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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 (character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) E, integer, dimension( * ) IPIV, real ANORM, real RCOND, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

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:

June 2017

Contributors:

June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 173 of file ssycon_3.f.

Author

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