ZLAQGB(3F) ZLAQGB(3F)
ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals
and KU superdiagonals using the row and scaling factors in the vectors R
and C
SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
EQUED )
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 AB( LDAB, * )
ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
and KU superdiagonals using the row and scaling factors in the vectors R
and C.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB (input/output) COMPLEX*16 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,jku)<=i<=min(m,j+kl)
On exit, the equilibrated matrix, in the same storage format as
A. See EQUED for the form of the equilibrated matrix.
LDAB (input) INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
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ZLAQGB(3F) ZLAQGB(3F)
R (output) DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
ROWCND (output) DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
COLCND (output) DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
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equilibration, i.e., A has been replaced by diag(R) * A *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).
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.
ZLAQGB(3F) ZLAQGB(3F)
ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals
and KU superdiagonals using the row and scaling factors in the vectors R
and C
SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
EQUED )
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 AB( LDAB, * )
ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
and KU superdiagonals using the row and scaling factors in the vectors R
and C.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB (input/output) COMPLEX*16 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,jku)<=i<=min(m,j+kl)
On exit, the equilibrated matrix, in the same storage format as
A. See EQUED for the form of the equilibrated matrix.
LDAB (input) INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
Page 1
ZLAQGB(3F) ZLAQGB(3F)
R (output) DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
ROWCND (output) DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
COLCND (output) DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
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).
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.
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