond
);
Include Files
  • mkl.h
Description
The routine estimates the reciprocal of the condition number of a 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
||
∞
 =k
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
a
 stores the upper triangle of
A
, other array elements are not referenced.
If
uplo
 =
'L'
, the array
a
 stores the lower triangle of
A
, other array elements are not referenced.
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
a
.
n
The order of the matrix
A
;
n
≥
 0.
a
The array
a
of size max(1,
lda
*
n
)
 contains the matrix
A
.
lda
The leading dimension of
a
;
lda
≥
 max(1,
n
)
.
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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.