LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine zppequ | ( | character | UPLO, |
integer | N, | ||
complex*16, dimension( * ) | AP, | ||
double precision, dimension( * ) | S, | ||
double precision | SCOND, | ||
double precision | AMAX, | ||
integer | INFO | ||
) |
ZPPEQU
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ZPPEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal. 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.
[in] | UPLO | UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | AP | AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
[out] | S | S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. |
[out] | SCOND | SCOND is DOUBLE PRECISION If INFO = 0, S 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. |
[out] | AMAX | AMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive. |
Definition at line 119 of file zppequ.f.