Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?sycon_3

Estimates the reciprocal of the condition number (in the 1-norm) of a real or complex symmetric matrix A using the factorization computed by
?sytrf_rk
.
lapack_int
LAPACKE_ssycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
float
*
A
,
lapack_int
lda
,
const
float
*
e
,
const
lapack_int
*
ipiv
,
float
anorm
,
float
*
rcond
);
lapack_int
LAPACKE_dsycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
double
*
A
,
lapack_int
lda
,
const
double
*
e
,
const
lapack_int
*
ipiv
,
double
anorm
,
double
*
rcond
);
lapack_int
LAPACKE_csycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
,
float
anorm
,
float
*
rcond
);
lapack_int
LAPACKE_zsycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
,
double
anorm
,
double
*
rcond
);
Description
?sycon_3
 estimates the reciprocal of the condition number (in the 1-norm) of a real or complex symmetric matrix A using the factorization computed by
?sytrf_rk
. A = P*U*D*(U
T
)*(P
T
) or A = P*L*D*(L
T
)*(P
T
), where U (or L) is unit upper (or lower) triangular matrix, U
T
 (or L
T
) is the transpose of U (or L), P is a permutation matrix, P
T
 is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as
rcond
 = 1 / (
anorm
 * norm(inv(A))).
This routine uses BLAS3 solver
?sytrs_3
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
  • =
    'U'
    : Upper triangular. The form is A = P*U*D*(U
    T
    )*(P
    T
    ).
  • =
    'L'
    : Lower triangular. The form is A = P*L*D*(L
    T
    )*(P
    T
    ).
n
The order of the matrix A.
n
 ≥ 0.
A
Array of size max(1,
lda
*
n
).
 Diagonal of the block diagonal matrix D and factors U or L as computed by
?sytrf_rk
:
  • Only
     diagonal elements of the symmetric block diagonal matrix D on the diagonal of A; that is, D(
    k
    ,
    k
    ) = A(
    k
    ,
    k
    ). Superdiagonal (or subdiagonal) elements of D should be provided on entry in array
    e
    ).
    —and—
  • If
    uplo
     =
    'U'
    , factor U in the superdiagonal part of A. If
    uplo
     =
    'L'
    , factor L in the subdiagonal part of A.
lda
The leading dimension of the array
A
.
e
Array of size
n
.
 On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If
uplo
 =
'U'
, e(
i
) = D(
i
-
1,
i
),
i
=2:N, and e(1) is not referenced. If
uplo
 =
'L'
, e(
i
) = D(
i
+1,
i
),
i
=1:N
-
1, and e(
n
) is not referenced.
For 1-by-1 diagonal block D(
k
), where 1 ≤
k
 ≤
n
, the element
e
[
k
-
1] is not referenced in both the
uplo
 =
'U'
 and
uplo
 =
'L'
 cases.
ipiv
Array of size
n
.
 Details of the interchanges and the block structure of D as determined by
?sytrf_rk
.
anorm
The 1-norm of the original matrix A.
Output Parameters
rcond
The reciprocal of the condition number of the matrix A, computed as
rcond
 = 1/(
anorm
 *
AINVNM
), where
AINVNM
 is an estimate of the 1-norm of inv(A) computed in this routine.
Return Values
This function returns a value
info
.
= 0: Successful exit.
< 0: If
info
 =
-i
, the
i
th
 argument had an illegal value.

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