.TH "SRC/ssysv_aa_2stage.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/ssysv_aa_2stage.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBssysv_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)"
.br
.RI "\fB SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ssysv_aa_2stage (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fB SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SSYSV_AA_2STAGE computes the solution to a real system of
!> linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
!> matrices\&.
!>
!> Aasen's 2-stage algorithm is used to factor A as
!>    A = U**T * T * U,  if UPLO = 'U', or
!>    A = L * T * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is symmetric and band\&. The matrix T is
!> then LU-factored with partial pivoting\&. The factored form of A
!> is then used to solve the system of equations A * X = B\&.
!>
!> 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
!>          = '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
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the symmetric matrix A\&.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced\&.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced\&.
!>
!>          On exit, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U')\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITB\fP 
.PP
.nf
!>          TB is REAL array, dimension (MAX(1,LTB))
!>          On exit, details of the LU factorization of the band matrix\&.
!> 
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
!>          LTB is INTEGER
!>          The size of the array TB\&. LTB >= MAX(1,4*N), internally
!>          used to select NB such that LTB >= (3*NB+1)*N\&.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i\&.e\&.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k)\&.
!> 
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i\&.e\&.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL workspace of size (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 size of WORK\&. LWORK >= MAX(1,N), internally used to
!>          select NB such that LWORK >= N*NB\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates 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, band LU factorization failed on i-th column
!> 
.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

.PP
Definition at line \fB185\fP of file \fBssysv_aa_2stage\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.