---
name: "cppequ"
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/cppequ.f"
---

# cppequ(3)

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

## NAME

SRC/cppequ.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cppequ** (uplo, n, ap, s, scond, amax, info)\
 **CPPEQU**

## Function/Subroutine Documentation

### subroutine cppequ (character uplo, integer n, complex, dimension( \* ) ap, real, dimension( \* ) s, real scond, real amax, integer info)

**CPPEQU**

**Purpose:**

```
!>
!> CPPEQU computes row and column scalings intended to equilibrate a
!> Hermitian positive definite matrix A in packed storage 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 triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*AP*

```
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          The upper or lower triangle of the Hermitian matrix A, packed
!>          columnwise in a linear array.  The j-th column of A is stored
!>          in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **116** of file **cppequ.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.