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ssycon_3.f(3) LAPACK ssycon_3.f(3)

NAME

ssycon_3.f -

SYNOPSIS

Functions/Subroutines


subroutine ssycon_3 (UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
 
SSYCON_3

Function/Subroutine Documentation

subroutine ssycon_3 (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )E, integer, dimension( * )IPIV, realANORM, realRCOND, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

SSYCON_3
Purpose:
 SSYCON_3 estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric matrix A using the factorization
 computed by DSYTRF_RK or DSYTRF_BK:
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 SSYTRS_3.
Parameters:
UPLO
          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are
          stored as an upper or lower triangular matrix:
          = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
          = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).
N
          N is INTEGER
          The order of the matrix A.  N >= 0.
A
          A is REAL array, dimension (LDA,N)
          Diagonal of the block diagonal matrix D and factors U or L
          as computed by SSYTRF_RK and SSYTRF_BK:
            a) ONLY diagonal elements of the symmetric block diagonal
               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
               (superdiagonal (or subdiagonal) elements of D
                should be provided on entry in array E), and
            b) If UPLO = 'U': factor U in the superdiagonal part of A.
               If UPLO = 'L': factor L in the subdiagonal part of A.
LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
E
          E is REAL 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, where
          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.
IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF_RK or SSYTRF_BK.
ANORM
          ANORM is REAL
          The 1-norm of the original matrix A.
RCOND
          RCOND is REAL
          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
          WORK is REAL array, dimension (2*N)
IWORK
          IWORK is INTEGER array, dimension (N)
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Contributors:
December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Author

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