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

.in +1c
.ti -1c
.RI "subroutine \fBchptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBCHPTRI\fP "
.ti -1c
.RI "subroutine \fBcsptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBCSPTRI\fP "
.ti -1c
.RI "subroutine \fBdsptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBDSPTRI\fP "
.ti -1c
.RI "subroutine \fBssptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBSSPTRI\fP "
.ti -1c
.RI "subroutine \fBzhptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBZHPTRI\fP "
.ti -1c
.RI "subroutine \fBzsptri\fP (uplo, n, ap, ipiv, work, info)"
.br
.RI "\fBZSPTRI\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
!>
!> CHPTRI computes the inverse of a complex Hermitian indefinite matrix
!> A in packed storage using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by CHPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by CHPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (Hermitian) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 CHPTRF\&.
!> 
.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 \fB108\fP of file \fBchptri\&.f\fP\&.
.SS "subroutine csptri (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CSPTRI computes the inverse of a complex symmetric indefinite matrix
!> A in packed storage using the factorization A = U*D*U**T or
!> A = L*D*L**T computed by CSPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by CSPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 CSPTRF\&.
!> 
.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 \fB108\fP of file \fBcsptri\&.f\fP\&.
.SS "subroutine dsptri (character uplo, integer n, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> DSPTRI computes the inverse of a real symmetric indefinite matrix
!> A in packed storage using the factorization A = U*D*U**T or
!> A = L*D*L**T computed by DSPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by DSPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 DSPTRF\&.
!> 
.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 \fB108\fP of file \fBdsptri\&.f\fP\&.
.SS "subroutine ssptri (character uplo, integer n, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> SSPTRI computes the inverse of a real symmetric indefinite matrix
!> A in packed storage using the factorization A = U*D*U**T or
!> A = L*D*L**T computed by SSPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is REAL array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by SSPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 SSPTRF\&.
!> 
.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 \fB108\fP of file \fBssptri\&.f\fP\&.
.SS "subroutine zhptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
!> A in packed storage using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by ZHPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by ZHPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (Hermitian) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 ZHPTRF\&.
!> 
.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 \fB108\fP of file \fBzhptri\&.f\fP\&.
.SS "subroutine zsptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
!> A in packed storage using the factorization A = U*D*U**T or
!> A = L*D*L**T computed by ZSPTRF\&.
!> 
.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
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by ZSPTRF,
!>          stored as a packed triangular matrix\&.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix\&. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 ZSPTRF\&.
!> 
.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 \fB108\fP of file \fBzsptri\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.