.TH "SRC/ssytri_3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/ssytri_3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBssytri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)"
.br
.RI "\fBSSYTRI_3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ssytri_3 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fBSSYTRI_3\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!> SSYTRI_3 computes the inverse of a real symmetric indefinite
!> matrix A using the factorization computed by SSYTRF_RK or SSYTRF_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\&.
!>
!> SSYTRI_3 sets the leading dimension of the workspace  before calling
!> SSYTRI_3X that actually computes the inverse\&.  This is the blocked
!> version of the algorithm, calling Level 3 BLAS\&.
!> 
.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 triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored\&.
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, if INFO = 0, the symmetric inverse of the original
!>          matrix\&.
!>             If UPLO = 'U': the upper triangular part of the inverse
!>             is formed and the part of A below the diagonal is not
!>             referenced;
!>             If UPLO = 'L': the lower triangular part of the inverse
!>             is formed and the part of A above the diagonal is not
!>             referenced\&.
!> 
.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
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))\&.
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The length of WORK\&.
!>          If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3)\&.
!>
!>          If LWORK = -1, then a workspace query is assumed;
!>          the routine only calculates the optimal size of the optimal
!>          size of the WORK array, returns this value as the first
!>          entry of the WORK array, and no error message related to
!>          LWORK is issued by XERBLA\&.
!> 
.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
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed\&.
!> 
.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
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\fBContributors:\fP
.RS 4

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.nf
!>
!>  November 2017,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!> 
.fi
.PP
 
.RE
.PP

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Definition at line \fB169\fP of file \fBssytri_3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.