# poequb - Man Page

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

## 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
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

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
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

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
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

NAG Ltd.

Definition at line 117 of file spoequb.f.

### 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
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