table of contents
| poequb(3) | LAPACK | poequb(3) |
NAME¶
poequb - poequb: equilibration, power of 2
SYNOPSIS¶
Functions¶
subroutine cpoequb (n, a, lda, s, scond, amax, info)
CPOEQUB subroutine dpoequb (n, a, lda, s, scond, amax, info)
DPOEQUB subroutine spoequb (n, a, lda, s, scond, amax, info)
SPOEQUB subroutine zpoequb (n, a, lda, s, scond, amax, info)
ZPOEQUB
Detailed Description¶
Function Documentation¶
subroutine cpoequb (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)¶
CPOEQUB
Purpose:
CPOEQUB computes row and column scalings intended to equilibrate a
Hermitian positive definite matrix A and reduce its condition number
(with respect to the two-norm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
This routine differs from CPOEQU 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 diagonal entries are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N)
The N-by-N Hermitian positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S
S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND
SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
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, the i-th diagonal element is nonpositive.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dpoequb (integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)¶
DPOEQUB
Purpose:
DPOEQUB computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A and reduce its condition number
(with respect to the two-norm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
This routine differs from DPOEQU 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 diagonal entries are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The N-by-N symmetric positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S
S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND
SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
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, the i-th diagonal element is nonpositive.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine spoequb (integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)¶
SPOEQUB
Purpose:
SPOEQUB computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A and reduce its condition number
(with respect to the two-norm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
This routine differs from SPOEQU 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 diagonal entries are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N)
The N-by-N symmetric positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S
S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND
SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
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, the i-th diagonal element is nonpositive.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)¶
ZPOEQUB
Purpose:
ZPOEQUB computes row and column scalings intended to equilibrate a
Hermitian positive definite matrix A and reduce its condition number
(with respect to the two-norm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
This routine differs from ZPOEQU 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 diagonal entries are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N Hermitian positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S
S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND
SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
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, the i-th diagonal element is nonpositive.
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 |