laqgb(3) LAPACK laqgb(3)
NAME
laqgb - laqgb: row/col scale matrix
SYNOPSIS
Functions
subroutine claqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax,
equed)
CLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
subroutine dlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax,
equed)
DLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
subroutine slaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax,
equed)
SLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
subroutine zlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax,
equed)
ZLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
Detailed Description
Function Documentation
subroutine claqgb (integer m, integer n, integer kl, integer ku, complex,
dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,
dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)
CLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
Purpose:
CLAQGB 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.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB
AB is COMPLEX 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)
On exit, the equilibrated matrix, in the same storage format
as A. See EQUED for the form of the equilibrated matrix.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R
R is REAL array, dimension (M)
The row scale factors for A.
C
C is REAL array, dimension (N)
The column scale factors for A.
ROWCND
ROWCND is REAL
Ratio of the smallest R(i) to the largest R(i).
COLCND
COLCND is REAL
Ratio of the smallest C(i) to the largest C(i).
AMAX
AMAX is REAL
Absolute value of largest matrix entry.
EQUED
EQUED is 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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dlaqgb (integer m, integer n, integer kl, integer ku, double
precision, dimension( ldab, * ) ab, integer ldab, double precision,
dimension( * ) r, double precision, dimension( * ) c, double precision
rowcnd, double precision colcnd, double precision amax, character equed)
DLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
Purpose:
DLAQGB 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.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB
AB is DOUBLE PRECISION 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)
On exit, the equilibrated matrix, in the same storage format
as A. See EQUED for the form of the equilibrated matrix.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R
R is DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
C
C is DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
ROWCND
ROWCND is DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
COLCND
COLCND is DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
AMAX
AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED
EQUED is 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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine slaqgb (integer m, integer n, integer kl, integer ku, real,
dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,
dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)
SLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
Purpose:
SLAQGB 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.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB
AB is REAL 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)
On exit, the equilibrated matrix, in the same storage format
as A. See EQUED for the form of the equilibrated matrix.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R
R is REAL array, dimension (M)
The row scale factors for A.
C
C is REAL array, dimension (N)
The column scale factors for A.
ROWCND
ROWCND is REAL
Ratio of the smallest R(i) to the largest R(i).
COLCND
COLCND is REAL
Ratio of the smallest C(i) to the largest C(i).
AMAX
AMAX is REAL
Absolute value of largest matrix entry.
EQUED
EQUED is 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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zlaqgb (integer m, integer n, integer kl, integer ku, complex*16,
dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
r, double precision, dimension( * ) c, double precision rowcnd, double
precision colcnd, double precision amax, character equed)
ZLAQGB scales a general band matrix, using row and column scaling
factors computed by sgbequ.
Purpose:
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.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB
AB is 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,j-ku)<=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
LDAB is INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R
R is DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
C
C is DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
ROWCND
ROWCND is DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
COLCND
COLCND is DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
AMAX
AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED
EQUED is 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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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