geequb#

Functions

void sgeequb(
    const INT           m,
    const INT           n,
    const f32* restrict A,
    const INT           lda,
          f32* restrict R,
          f32* restrict C,
          f32*          rowcnd,
          f32*          colcnd,
          f32*          amax,
          INT*          info
);
void sgeequb(const INT m, const INT n, const f32 *restrict A, const INT lda, f32 *restrict R, f32 *restrict C, f32 *rowcnd, f32 *colcnd, f32 *amax, INT *info)#

SGEEQUB computes row and column scalings intended to equilibrate an m-by-n 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 an absolute value of at most the radix.

R(i) and C(j) are restricted to be a power of the radix 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.

This routine differs from SGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries’ magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

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
A

Array of dimension (lda, n). The m-by-n matrix whose equilibration factors are to be computed.

in
lda

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

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 dgeequb(
    const INT           m,
    const INT           n,
    const f64* restrict A,
    const INT           lda,
          f64* restrict R,
          f64* restrict C,
          f64*          rowcnd,
          f64*          colcnd,
          f64*          amax,
          INT*          info
);
void dgeequb(const INT m, const INT n, const f64 *restrict A, const INT lda, f64 *restrict R, f64 *restrict C, f64 *rowcnd, f64 *colcnd, f64 *amax, INT *info)#

DGEEQUB computes row and column scalings intended to equilibrate an m-by-n 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 an absolute value of at most the radix.

R(i) and C(j) are restricted to be a power of the radix 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.

This routine differs from DGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries’ magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

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
A

Array of dimension (lda, n). The m-by-n matrix whose equilibration factors are to be computed.

in
lda

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

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 cgeequb(
    const INT           m,
    const INT           n,
    const c64* restrict A,
    const INT           lda,
          f32* restrict R,
          f32* restrict C,
          f32*          rowcnd,
          f32*          colcnd,
          f32*          amax,
          INT*          info
);
void cgeequb(const INT m, const INT n, const c64 *restrict A, const INT lda, f32 *restrict R, f32 *restrict C, f32 *rowcnd, f32 *colcnd, f32 *amax, INT *info)#

CGEEQUB computes row and column scalings intended to equilibrate an m-by-n 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 an absolute value of at most the radix.

R(i) and C(j) are restricted to be a power of the radix 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.

This routine differs from CGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries’ magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

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
A

Array of dimension (lda, n). The m-by-n matrix whose equilibration factors are to be computed.

in
lda

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

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 zgeequb(
    const INT            m,
    const INT            n,
    const c128* restrict A,
    const INT            lda,
          f64*  restrict R,
          f64*  restrict C,
          f64*           rowcnd,
          f64*           colcnd,
          f64*           amax,
          INT*           info
);
void zgeequb(const INT m, const INT n, const c128 *restrict A, const INT lda, f64 *restrict R, f64 *restrict C, f64 *rowcnd, f64 *colcnd, f64 *amax, INT *info)#

ZGEEQUB computes row and column scalings intended to equilibrate an m-by-n 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 an absolute value of at most the radix.

R(i) and C(j) are restricted to be a power of the radix 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.

This routine differs from ZGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries’ magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

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
A

Array of dimension (lda, n). The m-by-n matrix whose equilibration factors are to be computed.

in
lda

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

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)