gbtrf#

sgbtrf

Functions

void sgbtrf(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
          f32* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          INT*          info
);

void sgbtrf(const INT m, const INT n, const INT kl, const INT ku, f32 *restrict AB, const INT ldab, INT *restrict ipiv, INT *info)#

SGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

On exit, details of the factorization: U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

Parameters

in

m

The number of rows of the matrix A. m >= 0.

in

n

The number of columns of the matrix A. n >= 0.

in

kl

The number of subdiagonals within the band of A. kl >= 0.

in

ku

The number of superdiagonals within the band of A. ku >= 0.

inout

AB

Double precision array, dimension (ldab, n). On entry, the matrix A in band storage, in rows kl to 2*kl+ku; rows 0 to kl-1 of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB[kl+ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(m-1,j+kl).

in

ldab

The leading dimension of the array AB. ldab >= 2*kl+ku+1.

out

ipiv

Integer array, dimension (min(m,n)). The pivot indices; for 0 <= i < min(m,n), row i of the matrix was interchanged with row ipiv[i]. 0-based indexing.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i-1,i-1) 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.

dgbtrf

Functions

void dgbtrf(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
          f64* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          INT*          info
);

void dgbtrf(const INT m, const INT n, const INT kl, const INT ku, f64 *restrict AB, const INT ldab, INT *restrict ipiv, INT *info)#

DGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

On exit, details of the factorization: U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

Parameters

in

m

The number of rows of the matrix A. m >= 0.

in

n

The number of columns of the matrix A. n >= 0.

in

kl

The number of subdiagonals within the band of A. kl >= 0.

in

ku

The number of superdiagonals within the band of A. ku >= 0.

inout

AB

Double precision array, dimension (ldab, n). On entry, the matrix A in band storage, in rows kl to 2*kl+ku; rows 0 to kl-1 of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB[kl+ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(m-1,j+kl).

in

ldab

The leading dimension of the array AB. ldab >= 2*kl+ku+1.

out

ipiv

Integer array, dimension (min(m,n)). The pivot indices; for 0 <= i < min(m,n), row i of the matrix was interchanged with row ipiv[i]. 0-based indexing.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i-1,i-1) 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.

cgbtrf

Functions

void cgbtrf(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
          c64* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          INT*          info
);

void cgbtrf(const INT m, const INT n, const INT kl, const INT ku, c64 *restrict AB, const INT ldab, INT *restrict ipiv, INT *info)#

CGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

On exit, details of the factorization: U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

Parameters

in

m

The number of rows of the matrix A. m >= 0.

in

n

The number of columns of the matrix A. n >= 0.

in

kl

The number of subdiagonals within the band of A. kl >= 0.

in

ku

The number of superdiagonals within the band of A. ku >= 0.

inout

AB

Single complex array, dimension (ldab, n). On entry, the matrix A in band storage, in rows kl to 2*kl+ku; rows 0 to kl-1 of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB[kl+ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(m-1,j+kl).

in

ldab

The leading dimension of the array AB. ldab >= 2*kl+ku+1.

out

ipiv

Integer array, dimension (min(m,n)). The pivot indices; for 0 <= i < min(m,n), row i of the matrix was interchanged with row ipiv[i]. 0-based indexing.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i-1,i-1) 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.

zgbtrf

Functions

void zgbtrf(
    const INT            m,
    const INT            n,
    const INT            kl,
    const INT            ku,
          c128* restrict AB,
    const INT            ldab,
          INT*  restrict ipiv,
          INT*           info
);

void zgbtrf(const INT m, const INT n, const INT kl, const INT ku, c128 *restrict AB, const INT ldab, INT *restrict ipiv, INT *info)#

ZGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

On exit, details of the factorization: U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

Parameters

in

m

The number of rows of the matrix A. m >= 0.

in

n

The number of columns of the matrix A. n >= 0.

in

kl

The number of subdiagonals within the band of A. kl >= 0.

in

ku

The number of superdiagonals within the band of A. ku >= 0.

inout

AB

Double complex array, dimension (ldab, n). On entry, the matrix A in band storage, in rows kl to 2*kl+ku; rows 0 to kl-1 of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB[kl+ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(m-1,j+kl).

in

ldab

The leading dimension of the array AB. ldab >= 2*kl+ku+1.

out

ipiv

Integer array, dimension (min(m,n)). The pivot indices; for 0 <= i < min(m,n), row i of the matrix was interchanged with row ipiv[i]. 0-based indexing.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i-1,i-1) 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.

gbtrf#

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