?sycon

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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 .

Syntax

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: CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

n: Specifies the order of the matrix A . The value of n must be at least zero.

A

REAL for ssycon_3 DOUBLE PRECISION for dsycon_3 COMPLEX for csycon_3 COMPLEX*16 for zsycon_3

Array of size max(1, lda * n ). Diagonal of the block diagonal matrix D and factors U or L as computed by ?sytrf_rk :

lda

INTEGER

The leading dimension of the array A .

e

REAL for ssycon_3 DOUBLE PRECISION for dsycon_3 COMPLEX for csycon_3 COMPLEX*16 for zsycon_3

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.

ipiv

INTEGER

Array of size n . Details of the interchanges and the block structure of D as determined by ?sytrf_rk .

anorm

REAL for ssycon_3 DOUBLE PRECISION for dsycon_3 REAL for csycon_3 DOUBLE PRECISION for zsycon_3 The 1-norm of the original matrix A.

Output Parameters

rcond: REAL for ssycon_3 DOUBLE PRECISION for dsycon_3 REAL for csycon_3 DOUBLE PRECISION for zsycon_3 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.
work: REAL for ssycon_3 DOUBLE PRECISION for dsycon_3 COMPLEX for csycon_3 COMPLEX*16 for zsycon_3 Array, dimension (2* n )
iwork: INTEGER Array, dimension ( n ).

Return Values

This function returns a value info .

If info = 0, the execution is successful.
If info = -i , the i^th argument had an illegal value.

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