Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?tbcon

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

Syntax

lapack_int LAPACKE_stbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const float*
ab
,
lapack_int
ldab
,
float*
rcond
);
lapack_int LAPACKE_dtbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const double*
ab
,
lapack_int
ldab
,
double*
rcond
);
lapack_int LAPACKE_ctbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const lapack_complex_float*
ab
,
lapack_int
ldab
,
float*
rcond
);
lapack_int LAPACKE_ztbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const lapack_complex_double*
ab
,
lapack_int
ldab
,
double*
rcond
);
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

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