hprfs

chprfs

Functions

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

CHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite 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, i.e., the number of columns of the matrices B and X. nrhs>=0.

in

AP

Array of dimension n*(n+1)/2. The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1.

in

AFP

Array of dimension n*(n+1)/2. The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by chptrf, stored as a packed triangular matrix.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by chptrf.

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 chptrs. 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) (the j-th column of the solution matrix X). If xtrue is the true solution corresponding to X(j), ferr[j] is an estimated upper bound for the magnitude of the largest element in (X(j)-xtrue) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for rcond, and is almost always a slight overestimate of the true error.

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

out

work

Workspace array of dimension 2*n.

out

rwork

Workspace array of dimension n.

out

info

• info=0: successful exit

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

zhprfs

Functions

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

ZHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite 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, i.e., the number of columns of the matrices B and X. nrhs>=0.

in

AP

Array of dimension n*(n+1)/2. The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1.

in

AFP

Array of dimension n*(n+1)/2. The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by zhptrf, stored as a packed triangular matrix.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by zhptrf.

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 zhptrs. 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) (the j-th column of the solution matrix X). If xtrue is the true solution corresponding to X(j), ferr[j] is an estimated upper bound for the magnitude of the largest element in (X(j)-xtrue) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for rcond, and is almost always a slight overestimate of the true error.

out

berr

Array of dimension nrhs. The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

out

work

Workspace array of dimension 2*n.

out

rwork

Workspace array of dimension n.

out

info

• info=0: successful exit

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