gbrfs#

sgbrfs

Functions

void sgbrfs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const f32*  restrict AB,
    const INT            ldab,
    const f32*  restrict AFB,
    const INT            ldafb,
    const INT*  restrict ipiv,
    const f32*  restrict B,
    const INT            ldb,
          f32*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void sgbrfs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const f32 *restrict AB, const INT ldab, const f32 *restrict AFB, const INT ldafb, const INT *restrict ipiv, const f32 *restrict B, const INT ldb, f32 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, f32 *restrict work, INT *restrict iwork, INT *info)#

SGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.

Parameters

in

trans

Specifies the form of the system of equations:

'N': A * X = B (No transpose)
'T': A**T * X = B (Transpose)
'C': A**H * X = B (Conjugate transpose = Transpose)

in

n

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. nrhs>=0.

in

AB

Array of dimension (ldab, n). The original band matrix A, stored in rows 0 to kl+ku. The j-th column of A is stored in the j-th column of AB: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(n-1,j+kl).

in

ldab

The leading dimension of AB. ldab>=kl+ku+1.

in

AFB

Array of dimension (ldafb, n). The LU factorization of A, as computed by SGBTRF. U is stored in rows 0 to kl+ku, and the multipliers are stored in rows kl+ku+1 to 2*kl+ku.

in

ldafb

The leading dimension of AFB. ldafb>=2*kl+ku+1.

in

ipiv

Array of dimension n. The pivot indices from SGBTRF.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

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

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by SGBTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension nrhs. The estimated forward error bound for each solution vector X(j).

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j).

out

work

Workspace array of dimension (3*n).

out

iwork

Integer workspace array of dimension (n).

out

info

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

dgbrfs

Functions

void dgbrfs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const f64*  restrict AB,
    const INT            ldab,
    const f64*  restrict AFB,
    const INT            ldafb,
    const INT*  restrict ipiv,
    const f64*  restrict B,
    const INT            ldb,
          f64*  restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void dgbrfs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const f64 *restrict AB, const INT ldab, const f64 *restrict AFB, const INT ldafb, const INT *restrict ipiv, const f64 *restrict B, const INT ldb, f64 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, f64 *restrict work, INT *restrict iwork, INT *info)#

DGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.

Parameters

in

trans

Specifies the form of the system of equations:

'N': A * X = B (No transpose)
'T': A**T * X = B (Transpose)
'C': A**H * X = B (Conjugate transpose = Transpose)

in

n

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. nrhs>=0.

in

AB

Array of dimension (ldab, n). The original band matrix A, stored in rows 0 to kl+ku. The j-th column of A is stored in the j-th column of AB: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(n-1,j+kl).

in

ldab

The leading dimension of AB. ldab>=kl+ku+1.

in

AFB

Array of dimension (ldafb, n). The LU factorization of A, as computed by DGBTRF. U is stored in rows 0 to kl+ku, and the multipliers are stored in rows kl+ku+1 to 2*kl+ku.

in

ldafb

The leading dimension of AFB. ldafb>=2*kl+ku+1.

in

ipiv

Array of dimension n. The pivot indices from DGBTRF.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

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

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by DGBTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension nrhs. The estimated forward error bound for each solution vector X(j).

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j).

out

work

Workspace array of dimension (3*n).

out

iwork

Integer workspace array of dimension (n).

out

info

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

cgbrfs

Functions

void cgbrfs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const c64*  restrict AB,
    const INT            ldab,
    const c64*  restrict AFB,
    const INT            ldafb,
    const INT*  restrict ipiv,
    const c64*  restrict B,
    const INT            ldb,
          c64*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);

void cgbrfs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const c64 *restrict AB, const INT ldab, const c64 *restrict AFB, const INT ldafb, const INT *restrict ipiv, const c64 *restrict B, const INT ldb, c64 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, c64 *restrict work, f32 *restrict rwork, INT *info)#

CGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.

Parameters

in

trans

Specifies the form of the system of equations:

'N': A * X = B (No transpose)
'T': A**T * X = B (Transpose)
'C': A**H * X = B (Conjugate transpose)

in

n

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. nrhs>=0.

in

AB

Array of dimension (ldab, n). The original band matrix A, stored in rows 0 to kl+ku. The j-th column of A is stored in the j-th column of AB: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(n-1,j+kl).

in

ldab

The leading dimension of AB. ldab>=kl+ku+1.

in

AFB

Array of dimension (ldafb, n). The LU factorization of A, as computed by CGBTRF. U is stored in rows 0 to kl+ku, and the multipliers are stored in rows kl+ku+1 to 2*kl+ku.

in

ldafb

The leading dimension of AFB. ldafb>=2*kl+ku+1.

in

ipiv

Array of dimension n. The pivot indices from CGBTRF.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

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

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by CGBTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension nrhs. The estimated forward error bound for each solution vector X(j).

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j).

out

work

Complex workspace array of dimension (2*n).

out

rwork

Real workspace array of dimension (n).

out

info

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

zgbrfs

Functions

void zgbrfs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const c128* restrict AB,
    const INT            ldab,
    const c128* restrict AFB,
    const INT            ldafb,
    const INT*  restrict ipiv,
    const c128* restrict B,
    const INT            ldb,
          c128* restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);

void zgbrfs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const c128 *restrict AB, const INT ldab, const c128 *restrict AFB, const INT ldafb, const INT *restrict ipiv, const c128 *restrict B, const INT ldb, c128 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, c128 *restrict work, f64 *restrict rwork, INT *info)#

ZGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.

Parameters

in

trans

Specifies the form of the system of equations:

'N': A * X = B (No transpose)
'T': A**T * X = B (Transpose)
'C': A**H * X = B (Conjugate transpose)

in

n

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. nrhs>=0.

in

AB

Array of dimension (ldab, n). The original band matrix A, stored in rows 0 to kl+ku. The j-th column of A is stored in the j-th column of AB: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(n-1,j+kl).

in

ldab

The leading dimension of AB. ldab>=kl+ku+1.

in

AFB

Array of dimension (ldafb, n). The LU factorization of A, as computed by ZGBTRF. U is stored in rows 0 to kl+ku, and the multipliers are stored in rows kl+ku+1 to 2*kl+ku.

in

ldafb

The leading dimension of AFB. ldafb>=2*kl+ku+1.

in

ipiv

Array of dimension n. The pivot indices from ZGBTRF.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

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

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by ZGBTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension nrhs. The estimated forward error bound for each solution vector X(j).

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j).

out

work

Complex workspace array of dimension (2*n).

out

rwork

Real workspace array of dimension (n).

out

info

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