poequ(3)

NAME
poequ - poequ: equilibration

SYNOPSIS

  Functions
subroutine cpoequ (n, a, lda, s, scond, amax, info)
CPOEQU
subroutine dpoequ (n, a, lda, s, scond, amax, info)
DPOEQU
subroutine spoequ (n, a, lda, s, scond, amax, info)
SPOEQU
subroutine zpoequ (n, a, lda, s, scond, amax, info)
ZPOEQU

Detailed Description

Function Documentation

  subroutine cpoequ (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

CPOEQU

Purpose:

     CPOEQU computes row and column scalings intended to equilibrate a
     Hermitian positive definite matrix A 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
    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
              The N-by-N Hermitian positive definite matrix whose scaling
              factors are to be computed.  Only the diagonal elements of A
              are referenced.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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 112 of file cpoequ.f.

  subroutine dpoequ (integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

DPOEQU

Purpose:

     DPOEQU computes row and column scalings intended to equilibrate a
     symmetric positive definite matrix A 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
    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              The N-by-N symmetric positive definite matrix whose scaling
              factors are to be computed.  Only the diagonal elements of A
              are referenced.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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 111 of file dpoequ.f.

  subroutine spoequ (integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

SPOEQU

Purpose:

     SPOEQU computes row and column scalings intended to equilibrate a
     symmetric positive definite matrix A 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
    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    A

              A is REAL array, dimension (LDA,N)
              The N-by-N symmetric positive definite matrix whose scaling
              factors are to be computed.  Only the diagonal elements of A
              are referenced.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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 111 of file spoequ.f.

  subroutine zpoequ (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

ZPOEQU

Purpose:

     ZPOEQU computes row and column scalings intended to equilibrate a
     Hermitian positive definite matrix A 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
    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              The N-by-N Hermitian positive definite matrix whose scaling
              factors are to be computed.  Only the diagonal elements of A
              are referenced.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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 112 of file zpoequ.f.

Author

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