?laqgb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?laqgb

Scales a general band matrix, using row and column scaling factors computed by ?gbequ.

Syntax

call slaqgb( m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed )

call dlaqgb( m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed )

call claqgb( m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed )

call zlaqgb( m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed )

Include Files

mkl.fi

Description

The routine 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.

Input Parameters

m

INTEGER. The number of rows of the matrix A. m≥ 0.

n

INTEGER. The number of columns of the matrix A. n≥ 0.

kl

INTEGER. The number of subdiagonals within the band of A. kl≥ 0.

ku

INTEGER. The number of superdiagonals within the band of A. ku≥ 0.

ab

REAL for slaqgb

DOUBLE PRECISION for dlaqgb

COMPLEX for claqgb

DOUBLE COMPLEX for zlaqgb

Array, DIMENSION (ldab,n). On entry, the matrix A in band storage, in rows 1 to kl+ku+1. The j-th column of A is stored in the j-th column of the array ab as follows: ab(ku+1+i-j,j) = A(i,j) for max(1,j-ku) ≤ i ≤ min(m,j+kl).

ldab

INTEGER. The leading dimension of the array ab.

lda≥kl+ku+1.

amax

REAL for slaqgb/claqgb

DOUBLE PRECISION for dlaqgb/zlaqgb

Absolute value of largest matrix entry.

r, c

REAL for slaqgb/claqgb

DOUBLE PRECISION for dlaqgb/zlaqgb

Arrays r (m), c (n). Contain the row and column scale factors for A, respectively.

rowcnd

REAL for slaqgb/claqgb

DOUBLE PRECISION for dlaqgb/zlaqgb

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

colcnd

REAL for slaqgb/claqgb

DOUBLE PRECISION for dlaqgb/zlaqgb

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

Output Parameters

ab

On exit, the equilibrated matrix, in the same storage format as A.

See equed for the form of the equilibrated matrix.

equed

CHARACTER*1.

Specifies the form of equilibration that was done.

If equed = 'N': No equilibration

If equed = 'R': Row equilibration, that is, A has been premultiplied by diag(r).

If equed = 'C': Column equilibration, that is, A has been postmultiplied by diag(c).

If equed = 'B': Both row and column equilibration, that is, A has been replaced by diag(r)*A*diag(c).

Application Notes

The routine uses internal parameters thresh, large, and small, which have the following meaning. thresh is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors. If rowcnd < thresh, row scaling is done, and if colcnd < thresh, column scaling is done. large and small are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element. If amax > large or amax < small, row scaling is done.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laqgb