ZGBEQU(3F) ZGBEQU(3F)
ZGBEQU - compute row and column scalings intended to equilibrate an Mby-N
band matrix A and reduce its condition number
SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INFO )
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 AB( LDAB, * )
ZGBEQU computes row and column scalings intended to equilibrate an M-by-N
band matrix A and reduce its condition number. R returns the row scale
factors and C the column scale factors, chosen to try to make the largest
element in each row and column of the matrix B with elements
B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe number
and BIGNUM = largest safe number. Use of these scaling factors is not
guaranteed to reduce the condition number of A but works well in
practice.
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) COMPLEX*16 array, dimension (LDAB,N)
The band matrix A, stored 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 (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
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ZGBEQU(3F) ZGBEQU(3F)
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) DOUBLE PRECISION
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is
neither too large nor too small, it is not worth scaling by R.
COLCND (output) DOUBLE PRECISION
If INFO = 0, COLCND contains the ratio of the smallest C(i) to
the largest C(i). If COLCND >= 0.1, it is not worth scaling by
C.
AMAX (output) DOUBLE PRECISION
Absolute value of largest matrix element. If AMAX is very close
to overflow or very close to underflow, the matrix should be
scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero
ZGBEQU(3F) ZGBEQU(3F)
ZGBEQU - compute row and column scalings intended to equilibrate an Mby-N
band matrix A and reduce its condition number
SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INFO )
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 AB( LDAB, * )
ZGBEQU computes row and column scalings intended to equilibrate an M-by-N
band matrix A and reduce its condition number. R returns the row scale
factors and C the column scale factors, chosen to try to make the largest
element in each row and column of the matrix B with elements
B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe number
and BIGNUM = largest safe number. Use of these scaling factors is not
guaranteed to reduce the condition number of A but works well in
practice.
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) COMPLEX*16 array, dimension (LDAB,N)
The band matrix A, stored 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 (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
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ZGBEQU(3F) ZGBEQU(3F)
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) DOUBLE PRECISION
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is
neither too large nor too small, it is not worth scaling by R.
COLCND (output) DOUBLE PRECISION
If INFO = 0, COLCND contains the ratio of the smallest C(i) to
the largest C(i). If COLCND >= 0.1, it is not worth scaling by
C.
AMAX (output) DOUBLE PRECISION
Absolute value of largest matrix element. If AMAX is very close
to overflow or very close to underflow, the matrix should be
scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero
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