gttrf#

sgttrf

Functions

void sgttrf(
    const INT           n,
          f32* restrict DL,
          f32* restrict D,
          f32* restrict DU,
          f32* restrict DU2,
          INT* restrict ipiv,
          INT*          info
);

void sgttrf(const INT n, f32 *restrict DL, f32 *restrict D, f32 *restrict DU, f32 *restrict DU2, INT *restrict ipiv, INT *info)#

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

in

n

The order of the matrix A. n>=0.

inout

DL

Array of dimension (n-1). On entry, the (n-1) sub-diagonal elements of A. On exit, the (n-1) multipliers that define the matrix L from the LU factorization of A.

inout

D

Array of dimension (n). On entry, the diagonal elements of A. On exit, the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

inout

DU

Array of dimension (n-1). On entry, the (n-1) super-diagonal elements of A. On exit, the (n-1) elements of the first super-diagonal of U.

out

DU2

Array of dimension (n-2). On exit, the (n-2) elements of the second super-diagonal of U.

out

ipiv

Array of dimension (n). The pivot indices; for 0<=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.

out

info

info=0: successful exit
info<0: if info=-k, the k-th argument had an illegal value
info>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.

dgttrf

Functions

void dgttrf(
    const INT           n,
          f64* restrict DL,
          f64* restrict D,
          f64* restrict DU,
          f64* restrict DU2,
          INT* restrict ipiv,
          INT*          info
);

void dgttrf(const INT n, f64 *restrict DL, f64 *restrict D, f64 *restrict DU, f64 *restrict DU2, INT *restrict ipiv, INT *info)#

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

in

n

The order of the matrix A. n>=0.

inout

DL

Array of dimension (n-1). On entry, the (n-1) sub-diagonal elements of A. On exit, the (n-1) multipliers that define the matrix L from the LU factorization of A.

inout

D

Array of dimension (n). On entry, the diagonal elements of A. On exit, the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

inout

DU

Array of dimension (n-1). On entry, the (n-1) super-diagonal elements of A. On exit, the (n-1) elements of the first super-diagonal of U.

out

DU2

Array of dimension (n-2). On exit, the (n-2) elements of the second super-diagonal of U.

out

ipiv

Array of dimension (n). The pivot indices; for 0<=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.

out

info

info=0: successful exit
info<0: if info=-k, the k-th argument had an illegal value
info>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.

cgttrf

Functions

void cgttrf(
    const INT           n,
          c64* restrict DL,
          c64* restrict D,
          c64* restrict DU,
          c64* restrict DU2,
          INT* restrict ipiv,
          INT*          info
);

void cgttrf(const INT n, c64 *restrict DL, c64 *restrict D, c64 *restrict DU, c64 *restrict DU2, INT *restrict ipiv, INT *info)#

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

in

n

The order of the matrix A. n>=0.

inout

DL

Array of dimension (n-1). On entry, the (n-1) sub-diagonal elements of A. On exit, the (n-1) multipliers that define the matrix L from the LU factorization of A.

inout

D

Array of dimension (n). On entry, the diagonal elements of A. On exit, the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

inout

DU

Array of dimension (n-1). On entry, the (n-1) super-diagonal elements of A. On exit, the (n-1) elements of the first super-diagonal of U.

out

DU2

Array of dimension (n-2). On exit, the (n-2) elements of the second super-diagonal of U.

out

ipiv

Array of dimension (n). The pivot indices; for 0<=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.

out

info

info=0: successful exit
info<0: if info=-k, the k-th argument had an illegal value
info>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.

zgttrf

Functions

void zgttrf(
    const INT            n,
          c128* restrict DL,
          c128* restrict D,
          c128* restrict DU,
          c128* restrict DU2,
          INT*  restrict ipiv,
          INT*           info
);

void zgttrf(const INT n, c128 *restrict DL, c128 *restrict D, c128 *restrict DU, c128 *restrict DU2, INT *restrict ipiv, INT *info)#

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

in

n

The order of the matrix A. n>=0.

inout

DL

Array of dimension (n-1). On entry, the (n-1) sub-diagonal elements of A. On exit, the (n-1) multipliers that define the matrix L from the LU factorization of A.

inout

D

Array of dimension (n). On entry, the diagonal elements of A. On exit, the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

inout

DU

Array of dimension (n-1). On entry, the (n-1) super-diagonal elements of A. On exit, the (n-1) elements of the first super-diagonal of U.

out

DU2

Array of dimension (n-2). On exit, the (n-2) elements of the second super-diagonal of U.

out

ipiv

Array of dimension (n). The pivot indices; for 0<=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.

out

info

info=0: successful exit
info<0: if info=-k, the k-th argument had an illegal value
info>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.