.TH "ssycon_3.f" 3 "Wed May 24 2017" "Version 3.7.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ssycon_3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBssycon_3\fP (UPLO, \fBN\fP, A, \fBLDA\fP, E, IPIV, ANORM, RCOND, WORK, IWORK, INFO)"
.br
.RI "\fBSSYCON_3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBSSYCON_3\fP  
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\fBPurpose: \fP
.RS 4

.PP
.nf
 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.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          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).
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A.  N >= 0.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          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.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF_RK or SSYTRF_BK.
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
          ANORM is REAL
          The 1-norm of the original matrix A.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          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.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (N)
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBDate:\fP
.RS 4
December 2016 
.RE
.PP
\fBContributors: \fP
.RS 4

.RE
.PP
December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
.PP
September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.