gttrf(3) Library Functions Manual gttrf(3)

gttrf - gttrf: triangular factor


subroutine cgttrf (n, dl, d, du, du2, ipiv, info)
CGTTRF subroutine dgttrf (n, dl, d, du, du2, ipiv, info)
DGTTRF subroutine sgttrf (n, dl, d, du, du2, ipiv, info)
SGTTRF subroutine zgttrf (n, dl, d, du, du2, ipiv, info)
ZGTTRF

CGTTRF

Purpose:

 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.

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file cgttrf.f.

DGTTRF

Purpose:

 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.

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file dgttrf.f.

SGTTRF

Purpose:

 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.

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file sgttrf.f.

ZGTTRF

Purpose:

 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.

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file zgttrf.f.

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