?poequb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

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

call spoequb ( n , a , lda , s , scond , amax , info )

call dpoequb ( n , a , lda , s , scond , amax , info )

call cpoequb ( n , a , lda , s , scond , amax , info )

call zpoequb ( n , a , lda , s , scond , amax , info )

Include Files

mkl.fi , mkl_lapack.f90

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

n

INTEGER . The order of the matrix A ; n≥ 0 .

a

REAL for spoequb

DOUBLE PRECISION for dpoequb

COMPLEX for cpoequb

DOUBLE COMPLEX for zpoequb .

Array: size lda by * .

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.

The second dimension of a must be at least max(1,n) .

lda

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

Output Parameters

s

REAL for single precision flavors

DOUBLE PRECISION for double precision flavors.

Array, size ( n ).

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

scond

REAL for single precision flavors

DOUBLE PRECISION for double precision flavors.

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

REAL for single precision flavors

DOUBLE PRECISION for double precision flavors.

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

info

INTEGER .

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

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?poequb

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values