Man page - poequb(3)

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Manual

poequb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cpoequb (integer n, complex, dimension( lda, * ) a, integer lda,real, dimension( * ) s, real scond, real amax, integer info)
subroutine dpoequb (integer n, double precision, dimension( lda, * ) a,integer lda, double precision, dimension( * ) s, double precisionscond, double precision amax, integer info)
subroutine spoequb (integer n, real, dimension( lda, * ) a, integer lda,real, dimension( * ) s, real scond, real amax, integer info)
subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integerlda, double precision, dimension( * ) s, double precision scond, doubleprecision amax, integer info)
Author

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 precisionscond, 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, integerlda, double precision, dimension( * ) s, double precision scond, doubleprecision 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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