ppequ(3) Library Functions Manual ppequ(3) NAME ppequ - ppequ: equilibration SYNOPSIS Functions subroutine cppequ (uplo, n, ap, s, scond, amax, info) CPPEQU subroutine dppequ (uplo, n, ap, s, scond, amax, info) DPPEQU subroutine sppequ (uplo, n, ap, s, scond, amax, info) SPPEQU subroutine zppequ (uplo, n, ap, s, scond, amax, info) ZPPEQU Detailed Description Function Documentation subroutine cppequ (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, integer info) CPPEQU Purpose: !> !> CPPEQU 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. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> AP !> AP is COMPLEX 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. !> S !> S is REAL array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !> SCOND !> SCOND is REAL !> 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. !> AMAX !> AMAX is REAL !> Absolute value of largest matrix element. If AMAX is very !> close to overflow or very close to underflow, the matrix !> should be scaled. !> 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. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 116 of file cppequ.f. subroutine dppequ (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info) DPPEQU Purpose: !> !> DPPEQU computes row and column scalings intended to equilibrate a !> symmetric 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. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> AP !> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) !> The upper or lower triangle of the symmetric 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. !> S !> S is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !> 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. !> 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. !> 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. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file dppequ.f. subroutine sppequ (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, integer info) SPPEQU Purpose: !> !> SPPEQU computes row and column scalings intended to equilibrate a !> symmetric 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. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> AP !> AP is REAL array, dimension (N*(N+1)/2) !> The upper or lower triangle of the symmetric 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. !> S !> S is REAL array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !> SCOND !> SCOND is REAL !> 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. !> AMAX !> AMAX is REAL !> Absolute value of largest matrix element. If AMAX is very !> close to overflow or very close to underflow, the matrix !> should be scaled. !> 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. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 115 of file sppequ.f. subroutine zppequ (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info) ZPPEQU Purpose: !> !> 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. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> 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. !> S !> S is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !> 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. !> 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. !> 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. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 116 of file zppequ.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 ppequ(3)