table of contents
| geequb(3) | LAPACK | geequb(3) |
NAME¶
geequb - geequb: equilibration, power of 2
SYNOPSIS¶
Functions¶
subroutine cgeequb (m, n, a, lda, r, c, rowcnd, colcnd,
amax, info)
CGEEQUB subroutine dgeequb (m, n, a, lda, r, c, rowcnd, colcnd,
amax, info)
DGEEQUB subroutine sgeequb (m, n, a, lda, r, c, rowcnd, colcnd,
amax, info)
SGEEQUB subroutine zgeequb (m, n, a, lda, r, c, rowcnd, colcnd,
amax, info)
ZGEEQUB
Detailed Description¶
Function Documentation¶
subroutine cgeequb (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)¶
CGEEQUB
Purpose:
CGEEQUB computes row and column scalings intended to equilibrate an
M-by-N 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 an absolute value of at most
the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from CGEEQU by restricting the scaling factors
to a power of the radix. Barring over- and underflow, scaling by
these factors introduces no additional rounding errors. However, the
scaled entries' magnitudes are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
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.
A
A is COMPLEX array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
R
R is REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C
C is REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND
ROWCND is REAL
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
COLCND is REAL
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
AMAX is REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
INFO
INFO is 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dgeequb (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)¶
DGEEQUB
Purpose:
DGEEQUB computes row and column scalings intended to equilibrate an
M-by-N 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 an absolute value of at most
the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from DGEEQU by restricting the scaling factors
to a power of the radix. Barring over- and underflow, scaling by
these factors introduces no additional rounding errors. However, the
scaled entries' magnitudes are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
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.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
R
R is DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C
C is DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND
ROWCND is 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
COLCND is 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
AMAX is 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
INFO is 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sgeequb (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)¶
SGEEQUB
Purpose:
SGEEQUB computes row and column scalings intended to equilibrate an
M-by-N 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 an absolute value of at most
the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from SGEEQU by restricting the scaling factors
to a power of the radix. Barring over- and underflow, scaling by
these factors introduces no additional rounding errors. However, the
scaled entries' magnitudes are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
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.
A
A is REAL array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
R
R is REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C
C is REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND
ROWCND is REAL
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
COLCND is REAL
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
AMAX is REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
INFO
INFO is 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zgeequb (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)¶
ZGEEQUB
Purpose:
ZGEEQUB computes row and column scalings intended to equilibrate an
M-by-N 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 an absolute value of at most
the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from ZGEEQU by restricting the scaling factors
to a power of the radix. Barring over- and underflow, scaling by
these factors introduces no additional rounding errors. However, the
scaled entries' magnitudes are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
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.
A
A is COMPLEX*16 array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
R
R is DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C
C is DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND
ROWCND is 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
COLCND is 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
AMAX is 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
INFO is 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |