la_gerpvgrw

sla_gerpvgrw

Functions

f32 sla_gerpvgrw(
    const INT           n,
    const INT           ncols,
    const f32* restrict A,
    const INT           lda,
    const f32* restrict AF,
    const INT           ldaf
);

f32 sla_gerpvgrw(const INT n, const INT ncols, const f32 *restrict A, const INT lda, const f32 *restrict AF, const INT ldaf)

SLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U).

The “max absolute element” norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Parameters

in

n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in

ncols

The number of columns of the matrix A. ncols >= 0.

in

A

Single precision array, dimension (lda, n). On entry, the N-by-N matrix A.

in

lda

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

in

AF

Single precision array, 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).

Returns:

The reciprocal pivot growth factor.

dla_gerpvgrw

Functions

f64 dla_gerpvgrw(
    const INT           n,
    const INT           ncols,
    const f64* restrict A,
    const INT           lda,
    const f64* restrict AF,
    const INT           ldaf
);

f64 dla_gerpvgrw(const INT n, const INT ncols, const f64 *restrict A, const INT lda, const f64 *restrict AF, const INT ldaf)

DLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U).

The “max absolute element” norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Parameters

in

n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in

ncols

The number of columns of the matrix A. ncols >= 0.

in

A

Double precision array, dimension (lda, n). On entry, the N-by-N matrix A.

in

lda

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

in

AF

Double precision array, 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).

Returns:

The reciprocal pivot growth factor.

cla_gerpvgrw

Functions

f32 cla_gerpvgrw(
    const INT           n,
    const INT           ncols,
    const c64* restrict A,
    const INT           lda,
    const c64* restrict AF,
    const INT           ldaf
);

f32 cla_gerpvgrw(const INT n, const INT ncols, const c64 *restrict A, const INT lda, const c64 *restrict AF, const INT ldaf)

CLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U).

The “max absolute element” norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Parameters

in

n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in

ncols

The number of columns of the matrix A. ncols >= 0.

in

A

Complex array, dimension (lda, n). On entry, the N-by-N matrix A.

in

lda

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

in

AF

Complex array, 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).

Returns:

The reciprocal pivot growth factor.

zla_gerpvgrw

Functions

f64 zla_gerpvgrw(
    const INT            n,
    const INT            ncols,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict AF,
    const INT            ldaf
);

f64 zla_gerpvgrw(const INT n, const INT ncols, const c128 *restrict A, const INT lda, const c128 *restrict AF, const INT ldaf)

ZLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U).

The “max absolute element” norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Parameters

in

n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in

ncols

The number of columns of the matrix A. ncols >= 0.

in

A

Complex array, dimension (lda, n). On entry, the N-by-N matrix A.

in

lda

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

in

AF

Complex array, 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).

Returns:

The reciprocal pivot growth factor.