.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 (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 >= 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 LWORK
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The size of WORK\&. LWORK >= 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 \fB184\fP of file \fBssysv_aa_2stage\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.