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| poequ(3) | LAPACK | poequ(3) |
NAME¶
poequ - poequ: equilibration
SYNOPSIS¶
Functions¶
subroutine cpoequ (n, a, lda, s, scond, amax, info)
CPOEQU subroutine dpoequ (n, a, lda, s, scond, amax, info)
DPOEQU subroutine spoequ (n, a, lda, s, scond, amax, info)
SPOEQU subroutine zpoequ (n, a, lda, s, scond, amax, info)
ZPOEQU
Detailed Description¶
Function Documentation¶
subroutine cpoequ (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)¶
CPOEQU
Purpose:
CPOEQU 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.
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 dpoequ (integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)¶
DPOEQU
Purpose:
DPOEQU 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.
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 spoequ (integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)¶
SPOEQU
Purpose:
SPOEQU 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.
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 zpoequ (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)¶
ZPOEQU
Purpose:
ZPOEQU 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.
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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| Tue Jan 28 2025 00:54:31 | Version 3.12.0 |