?poequ

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?poequ

Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite matrix and reduce its condition number.

Syntax

lapack_int LAPACKE_spoequ ( intmatrix_layout , lapack_intn , const float*a , lapack_intlda , float*s , float*scond , float*amax );

lapack_int LAPACKE_dpoequ ( intmatrix_layout , lapack_intn , const double*a , lapack_intlda , double*s , double*scond , double*amax );

lapack_int LAPACKE_cpoequ ( intmatrix_layout , lapack_intn , const lapack_complex_float*a , lapack_intlda , float*s , float*scond , float*amax );

lapack_int LAPACKE_zpoequ ( intmatrix_layout , lapack_intn , const lapack_complex_double*a , lapack_intlda , double*s , double*scond , double*amax );

Include Files

mkl.h

Description

spoequ dpoequ cpoequ zpoequ poequ

The routine computes row and column scalings intended to equilibrate a symmetric (Hermitian) positive-definite matrix A and reduce its condition number (with respect to the two-norm).

The output array s returns scale factors such that s[i - 1] contains

\[\frac{1}{\sqrt{a_{i,i}}}\]

These factors are chosen so that the scaled matrix B with elements \(B_{ij}=s[i-1]*a_{ij}*s[j-1]\) has diagonal elements equal to 1.

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.

See ?laqsy (Scales a symmetric/Hermitian matrix, using scaling factors computed by ?syequ, ?syequb, ?poequ , or ?poequb.) auxiliary function that uses scaling factors computed by ?poequ .

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

n

The order of the matrix A ; n≥ 0 .

a

Array: size max(1, lda * n ) .

Contains the n -by- n symmetric or Hermitian positive definite matrix A whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

lda

The leading dimension of a ; lda≥ max(1,n) .

Output Parameters

s

Array, size n .

If info = 0 , the array s contains the scale factors for A .

scond

If info = 0 , scond contains the ratio of the smallest s[i] to the largest s[i] .

amax

Absolute value of the largest element of the matrix A .

Return Values

This function returns a value info .

If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.
If info = i , the i -th diagonal element of A is nonpositive.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

If scond≥ 0.1 and amax is neither too large nor too small, it is not worth scaling by s .

If amax is very close to SMLNUM or very close to BIGNUM , the matrix \(A\) should be scaled.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?poequ

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes