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.

N

          N is INTEGER


          The order of the matrix A.

DL

          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.

D

          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.

DU

          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.

DU2

          DU2 is COMPLEX array, dimension (N-2)


          On exit, DU2 is overwritten by the (n-2) elements of the


          second super-diagonal of U.

IPIV

          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.

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 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.

N

          N is INTEGER


          The order of the matrix A.

DL

          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.

D

          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.

DU

          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.

DU2

          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.

IPIV

          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.

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 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.

N

          N is INTEGER


          The order of the matrix A.

DL

          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.

D

          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.

DU

          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.

DU2

          DU2 is REAL array, dimension (N-2)


          On exit, DU2 is overwritten by the (n-2) elements of the


          second super-diagonal of U.

IPIV

          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.

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 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

          N is INTEGER


          The order of the matrix A.

DL

          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.

D

          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.

DU

          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.

DU2

          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.

IPIV

          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.

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.