laqgb#

Functions

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

SLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and column scaling factors in the vectors R and C.

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.

inout
AB

On entry, the matrix A in band storage, in rows 0 to kl+ku. 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(m-1,j+kl). On exit, the equilibrated matrix in the same storage format. Array of dimension (ldab, n).

in
ldab

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

in
R

The row scale factors for A. Array of dimension (m).

in
C

The column scale factors for A. Array of dimension (n).

in
rowcnd

Ratio of the smallest R(i) to the largest R(i).

in
colcnd

Ratio of the smallest C(i) to the largest C(i).

in
amax

Absolute value of largest matrix entry.

out
equed

Specifies the form of equilibration that was done: = ‘N’: No equilibration = ‘R’: Row equilibration, i.e., A has been premultiplied by diag(R). = ‘C’: Column equilibration, i.e., A has been postmultiplied by diag(C). = ‘B’: Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

Functions

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

DLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and column scaling factors in the vectors R and C.

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.

inout
AB

On entry, the matrix A in band storage, in rows 0 to kl+ku. 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(m-1,j+kl). On exit, the equilibrated matrix in the same storage format. Array of dimension (ldab, n).

in
ldab

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

in
R

The row scale factors for A. Array of dimension (m).

in
C

The column scale factors for A. Array of dimension (n).

in
rowcnd

Ratio of the smallest R(i) to the largest R(i).

in
colcnd

Ratio of the smallest C(i) to the largest C(i).

in
amax

Absolute value of largest matrix entry.

out
equed

Specifies the form of equilibration that was done: = ‘N’: No equilibration = ‘R’: Row equilibration, i.e., A has been premultiplied by diag(R). = ‘C’: Column equilibration, i.e., A has been postmultiplied by diag(C). = ‘B’: Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

Functions

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

CLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and column scaling factors in the vectors R and C.

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.

inout
AB

On entry, the matrix A in band storage, in rows 0 to kl+ku. 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(m-1,j+kl). On exit, the equilibrated matrix in the same storage format. Array of dimension (ldab, n).

in
ldab

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

in
R

The row scale factors for A. Array of dimension (m).

in
C

The column scale factors for A. Array of dimension (n).

in
rowcnd

Ratio of the smallest R(i) to the largest R(i).

in
colcnd

Ratio of the smallest C(i) to the largest C(i).

in
amax

Absolute value of largest matrix entry.

out
equed

Specifies the form of equilibration that was done: = ‘N’: No equilibration = ‘R’: Row equilibration, i.e., A has been premultiplied by diag(R). = ‘C’: Column equilibration, i.e., A has been postmultiplied by diag(C). = ‘B’: Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

Functions

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

ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and column scaling factors in the vectors R and C.

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.

inout
AB

On entry, the matrix A in band storage, in rows 0 to kl+ku. 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(m-1,j+kl). On exit, the equilibrated matrix in the same storage format. Array of dimension (ldab, n).

in
ldab

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

in
R

The row scale factors for A. Array of dimension (m).

in
C

The column scale factors for A. Array of dimension (n).

in
rowcnd

Ratio of the smallest R(i) to the largest R(i).

in
colcnd

Ratio of the smallest C(i) to the largest C(i).

in
amax

Absolute value of largest matrix entry.

out
equed

Specifies the form of equilibration that was done: = ‘N’: No equilibration = ‘R’: Row equilibration, i.e., A has been premultiplied by diag(R). = ‘C’: Column equilibration, i.e., A has been postmultiplied by diag(C). = ‘B’: Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

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