?poequb

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?poequb

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

Syntax

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

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

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

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

Include Files

mkl.h

Description

spoequb dpoequb cpoequb zpoequb

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).

These factors are chosen so that the scaled matrix B with elements B_{i,j}=s(i)*A_{i,j}*s(j)B_{i,j}=s[i-1]*A_{i,j}*s[j-1] has diagonal elements equal to 1. s(i)s[i - 1] is a power of two nearest to, but not exceeding 1/sqrt(A_{i,i}) .

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.

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, m) .

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)s[i] to the largest s(i)s[i] . If scond≥ 0.1 , and amax is neither too large nor too small, it is not worth scaling by s .

amax

Absolute value of the largest element of the matrix A . If amax is very close to SMLNUM or BIGNUM , the matrix should be scaled.

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.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?poequb

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values