?sycon

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

call ssycon_3 ( uplo , n , A , lda , e , ipiv , anorm , rcond , work , iwork , info )

call dsycon_3 ( uplo , n , A , lda , e , ipiv , anorm , rcond , work , iwork , info )

call csycon_3 ( uplo , n , A , lda , e , ipiv , anorm , rcond , work , info )

call zsycon_3 ( uplo , n , A , lda , e , ipiv , anorm , rcond , work , info )

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

uplo

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

n

INTEGER The order of the matrix A. n ≥ 0.

A

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

Array, dimension ( 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 . lda ≥ max(1, n ).

e

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

Array, dimension ( 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, dimension ( 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 ).

info

INTEGER .

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

Return Values

No return value, info is an Output Parameter.

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