poequ(3)

Library Functions Manual

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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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 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.

Definition at line 112 of file cpoequ.f.

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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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 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.

Definition at line 111 of file dpoequ.f.

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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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 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.

Definition at line 111 of file spoequ.f.

subroutine zpoequ (integer n, complex16, 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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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 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.

Definition at line 112 of file zpoequ.f.

Author

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