gerfs

sgerfs

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

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

in

lda

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

in

AF

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

in

ldaf

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

in

ipiv

Array of dimension n. The pivot indices from sgetrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

The leading dimension of the array 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

dgerfs

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

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

in

lda

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

in

AF

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

in

ldaf

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

in

ipiv

Array of dimension n. The pivot indices from dgetrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

The leading dimension of the array 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

cgerfs

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

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

in

lda

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

in

AF

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

in

ldaf

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

in

ipiv

Array of dimension n. The pivot indices from cgetrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

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

out

ferr

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

out

berr

Real 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

zgerfs

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

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

in

lda

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

in

AF

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

in

ldaf

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

in

ipiv

Array of dimension n. The pivot indices from zgetrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

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

out

ferr

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

out

berr

Real 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