gbequ#

Functions

void sgbequ(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
    const f32* restrict AB,
    const INT           ldab,
          f32* restrict R,
          f32* restrict C,
          f32*          rowcnd,
          f32*          colcnd,
          f32*          amax,
          INT*          info
);
void sgbequ(const INT m, const INT n, const INT kl, const INT ku, const f32 *restrict AB, const INT ldab, f32 *restrict R, f32 *restrict C, f32 *rowcnd, f32 *colcnd, f32 *amax, INT *info)#

SGBEQU computes row and column scalings intended to equilibrate an m-by-n band matrix A and reduce its condition number.

R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

Parameters

in
m

The number of rows of the matrix A. m>=0.

in
n

The number of columns 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
AB

Array of dimension (ldab, n). The band matrix A, stored in band format. The matrix A is stored in rows 0 to kl+ku, so that AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(m-1,j+kl).

in
ldab

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

out
R

Array of dimension m. If info=0 or info>m, R contains the row scale factors for A.

out
C

Array of dimension n. If info=0, C contains the column scale factors for A.

out
rowcnd

If info=0 or info>m, rowcnd contains the ratio of the smallest R(i) to the largest R(i). If rowcnd>=0.1 and amax is neither too large nor too small, it is not worth scaling by R.

out
colcnd

If info=0, colcnd contains the ratio of the smallest C(j) to the largest C(j). If colcnd>=0.1, it is not worth scaling by C.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, and i is

    • i<=m: the i-th row of A is exactly zero (1-based)

    • i>m: the (i-m)-th column of A is exactly zero (1-based)

Functions

void dgbequ(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
    const f64* restrict AB,
    const INT           ldab,
          f64* restrict R,
          f64* restrict C,
          f64*          rowcnd,
          f64*          colcnd,
          f64*          amax,
          INT*          info
);
void dgbequ(const INT m, const INT n, const INT kl, const INT ku, const f64 *restrict AB, const INT ldab, f64 *restrict R, f64 *restrict C, f64 *rowcnd, f64 *colcnd, f64 *amax, INT *info)#

DGBEQU computes row and column scalings intended to equilibrate an m-by-n band matrix A and reduce its condition number.

R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

Parameters

in
m

The number of rows of the matrix A. m>=0.

in
n

The number of columns 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
AB

Array of dimension (ldab, n). The band matrix A, stored in band format. The matrix A is stored in rows 0 to kl+ku, so that AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(m-1,j+kl).

in
ldab

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

out
R

Array of dimension m. If info=0 or info>m, R contains the row scale factors for A.

out
C

Array of dimension n. If info=0, C contains the column scale factors for A.

out
rowcnd

If info=0 or info>m, rowcnd contains the ratio of the smallest R(i) to the largest R(i). If rowcnd>=0.1 and amax is neither too large nor too small, it is not worth scaling by R.

out
colcnd

If info=0, colcnd contains the ratio of the smallest C(j) to the largest C(j). If colcnd>=0.1, it is not worth scaling by C.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, and i is

    • i<=m: the i-th row of A is exactly zero (1-based)

    • i>m: the (i-m)-th column of A is exactly zero (1-based)

Functions

void cgbequ(
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
    const c64* restrict AB,
    const INT           ldab,
          f32* restrict R,
          f32* restrict C,
          f32*          rowcnd,
          f32*          colcnd,
          f32*          amax,
          INT*          info
);
void cgbequ(const INT m, const INT n, const INT kl, const INT ku, const c64 *restrict AB, const INT ldab, f32 *restrict R, f32 *restrict C, f32 *rowcnd, f32 *colcnd, f32 *amax, INT *info)#

CGBEQU computes row and column scalings intended to equilibrate an m-by-n band matrix A and reduce its condition number.

R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

Parameters

in
m

The number of rows of the matrix A. m>=0.

in
n

The number of columns 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
AB

Array of dimension (ldab, n). The band matrix A, stored in band format. The matrix A is stored in rows 0 to kl+ku, so that AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(m-1,j+kl).

in
ldab

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

out
R

Array of dimension m. If info=0 or info>m, R contains the row scale factors for A.

out
C

Array of dimension n. If info=0, C contains the column scale factors for A.

out
rowcnd

If info=0 or info>m, rowcnd contains the ratio of the smallest R(i) to the largest R(i). If rowcnd>=0.1 and amax is neither too large nor too small, it is not worth scaling by R.

out
colcnd

If info=0, colcnd contains the ratio of the smallest C(j) to the largest C(j). If colcnd>=0.1, it is not worth scaling by C.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, and i is

    • i<=m: the i-th row of A is exactly zero (1-based)

    • i>m: the (i-m)-th column of A is exactly zero (1-based)

Functions

void zgbequ(
    const INT            m,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const c128* restrict AB,
    const INT            ldab,
          f64*  restrict R,
          f64*  restrict C,
          f64*           rowcnd,
          f64*           colcnd,
          f64*           amax,
          INT*           info
);
void zgbequ(const INT m, const INT n, const INT kl, const INT ku, const c128 *restrict AB, const INT ldab, f64 *restrict R, f64 *restrict C, f64 *rowcnd, f64 *colcnd, f64 *amax, INT *info)#

ZGBEQU computes row and column scalings intended to equilibrate an m-by-n band matrix A and reduce its condition number.

R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

Parameters

in
m

The number of rows of the matrix A. m>=0.

in
n

The number of columns 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
AB

Array of dimension (ldab, n). The band matrix A, stored in band format. The matrix A is stored in rows 0 to kl+ku, so that AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku)<=i<=min(m-1,j+kl).

in
ldab

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

out
R

Array of dimension m. If info=0 or info>m, R contains the row scale factors for A.

out
C

Array of dimension n. If info=0, C contains the column scale factors for A.

out
rowcnd

If info=0 or info>m, rowcnd contains the ratio of the smallest R(i) to the largest R(i). If rowcnd>=0.1 and amax is neither too large nor too small, it is not worth scaling by R.

out
colcnd

If info=0, colcnd contains the ratio of the smallest C(j) to the largest C(j). If colcnd>=0.1, it is not worth scaling by C.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, and i is

    • i<=m: the i-th row of A is exactly zero (1-based)

    • i>m: the (i-m)-th column of A is exactly zero (1-based)