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 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 118 of file cpoequb.f.

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 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 117 of file dpoequb.f.

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 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 117 of file spoequb.f.

subroutine zpoequb (integer n, complex16, 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 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 118 of file zpoequb.f.

Author

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