gbsv#

sgbsv

Functions

void sgbsv(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           nrhs,
          f32* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          f32* restrict B,
    const INT           ldb,
          INT*          info
);

void sgbsv(const INT n, const INT kl, const INT ku, const INT nrhs, f32 *restrict AB, const INT ldab, INT *restrict ipiv, f32 *restrict B, const INT ldb, INT *info)#

SGBSV computes the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

n

The number of linear equations, i.e., the order 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).

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B (nrhs >= 0).

inout

AB

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(n-1,j+kl). 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. Array of dimension (ldab, n).

in

ldab

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

out

ipiv

The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i]. Array of dimension n, 0-based.

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

The leading dimension of the array B (ldb >= max(1,n)).

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 the solution has not been computed.

dgbsv

Functions

void dgbsv(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           nrhs,
          f64* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          f64* restrict B,
    const INT           ldb,
          INT*          info
);

void dgbsv(const INT n, const INT kl, const INT ku, const INT nrhs, f64 *restrict AB, const INT ldab, INT *restrict ipiv, f64 *restrict B, const INT ldb, INT *info)#

DGBSV computes the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

n

The number of linear equations, i.e., the order 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).

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B (nrhs >= 0).

inout

AB

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(n-1,j+kl). 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. Array of dimension (ldab, n).

in

ldab

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

out

ipiv

The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i]. Array of dimension n, 0-based.

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

The leading dimension of the array B (ldb >= max(1,n)).

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 the solution has not been computed.

cgbsv

Functions

void cgbsv(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           nrhs,
          c64* restrict AB,
    const INT           ldab,
          INT* restrict ipiv,
          c64* restrict B,
    const INT           ldb,
          INT*          info
);

void cgbsv(const INT n, const INT kl, const INT ku, const INT nrhs, c64 *restrict AB, const INT ldab, INT *restrict ipiv, c64 *restrict B, const INT ldb, INT *info)#

CGBSV computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

n

The number of linear equations, i.e., the order 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).

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B (nrhs >= 0).

inout

AB

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(n-1,j+kl). 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. Array of dimension (ldab, n).

in

ldab

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

out

ipiv

The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i]. Array of dimension n, 0-based.

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

The leading dimension of the array B (ldb >= max(1,n)).

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 the solution has not been computed.

zgbsv

Functions

void zgbsv(
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
          c128* restrict AB,
    const INT            ldab,
          INT*  restrict ipiv,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);

void zgbsv(const INT n, const INT kl, const INT ku, const INT nrhs, c128 *restrict AB, const INT ldab, INT *restrict ipiv, c128 *restrict B, const INT ldb, INT *info)#

ZGBSV computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

n

The number of linear equations, i.e., the order 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).

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B (nrhs >= 0).

inout

AB

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(n-1,j+kl). 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. Array of dimension (ldab, n).

in

ldab

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

out

ipiv

The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i]. Array of dimension n, 0-based.

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

The leading dimension of the array B (ldb >= max(1,n)).

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 the solution has not been computed.

gbsv#

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