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

.in +1c
.ti -1c
.RI "subroutine \fBcpttrf\fP (n, d, e, info)"
.br
.RI "\fBCPTTRF\fP "
.ti -1c
.RI "subroutine \fBdpttrf\fP (n, d, e, info)"
.br
.RI "\fBDPTTRF\fP "
.ti -1c
.RI "subroutine \fBspttrf\fP (n, d, e, info)"
.br
.RI "\fBSPTTRF\fP "
.ti -1c
.RI "subroutine \fBzpttrf\fP (n, d, e, info)"
.br
.RI "\fBZPTTRF\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cpttrf (integer n, real, dimension( * ) d, complex, dimension( * ) e, integer info)"

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

.PP
.nf
 CPTTRF computes the L*D*L**H factorization of a complex Hermitian
 positive definite tridiagonal matrix A\&.  The factorization may also
 be regarded as having the form A = U**H *D*U\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix
          A\&.  On exit, the n diagonal elements of the diagonal matrix
          D from the L*D*L**H factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix A\&.  On exit, the (n-1) subdiagonal elements of the
          unit bidiagonal factor L from the L*D*L**H factorization of A\&.
          E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**H *D*U factorization of A\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, the leading principal minor of order k
               is not positive; if k < N, the factorization could not
               be completed, while if k = N, the factorization was
               completed, but D(N) <= 0\&.
.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 dpttrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer info)"

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

.PP
.nf
 DPTTRF computes the L*D*L**T factorization of a real symmetric
 positive definite tridiagonal matrix A\&.  The factorization may also
 be regarded as having the form A = U**T*D*U\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix
          A\&.  On exit, the n diagonal elements of the diagonal matrix
          D from the L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix A\&.  On exit, the (n-1) subdiagonal elements of the
          unit bidiagonal factor L from the L*D*L**T factorization of A\&.
          E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**T*D*U factorization of A\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, the leading principal minor of order k
               is not positive; if k < N, the factorization could not
               be completed, while if k = N, the factorization was
               completed, but D(N) <= 0\&.
.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 spttrf (integer n, real, dimension( * ) d, real, dimension( * ) e, integer info)"

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

.PP
.nf
 SPTTRF computes the L*D*L**T factorization of a real symmetric
 positive definite tridiagonal matrix A\&.  The factorization may also
 be regarded as having the form A = U**T*D*U\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix
          A\&.  On exit, the n diagonal elements of the diagonal matrix
          D from the L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix A\&.  On exit, the (n-1) subdiagonal elements of the
          unit bidiagonal factor L from the L*D*L**T factorization of A\&.
          E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**T*D*U factorization of A\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, the leading principal minor of order k
               is not positive; if k < N, the factorization could not
               be completed, while if k = N, the factorization was
               completed, but D(N) <= 0\&.
.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 zpttrf (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, integer info)"

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

.PP
.nf
 ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
 positive definite tridiagonal matrix A\&.  The factorization may also
 be regarded as having the form A = U**H *D*U\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix
          A\&.  On exit, the n diagonal elements of the diagonal matrix
          D from the L*D*L**H factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX*16 array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix A\&.  On exit, the (n-1) subdiagonal elements of the
          unit bidiagonal factor L from the L*D*L**H factorization of A\&.
          E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**H *D*U factorization of A\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, the leading principal minor of order k
               is not positive; if k < N, the factorization could not
               be completed, while if k = N, the factorization was
               completed, but D(N) <= 0\&.
.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\&.