.TH "hetri" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hetri \- {he,sy}tri: triangular inverse
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchetri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBCHETRI\fP "
.ti -1c
.RI "subroutine \fBcsytri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBCSYTRI\fP "
.ti -1c
.RI "subroutine \fBdsytri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBDSYTRI\fP "
.ti -1c
.RI "subroutine \fBssytri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBSSYTRI\fP "
.ti -1c
.RI "subroutine \fBzhetri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBZHETRI\fP "
.ti -1c
.RI "subroutine \fBzsytri\fP (uplo, n, a, lda, ipiv, work, info)"
.br
.RI "\fBZSYTRI\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
!>
!> CHETRI computes the inverse of a complex Hermitian indefinite matrix
!> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
!> CHETRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by CHETRF\&.
!>
!>          On exit, if INFO = 0, the (Hermitian) 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
\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
\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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBchetri\&.f\fP\&.
.SS "subroutine csytri (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CSYTRI computes the inverse of a complex symmetric indefinite matrix
!> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
!> CSYTRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by CSYTRF\&.
!>
!>          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
\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
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (2*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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBcsytri\&.f\fP\&.
.SS "subroutine dsytri (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> DSYTRI computes the inverse of a real symmetric indefinite matrix
!> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
!> DSYTRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by DSYTRF\&.
!>
!>          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
\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
\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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBdsytri\&.f\fP\&.
.SS "subroutine ssytri (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> SSYTRI computes the inverse of a real symmetric indefinite matrix
!> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
!> SSYTRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by SSYTRF\&.
!>
!>          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
\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
\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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBssytri\&.f\fP\&.
.SS "subroutine zhetri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZHETRI computes the inverse of a complex Hermitian indefinite matrix
!> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
!> ZHETRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by ZHETRF\&.
!>
!>          On exit, if INFO = 0, the (Hermitian) 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
\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
\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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBzhetri\&.f\fP\&.
.SS "subroutine zsytri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZSYTRI computes the inverse of a complex symmetric indefinite matrix
!> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
!> ZSYTRF\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by ZSYTRF\&.
!>
!>          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
\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
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (2*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
!>          > 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
.PP

.PP
Definition at line \fB113\fP of file \fBzsytri\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.