geequb(3)

NAME
geequb - geequb: equilibration, power of 2

SYNOPSIS

  Functions
subroutine cgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
CGEEQUB
subroutine dgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
DGEEQUB
subroutine sgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
SGEEQUB
subroutine zgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
ZGEEQUB

Detailed Description

Function Documentation

  subroutine cgeequb (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

CGEEQUB

Purpose:

    !>
    !> CGEEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N matrix A and reduce its condition number.  R returns the row
    !> scale factors and C the column scale factors, chosen to try to make
    !> the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix between
    !> SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
    !> of these scaling factors is not guaranteed to reduce the condition
    !> number of A but works well in practice.
    !>
    !> This routine differs from CGEEQU 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 entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The M-by-N matrix whose equilibration factors are
    !>          to be computed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          If INFO = 0 or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          If INFO = 0,  C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is REAL
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    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,  and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 145 of file cgeequb.f.

  subroutine dgeequb (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

DGEEQUB

Purpose:

    !>
    !> DGEEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N matrix A and reduce its condition number.  R returns the row
    !> scale factors and C the column scale factors, chosen to try to make
    !> the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix between
    !> SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
    !> of these scaling factors is not guaranteed to reduce the condition
    !> number of A but works well in practice.
    !>
    !> This routine differs from DGEEQU 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 entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          The M-by-N matrix whose equilibration factors are
    !>          to be computed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          If INFO = 0 or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0,  C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    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,  and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 144 of file dgeequb.f.

  subroutine sgeequb (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

SGEEQUB

Purpose:

    !>
    !> SGEEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N matrix A and reduce its condition number.  R returns the row
    !> scale factors and C the column scale factors, chosen to try to make
    !> the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix between
    !> SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
    !> of these scaling factors is not guaranteed to reduce the condition
    !> number of A but works well in practice.
    !>
    !> This routine differs from SGEEQU 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 entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          The M-by-N matrix whose equilibration factors are
    !>          to be computed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          If INFO = 0 or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          If INFO = 0,  C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is REAL
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    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,  and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 144 of file sgeequb.f.

  subroutine zgeequb (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

ZGEEQUB

Purpose:

    !>
    !> ZGEEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N matrix A and reduce its condition number.  R returns the row
    !> scale factors and C the column scale factors, chosen to try to make
    !> the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix between
    !> SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
    !> of these scaling factors is not guaranteed to reduce the condition
    !> number of A but works well in practice.
    !>
    !> This routine differs from ZGEEQU 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 entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The M-by-N matrix whose equilibration factors are
    !>          to be computed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          If INFO = 0 or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0,  C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    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,  and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 145 of file zgeequb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.