.TH "hetri" 3 "Wed Feb 7 2024 11:30:40" "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

.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

.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

.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

.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

.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

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