Visible to Intel only — GUID: GUID-E444F8B5-430A-4228-B9E3-425DA7502A48
Visible to Intel only — GUID: GUID-E444F8B5-430A-4228-B9E3-425DA7502A48
?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If equed = 'B': Both row and column equilibration, that is, A has been replaced by diag(r)*A*diag(c).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.