---
name: "cpbequ"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cpbequ.f"
---

# cpbequ(3)

Part of [cpbequ.f(3)](/cpbequ.f/3.md).

## NAME

SRC/cpbequ.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cpbequ** (uplo, n, kd, ab, ldab, s, scond, amax, info)\
 **CPBEQU**

## Function/Subroutine Documentation

### subroutine cpbequ (character uplo, integer n, integer kd, complex, dimension( ldab, \* ) ab, integer ldab, real, dimension( \* ) s, real scond, real amax, integer info)

**CPBEQU**

**Purpose:**

```
!>
!> CPBEQU 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 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 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 **129** of file **cpbequ.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.