poequb(3)

NAME
poequb - poequb: equilibration, power of 2

SYNOPSIS

  Functions

subroutine cpoequb (n, a, lda, s, scond, amax, info)
CPOEQUB
subroutine dpoequb (n, a, lda, s, scond, amax, info)
DPOEQUB
subroutine spoequb (n, a, lda, s, scond, amax, info)
SPOEQUB
subroutine zpoequb (n, a, lda, s, scond, amax, info)
ZPOEQUB

Detailed Description

Function Documentation

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

CPOEQUB

Purpose:

    !>
    !> CPOEQUB 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.
    !>
    !> This routine differs from CPOEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled diagonal entries are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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.

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

DPOEQUB

Purpose:

    !>
    !> DPOEQUB 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.
    !>
    !> This routine differs from DPOEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled diagonal entries are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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.

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

SPOEQUB

Purpose:

    !>
    !> SPOEQUB 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.
    !>
    !> This routine differs from SPOEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled diagonal entries are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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.

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

ZPOEQUB

Purpose:

    !>
    !> ZPOEQUB 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.
    !>
    !> This routine differs from ZPOEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled diagonal entries are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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.

Author

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