.TH "hetrs2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hetrs2 \- {he,sy}trs2: solve using factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchetrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBCHETRS2\fP "
.ti -1c
.RI "subroutine \fBcsytrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBCSYTRS2\fP "
.ti -1c
.RI "subroutine \fBdsytrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBDSYTRS2\fP "
.ti -1c
.RI "subroutine \fBssytrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBSSYTRS2\fP "
.ti -1c
.RI "subroutine \fBzhetrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBZHETRS2\fP "
.ti -1c
.RI "subroutine \fBzsytrs2\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)"
.br
.RI "\fBZSYTRS2\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chetrs2 (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)"

.PP
\fBCHETRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CHETRS2 solves a system of linear equations A*X = B with a complex
 Hermitian matrix A using the factorization A = U*D*U**H or
 A = L*D*L**H computed by CHETRF and converted by CSYCONV\&.
.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*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*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 array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CHETRF\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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 CHETRF\&.
.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
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX 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

.SS "subroutine csytrs2 (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)"

.PP
\fBCSYTRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CSYTRS2 solves a system of linear equations A*X = B with a complex
 symmetric matrix A using the factorization A = U*D*U**T or
 A = L*D*L**T computed by CSYTRF and converted by CSYCONV\&.
.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*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*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)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CSYTRF\&.
          Note that A is input / output\&. This might be counter-intuitive,
          and one may think that A is input only\&. A is input / output\&. This
          is because, at the start of the subroutine, we permute A in a
          'better' form and then we permute A back to its original form at
          the end\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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 CSYTRF\&.
.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
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX 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

.SS "subroutine dsytrs2 (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer info)"

.PP
\fBDSYTRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DSYTRS2 solves a system of linear equations A*X = B with a real
 symmetric matrix A using the factorization A = U*D*U**T or
 A = L*D*L**T computed by DSYTRF and converted by DSYCONV\&.
.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*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*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)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by DSYTRF\&.
          Note that A is input / output\&. This might be counter-intuitive,
          and one may think that A is input only\&. A is input / output\&. This
          is because, at the start of the subroutine, we permute A in a
          'better' form and then we permute A back to its original form at
          the end\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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 DSYTRF\&.
.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
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION 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

.SS "subroutine ssytrs2 (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer info)"

.PP
\fBSSYTRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SSYTRS2 solves a system of linear equations A*X = B with a real
 symmetric matrix A using the factorization A = U*D*U**T or
 A = L*D*L**T computed by SSYTRF and converted by SSYCONV\&.
.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*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*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)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by SSYTRF\&.
          Note that A is input / output\&. This might be counter-intuitive,
          and one may think that A is input only\&. A is input / output\&. This
          is because, at the start of the subroutine, we permute A in a
          'better' form and then we permute A back to its original form at
          the end\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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\&.
.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 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

.SS "subroutine zhetrs2 (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer info)"

.PP
\fBZHETRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZHETRS2 solves a system of linear equations A*X = B with a complex
 Hermitian matrix A using the factorization A = U*D*U**H or
 A = L*D*L**H computed by ZHETRF and converted by ZSYCONV\&.
.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*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*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)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZHETRF\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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 ZHETRF\&.
.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
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 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

.SS "subroutine zsytrs2 (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer info)"

.PP
\fBZSYTRS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZSYTRS2 solves a system of linear equations A*X = B with a complex
 symmetric matrix A using the factorization A = U*D*U**T or
 A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV\&.
.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*D*U**T;
          = 'L':  Lower triangular, form is A = L*D*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)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZSYTRF\&.
          Note that A is input / output\&. This might be counter-intuitive,
          and one may think that A is input only\&. A is input / output\&. This
          is because, at the start of the subroutine, we permute A in a
          'better' form and then we permute A back to its original form at
          the end\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.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 ZSYTRF\&.
.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
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 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

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