# zpbequ.f (3) - Linux Manuals

zpbequ.f -

## SYNOPSIS

### Functions/Subroutines

subroutine zpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
ZPBEQU

## Function/Subroutine Documentation

### subroutine zpbequ (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)

ZPBEQU

Purpose:

``` ZPBEQU computes row and column scalings intended to equilibrate a
Hermitian positive definite band 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:

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangular of A is stored;
= 'L':  Lower triangular of A is stored.
```

N

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

KD

```          KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
```

AB

```          AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array.  The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
```

LDAB

```          LDAB is INTEGER
The leading dimension of the array A.  LDAB >= KD+1.
```

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