geequ(3)

NAME
geequ - geequ: equilibration

SYNOPSIS

  Functions

subroutine cgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
CGEEQU
subroutine dgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
DGEEQU
subroutine sgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
SGEEQU
subroutine zgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
ZGEEQU

Detailed Description

Function Documentation

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

CGEEQU

Purpose:

    !>
    !> CGEEQU 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 absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be 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.
    !>

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.

  subroutine dgeequ (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)

DGEEQU

Purpose:

    !>
    !> DGEEQU 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 absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be 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.
    !>

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.

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

SGEEQU

Purpose:

    !>
    !> SGEEQU 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 absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be 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.
    !>

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.

  subroutine zgeequ (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)

ZGEEQU

Purpose:

    !>
    !> ZGEEQU 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 absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be 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.
    !>

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.

Author

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