.TH "hetrs_aa_2stage" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hetrs_aa_2stage \- {he,sy}trs_aa_2stage: triangular solve using factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchetrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBCHETRS_AA_2STAGE\fP "
.ti -1c
.RI "subroutine \fBcsytrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBCSYTRS_AA_2STAGE\fP "
.ti -1c
.RI "subroutine \fBdsytrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBDSYTRS_AA_2STAGE\fP "
.ti -1c
.RI "subroutine \fBssytrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBSSYTRS_AA_2STAGE\fP "
.ti -1c
.RI "subroutine \fBzhetrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBZHETRS_AA_2STAGE\fP "
.ti -1c
.RI "subroutine \fBzsytrs_aa_2stage\fP (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)"
.br
.RI "\fBZSYTRS_AA_2STAGE\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chetrs_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBCHETRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real
 hermitian matrix A using the factorization A = U**T*T*U or
 A = L*T*L**T computed by CHETRF_AA_2STAGE\&.
.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 = U**T*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**T\&.
.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 COMPLEX array, dimension (LDA,N)
          Details of factors computed by CHETRF_AA_2STAGE\&.
.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 COMPLEX array, dimension (LTB)
          Details of factors computed by CHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          CHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          CHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX 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
\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

.SS "subroutine csytrs_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBCSYTRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex
 symmetric matrix A using the factorization A = U**T*T*U or
 A = L*T*L**T computed by CSYTRF_AA_2STAGE\&.
.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 = U**T*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**T\&.
.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 COMPLEX array, dimension (LDA,N)
          Details of factors computed by CSYTRF_AA_2STAGE\&.
.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 COMPLEX array, dimension (LTB)
          Details of factors computed by CSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          CSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          CSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX 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
\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

.SS "subroutine dsytrs_aa_2stage (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBDSYTRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a real
 symmetric matrix A using the factorization A = U**T*T*U or
 A = L*T*L**T computed by DSYTRF_AA_2STAGE\&.
.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 = U**T*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**T\&.
.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 DOUBLE PRECISION array, dimension (LDA,N)
          Details of factors computed by DSYTRF_AA_2STAGE\&.
.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 DOUBLE PRECISION array, dimension (LTB)
          Details of factors computed by DSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          DSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          DSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION 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
\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

.SS "subroutine ssytrs_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, integer info)"

.PP
\fBSSYTRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a real
 symmetric matrix A using the factorization A = U**T*T*U or
 A = L*T*L**T computed by SSYTRF_AA_2STAGE\&.
.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 = U**T*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**T\&.
.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)
          Details of factors computed by SSYTRF_AA_2STAGE\&.
.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)
          Details of factors computed by SSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          SSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          SSYTRF_AA_2STAGE\&.
.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
\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

.SS "subroutine zhetrs_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBZHETRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a 
 hermitian matrix A using the factorization A = U**H*T*U or
 A = L*T*L**H computed by ZHETRF_AA_2STAGE\&.
.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 = U**H*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**H\&.
.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 COMPLEX*16 array, dimension (LDA,N)
          Details of factors computed by ZHETRF_AA_2STAGE\&.
.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 COMPLEX*16 array, dimension (LTB)
          Details of factors computed by ZHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          ZHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          ZHETRF_AA_2STAGE\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 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
\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

.SS "subroutine zsytrs_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBZSYTRS_AA_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex
 symmetric matrix A using the factorization A = U**T*T*U or
 A = L*T*L**T computed by ZSYTRF_AA_2STAGE\&.
.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 = U**T*T*U;
          = 'L':  Lower triangular, form is A = L*T*L**T\&.
.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 COMPLEX*16 array, dimension (LDA,N)
          Details of factors computed by ZSYTRF_AA_2STAGE\&.
.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 COMPLEX*16 array, dimension (LTB)
          Details of factors computed by ZSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fILTB\fP 
.PP
.nf
          LTB is INTEGER
          The size of the array TB\&. LTB >= 4*N\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          ZSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIIPIV2\fP 
.PP
.nf
          IPIV2 is INTEGER array, dimension (N)
          Details of the interchanges as computed by
          ZSYTRF_AA_2STAGE\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 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
\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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.