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

.in +1c
.ti -1c
.RI "subroutine \fBcgttrf\fP (n, dl, d, du, du2, ipiv, info)"
.br
.RI "\fBCGTTRF\fP "
.ti -1c
.RI "subroutine \fBdgttrf\fP (n, dl, d, du, du2, ipiv, info)"
.br
.RI "\fBDGTTRF\fP "
.ti -1c
.RI "subroutine \fBsgttrf\fP (n, dl, d, du, du2, ipiv, info)"
.br
.RI "\fBSGTTRF\fP "
.ti -1c
.RI "subroutine \fBzgttrf\fP (n, dl, d, du, du2, ipiv, info)"
.br
.RI "\fBZGTTRF\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgttrf (integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)"

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

.PP
.nf
 CGTTRF computes an LU factorization of a complex tridiagonal matrix A
 using elimination with partial pivoting and row interchanges\&.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is COMPLEX array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A\&.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is COMPLEX array, dimension (N)
          On entry, D must contain the diagonal elements of A\&.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is COMPLEX array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A\&.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is COMPLEX array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.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, U(k,k) is exactly zero\&. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations\&.
.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 dgttrf (integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)"

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

.PP
.nf
 DGTTRF computes an LU factorization of a real tridiagonal matrix A
 using elimination with partial pivoting and row interchanges\&.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A\&.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, D must contain the diagonal elements of A\&.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A\&.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.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, U(k,k) is exactly zero\&. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations\&.
.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 sgttrf (integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)"

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

.PP
.nf
 SGTTRF computes an LU factorization of a real tridiagonal matrix A
 using elimination with partial pivoting and row interchanges\&.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is REAL array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A\&.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          On entry, D must contain the diagonal elements of A\&.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is REAL array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A\&.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is REAL array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.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, U(k,k) is exactly zero\&. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations\&.
.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 zgttrf (integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)"

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

.PP
.nf
 ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
 using elimination with partial pivoting and row interchanges\&.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is COMPLEX*16 array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A\&.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is COMPLEX*16 array, dimension (N)
          On entry, D must contain the diagonal elements of A\&.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is COMPLEX*16 array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A\&.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is COMPLEX*16 array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.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, U(k,k) is exactly zero\&. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations\&.
.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\&.