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

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