Developer Reference for Intel® oneAPI Math Kernel Library for C
?ppequ
Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite matrix in packed storage and reduce its condition number.
Syntax
lapack_int LAPACKE_sppequ ( intmatrix_layout , charuplo , lapack_intn , const float*ap , float*s , float*scond , float*amax );
lapack_int LAPACKE_dppequ ( intmatrix_layout , charuplo , lapack_intn , const double*ap , double*s , double*scond , double*amax );
lapack_int LAPACKE_cppequ ( intmatrix_layout , charuplo , lapack_intn , const lapack_complex_float*ap , float*s , float*scond , float*amax );
lapack_int LAPACKE_zppequ ( intmatrix_layout , charuplo , lapack_intn , const lapack_complex_double*ap , double*s , double*scond , double*amax );
Include Files
mkl.h
Description
sppequ dppequ cppequ zppequ ppequ
The routine computes row and column scalings intended to equilibrate a symmetric (Hermitian) positive definite matrix A in packed storage 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 ?laqsp (Scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by ?ppequ.) auxiliary function that uses scaling factors computed by ?ppequ .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
uplo
Must be ‘U’ or ‘L’ .
Indicates whether the upper or lower triangular part of A is packed in the array ap :
If uplo = 'U' , the array ap stores the upper triangular part of the matrix A .
If uplo = 'L' , the array ap stores the lower triangular part of the matrix A .
n
The order of matrix A ; n≥ 0 .
ap
Array, size at least max(1,n(n+1)/2) . The array ap contains the upper or the lower triangular part of the matrix A (as specified by uplo ) in packed storage (see Matrix Storage Schemes ).
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.