# ssycon_3.f - Man Page

## 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

NAG Ltd.

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 169 of file ssycon_3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ssycon_3(3) is an alias of ssycon_3.f(3).

Thu Apr 1 2021 Version 3.9.1 LAPACK