la_gbrpvgrw#

Functions

f32 sla_gbrpvgrw(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           ncols,
    const f32* restrict AB,
    const INT           ldab,
    const f32* restrict AFB,
    const INT           ldafb
);
f32 sla_gbrpvgrw(const INT n, const INT kl, const INT ku, const INT ncols, const f32 *restrict AB, const INT ldab, const f32 *restrict AFB, const INT ldafb)#

SLA_GBRPVGRW 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
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
ncols

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

in
AB

Single precision array, dimension (ldab, n). On entry, the matrix A in band storage, in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl)

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

in
AFB

Single precision array, dimension (ldafb, n). Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku (0-based), and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldafb

The leading dimension of the array AFB. ldafb >= 2*kl+ku+1.

Returns:

The reciprocal pivot growth factor.

Functions

f64 dla_gbrpvgrw(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           ncols,
    const f64* restrict AB,
    const INT           ldab,
    const f64* restrict AFB,
    const INT           ldafb
);
f64 dla_gbrpvgrw(const INT n, const INT kl, const INT ku, const INT ncols, const f64 *restrict AB, const INT ldab, const f64 *restrict AFB, const INT ldafb)#

DLA_GBRPVGRW 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
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
ncols

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

in
AB

Double precision array, dimension (ldab, n). On entry, the matrix A in band storage, in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl)

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

in
AFB

Double precision array, dimension (ldafb, n). Details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku (0-based), and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldafb

The leading dimension of the array AFB. ldafb >= 2*kl+ku+1.

Returns:

The reciprocal pivot growth factor.

Functions

f32 cla_gbrpvgrw(
    const INT           n,
    const INT           kl,
    const INT           ku,
    const INT           ncols,
    const c64* restrict AB,
    const INT           ldab,
    const c64* restrict AFB,
    const INT           ldafb
);
f32 cla_gbrpvgrw(const INT n, const INT kl, const INT ku, const INT ncols, const c64 *restrict AB, const INT ldab, const c64 *restrict AFB, const INT ldafb)#

CLA_GBRPVGRW 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
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
ncols

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

in
AB

Single complex array, dimension (ldab, n). On entry, the matrix A in band storage, in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl)

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

in
AFB

Single complex array, dimension (ldafb, n). Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku (0-based), and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldafb

The leading dimension of the array AFB. ldafb >= 2*kl+ku+1.

Returns:

The reciprocal pivot growth factor.

Functions

f64 zla_gbrpvgrw(
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            ncols,
    const c128* restrict AB,
    const INT            ldab,
    const c128* restrict AFB,
    const INT            ldafb
);
f64 zla_gbrpvgrw(const INT n, const INT kl, const INT ku, const INT ncols, const c128 *restrict AB, const INT ldab, const c128 *restrict AFB, const INT ldafb)#

ZLA_GBRPVGRW 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
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
ncols

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

in
AB

Double complex array, dimension (ldab, n). On entry, the matrix A in band storage, in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl)

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

in
AFB

Double complex array, dimension (ldafb, n). Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku (0-based), and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldafb

The leading dimension of the array AFB. ldafb >= 2*kl+ku+1.

Returns:

The reciprocal pivot growth factor.