ZGTTRF(3F) ZGTTRF(3F)
ZGTTRF - compute an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges
SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
INTEGER INFO, N
INTEGER IPIV( * )
COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
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.
N (input) INTEGER
The order of the matrix A. N >= 0.
DL (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of A.
On exit, DL is overwritten by the (n-1) multipliers that define
the matrix L from the LU factorization of A.
D (input/output) 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.
DU (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.
DU2 (output) COMPLEX*16 array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the second
superdiagonal of U.
IPIV (output) 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.
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ZGTTRF(3F) ZGTTRF(3F)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) 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.
ZGTTRF(3F) ZGTTRF(3F)
ZGTTRF - compute an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges
SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
INTEGER INFO, N
INTEGER IPIV( * )
COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
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.
N (input) INTEGER
The order of the matrix A. N >= 0.
DL (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of A.
On exit, DL is overwritten by the (n-1) multipliers that define
the matrix L from the LU factorization of A.
D (input/output) 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.
DU (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.
DU2 (output) COMPLEX*16 array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the second
superdiagonal of U.
IPIV (output) 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.
Page 1
ZGTTRF(3F) ZGTTRF(3F)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) 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.
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