pprfs#

Functions

void spprfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict AP,
    const f32*  restrict AFP,
    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 spprfs(const char *uplo, const INT n, const INT nrhs, const f32 *restrict AP, const f32 *restrict AFP, 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)#

SPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, 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
AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

in
AFP

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPPTRF, packed columnwise. Array of dimension (n*(n+1)/2).

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 SPPTRS. 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

  • = 0: successful exit

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

Functions

void dpprfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict AP,
    const f64*  restrict AFP,
    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 dpprfs(const char *uplo, const INT n, const INT nrhs, const f64 *restrict AP, const f64 *restrict AFP, 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)#

DPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, 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
AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

in
AFP

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPPTRF, packed columnwise. Array of dimension (n*(n+1)/2).

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 DPPTRS. 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

  • = 0: successful exit

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

Functions

void cpprfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict AP,
    const c64*  restrict AFP,
    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 cpprfs(const char *uplo, const INT n, const INT nrhs, const c64 *restrict AP, const c64 *restrict AFP, 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)#

CPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, 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
AP

The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

in
AFP

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPPTRF, packed columnwise. Array of dimension (n*(n+1)/2).

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 CPPTRS. 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

Complex workspace array of dimension (2*n).

out
rwork

Single precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void zpprfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c128* restrict AP,
    const c128* restrict AFP,
    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 zpprfs(const char *uplo, const INT n, const INT nrhs, const c128 *restrict AP, const c128 *restrict AFP, 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)#

ZPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, 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
AP

The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

in
AFP

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPPTRF, packed columnwise. Array of dimension (n*(n+1)/2).

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 ZPPTRS. 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

Complex workspace array of dimension (2*n).

out
rwork

Double precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

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