gerfs#

Functions

void sgerfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict A,
    const INT            lda,
    const f32*  restrict AF,
    const INT            ldaf,
    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 sgerfs(const char *trans, const INT n, const INT nrhs, const f32 *restrict A, const INT lda, const f32 *restrict AF, const INT ldaf, 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)#

SGERFS improves the computed solution to a system of linear equations 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
nrhs

The number of right hand sides (nrhs >= 0).

in
A

The original N-by-N matrix A. Array of dimension (lda, n).

in
lda

The leading dimension of the array A (lda >= max(1,n)).

in
AF

The factors L and U from the factorization A = P*L*U as computed by sgetrf. Array of dimension (ldaf, n).

in
ldaf

The leading dimension of the array AF (ldaf >= max(1,n)).

in
ipiv

The pivot indices from sgetrf. Array of dimension n.

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

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

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

void dgerfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict A,
    const INT            lda,
    const f64*  restrict AF,
    const INT            ldaf,
    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 dgerfs(const char *trans, const INT n, const INT nrhs, const f64 *restrict A, const INT lda, const f64 *restrict AF, const INT ldaf, 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)#

DGERFS improves the computed solution to a system of linear equations 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
nrhs

The number of right hand sides (nrhs >= 0).

in
A

The original N-by-N matrix A. Array of dimension (lda, n).

in
lda

The leading dimension of the array A (lda >= max(1,n)).

in
AF

The factors L and U from the factorization A = P*L*U as computed by dgetrf. Array of dimension (ldaf, n).

in
ldaf

The leading dimension of the array AF (ldaf >= max(1,n)).

in
ipiv

The pivot indices from dgetrf. Array of dimension n.

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

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

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

void cgerfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict AF,
    const INT            ldaf,
    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 cgerfs(const char *trans, const INT n, const INT nrhs, const c64 *restrict A, const INT lda, const c64 *restrict AF, const INT ldaf, 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)#

CGERFS improves the computed solution to a system of linear equations 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
nrhs

The number of right hand sides (nrhs >= 0).

in
A

The original N-by-N matrix A. Complex array of dimension (lda, n).

in
lda

The leading dimension of the array A (lda >= max(1,n)).

in
AF

The factors L and U from the factorization A = P*L*U as computed by cgetrf. Complex array of dimension (ldaf, n).

in
ldaf

The leading dimension of the array AF (ldaf >= max(1,n)).

in
ipiv

The pivot indices from cgetrf. Array of dimension n.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X, as computed by cgetrs. On exit, the improved solution matrix X. Complex array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

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

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

void zgerfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict AF,
    const INT            ldaf,
    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 zgerfs(const char *trans, const INT n, const INT nrhs, const c128 *restrict A, const INT lda, const c128 *restrict AF, const INT ldaf, 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)#

ZGERFS improves the computed solution to a system of linear equations 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
nrhs

The number of right hand sides (nrhs >= 0).

in
A

The original N-by-N matrix A. Complex array of dimension (lda, n).

in
lda

The leading dimension of the array A (lda >= max(1,n)).

in
AF

The factors L and U from the factorization A = P*L*U as computed by zgetrf. Complex array of dimension (ldaf, n).

in
ldaf

The leading dimension of the array AF (ldaf >= max(1,n)).

in
ipiv

The pivot indices from zgetrf. Array of dimension n.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X, as computed by zgetrs. On exit, the improved solution matrix X. Complex array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

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

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

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