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.

Definition at line 138 of file cgeequ.f.

  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.

Definition at line 137 of file dgeequ.f.

  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.

Definition at line 137 of file sgeequ.f.

  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.

Definition at line 138 of file zgeequ.f.

Author

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