porfs#

Functions

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

SPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

The order of the matrix A. n >= 0.

in
nrhs

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

in
A

The symmetric matrix A. Array of dimension (lda, n).

in
lda

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

in
AF

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. Array of dimension (ldaf, n).

in
ldaf

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

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

The componentwise relative backward error. Array of dimension (nrhs).

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

DPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

The order of the matrix A. n >= 0.

in
nrhs

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

in
A

The symmetric matrix A. Array of dimension (lda, n).

in
lda

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

in
AF

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. Array of dimension (ldaf, n).

in
ldaf

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

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

The componentwise relative backward error. Array of dimension (nrhs).

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

CPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

The order of the matrix A. n >= 0.

in
nrhs

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

in
A

The Hermitian matrix A. Array of dimension (lda, n).

in
lda

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

in
AF

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. Array of dimension (ldaf, n).

in
ldaf

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

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

The componentwise relative backward error. Array of dimension (nrhs).

out
work

Complex workspace array of dimension (2*n).

out
rwork

Single precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

ZPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

The order of the matrix A. n >= 0.

in
nrhs

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

in
A

The Hermitian matrix A. Array of dimension (lda, n).

in
lda

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

in
AF

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. Array of dimension (ldaf, n).

in
ldaf

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

in
B

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

in
ldb

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

inout
X

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

in
ldx

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

out
ferr

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

out
berr

The componentwise relative backward error. Array of dimension (nrhs).

out
work

Complex workspace array of dimension (2*n).

out
rwork

Double precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

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