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geequb(3) LAPACK 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.

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.

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.

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.

Author

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