.TH "pptri" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
pptri \- pptri: triangular inverse
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcpptri\fP (uplo, n, ap, info)"
.br
.RI "\fBCPPTRI\fP "
.ti -1c
.RI "subroutine \fBdpptri\fP (uplo, n, ap, info)"
.br
.RI "\fBDPPTRI\fP "
.ti -1c
.RI "subroutine \fBspptri\fP (uplo, n, ap, info)"
.br
.RI "\fBSPPTRI\fP "
.ti -1c
.RI "subroutine \fBzpptri\fP (uplo, n, ap, info)"
.br
.RI "\fBZPPTRI\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CPPTRI computes the inverse of a complex Hermitian positive definite
 matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
 computed by CPPTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangular factor is stored in AP;
          = 'L':  Lower triangular factor is stored in AP\&.
.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 triangular factor U or L from the Cholesky
          factorization A = U**H*U or A = L*L**H, packed columnwise as
          a linear array\&.  The j-th column of U or L is stored in the
          array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n\&.

          On exit, the upper or lower triangle of the (Hermitian)
          inverse of A, overwriting the input factor U or L\&.
.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, the (i,i) element of the factor U or L is
                zero, and the 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 dpptri (character uplo, integer n, double precision, dimension( * ) ap, integer info)"

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

.PP
.nf
 DPPTRI computes the inverse of a real symmetric positive definite
 matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
 computed by DPPTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangular factor is stored in AP;
          = 'L':  Lower triangular factor is stored in AP\&.
.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 triangular factor U or L from the Cholesky
          factorization A = U**T*U or A = L*L**T, packed columnwise as
          a linear array\&.  The j-th column of U or L is stored in the
          array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n\&.

          On exit, the upper or lower triangle of the (symmetric)
          inverse of A, overwriting the input factor U or L\&.
.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, the (i,i) element of the factor U or L is
                zero, and the 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 spptri (character uplo, integer n, real, dimension( * ) ap, integer info)"

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

.PP
.nf
 SPPTRI computes the inverse of a real symmetric positive definite
 matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
 computed by SPPTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangular factor is stored in AP;
          = 'L':  Lower triangular factor is stored in AP\&.
.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 triangular factor U or L from the Cholesky
          factorization A = U**T*U or A = L*L**T, packed columnwise as
          a linear array\&.  The j-th column of U or L is stored in the
          array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n\&.

          On exit, the upper or lower triangle of the (symmetric)
          inverse of A, overwriting the input factor U or L\&.
.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, the (i,i) element of the factor U or L is
                zero, and the 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 zpptri (character uplo, integer n, complex*16, dimension( * ) ap, integer info)"

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

.PP
.nf
 ZPPTRI computes the inverse of a complex Hermitian positive definite
 matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
 computed by ZPPTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangular factor is stored in AP;
          = 'L':  Lower triangular factor is stored in AP\&.
.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 triangular factor U or L from the Cholesky
          factorization A = U**H*U or A = L*L**H, packed columnwise as
          a linear array\&.  The j-th column of U or L is stored in the
          array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n\&.

          On exit, the upper or lower triangle of the (Hermitian)
          inverse of A, overwriting the input factor U or L\&.
.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, the (i,i) element of the factor U or L is
                zero, and the 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\&.