Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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?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

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