Visible to Intel only — GUID: GUID-5949CC58-AD9C-48EA-A9EB-F1F5AE17F9FD
Visible to Intel only — GUID: GUID-5949CC58-AD9C-48EA-A9EB-F1F5AE17F9FD
?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, lapack.f90
Description
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 Bi,j=s(i)*Ai,j*s(j) has diagonal elements equal to 1. s(i) is a power of two nearest to, but not exceeding 1/sqrt(Ai,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) to the largest 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. |