p?laqsy

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

p?laqsy

Scales a symmetric/Hermitian matrix, using scaling factors computed by p?poequ .

Syntax

call pslaqsy(uplo, n, a, ia, ja, desca, sr, sc, scond, amax, equed)
call pdlaqsy(uplo, n, a, ia, ja, desca, sr, sc, scond, amax, equed)
call pclaqsy(uplo, n, a, ia, ja, desca, sr, sc, scond, amax, equed)
call pzlaqsy(uplo, n, a, ia, ja, desca, sr, sc, scond, amax, equed)

Include Files

mkl_scalapack.h

Description

pslaqsy pdlaqsy pclaqsy pzlaqsy The p?laqsy routine function equilibrates a symmetric distributed matrix sub( A ) = A ( ia : ia + n -1, ja:ja+n-1) using the scaling factors in the vectors sr and sc . The scaling factors are computed by p?poequ (Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite distributed matrix and reduce its condition number.) .

Input Parameters

uplo

(global) CHARACTER . Specifies the upper or lower triangular part of the symmetric distributed matrix sub(A) is to be referenced:

= ‘U’ : Upper triangular part; = ‘L’ : Lower triangular part.

n

(global) INTEGER .

The order of the distributed matrix sub( A ). n ≥ 0 .

a

(local). REAL for pslaqsy DOUBLE PRECISION for pdlaqsy COMPLEX for pclaqsy COMPLEX*16 for pzlaqsy .

Pointer into the local memory to an array of size ( lld_a , LOCc ( ja + n -1)) .

On entry, this array contains the local pieces of the distributed matrix sub( A ). On entry, the local pieces of the distributed symmetric matrix sub( A ). If uplo = 'U' , the leading n -by- n upper triangular part of sub( A ) contains the upper triangular part of the matrix, and the strictly lower triangular part of sub( A ) is not referenced. If uplo = 'L' , the leading n -by- n lower triangular part of sub( A ) contains the lower triangular part of the matrix, and the strictly upper triangular part of sub( A ) is not referenced.

ia , ja

(global) INTEGER .

The row and column indices in the global matrix A indicating the first row and the first column of the matrix sub( A ), respectively.

desca

(global and local) INTEGER array of size dlen_ . The array descriptor for the distributed matrix A.

sr

(local) REAL for pslaqsy DOUBLE PRECISION for pdlaqsy COMPLEX for pclaqsy COMPLEX*16 for pzlaqsy .

Array of size LOCr ( m_a ). The scale factors for A ( ia : ia + m -1, ja : ja + n -1). sr is aligned with the distributed matrix A , and replicated across every process column. sr is tied to the distributed matrix A .

sc

(local) REAL for pslaqsy DOUBLE PRECISION for pdlaqsy COMPLEX for pclaqsy COMPLEX*16 for pzlaqsy .

Array of size LOCc ( m_a ). The scale factors for A ( ia : ia + m -1, ja : ja + n -1). sc is aligned with the distributed matrix A , and replicated across every process column. sc is tied to the distributed matrix A .

scond

(global). REAL for pslaqsy

DOUBLE PRECISION for pdlaqsy COMPLEX for pclaqsy COMPLEX*16 for pzlaqsy .

Ratio of the smallest sr ( i ) (respectively sc ( j ) ) to the largest sr ( i ) (respectively sc ( j ) ), with ia ≤ i ≤ ia + n -1 and ja ≤ j ≤ ja + n -1 .

amax: (global). REAL for pslaqsy DOUBLE PRECISION for pdlaqsy COMPLEX for pclaqsy COMPLEX*16 for pzlaqsy . Absolute value of largest distributed submatrix entry.

Output Parameters

a

On exit, if equed = 'Y' , the equilibrated matrix:

diag(sr(ia:ia+n-1)) * sub(A) * diag(sc(ja:ja+n-1)) .

equed

(global) CHARACTER*1 .

Specifies whether or not equilibration was done. = ‘N’ : No equilibration. = ‘Y’ : Equilibration was done, that is, sub( A ) has been replaced by:

diag(sr(ia:ia+n-1)) * sub(A) * diag(sc(ja:ja+n-1)) .

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?laqsy

Syntax

Include Files

Description

Input Parameters

Output Parameters