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heequb(3) LAPACK heequb(3)

NAME

heequb - {he,sy}equb: equilibration, power of 2

SYNOPSIS

Functions


subroutine cheequb (uplo, n, a, lda, s, scond, amax, work, info)
CHEEQUB subroutine csyequb (uplo, n, a, lda, s, scond, amax, work, info)
CSYEQUB subroutine dsyequb (uplo, n, a, lda, s, scond, amax, work, info)
DSYEQUB subroutine ssyequb (uplo, n, a, lda, s, scond, amax, work, info)
SSYEQUB subroutine zheequb (uplo, n, a, lda, s, scond, amax, work, info)
ZHEEQUB subroutine zsyequb (uplo, n, a, lda, s, scond, amax, work, info)
ZSYEQUB

Detailed Description

Function Documentation

subroutine cheequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)

CHEEQUB

Purpose:



 CHEEQUB computes row and column scalings intended to equilibrate a


 Hermitian matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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 matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is COMPLEX array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine csyequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)

CSYEQUB

Purpose:



 CSYEQUB computes row and column scalings intended to equilibrate a


 symmetric matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A. N >= 0.

A



          A is COMPLEX array, dimension (LDA,N)


          The N-by-N symmetric matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is COMPLEX array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine dsyequb (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, double precision, dimension( * ) work, integer info)

DSYEQUB

Purpose:



 DSYEQUB computes row and column scalings intended to equilibrate a


 symmetric matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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 matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is DOUBLE PRECISION array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine ssyequb (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, real, dimension( * ) work, integer info)

SSYEQUB

Purpose:



 SSYEQUB computes row and column scalings intended to equilibrate a


 symmetric matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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 matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is REAL array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine zheequb (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)

ZHEEQUB

Purpose:



 ZHEEQUB computes row and column scalings intended to equilibrate a


 Hermitian matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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 matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is COMPLEX*16 array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine zsyequb (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)

ZSYEQUB

Purpose:



 ZSYEQUB computes row and column scalings intended to equilibrate a


 symmetric matrix A (with respect to the Euclidean norm) and reduce


 its condition number. The scale factors S are computed by the BIN


 algorithm (see references) so that the scaled matrix B with elements


 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of


 the smallest possible condition number over all possible diagonal


 scalings.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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 symmetric matrix whose scaling factors are to be


          computed.

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


          Largest absolute value of any matrix element. If AMAX is


          very close to overflow or very close to underflow, the


          matrix should be scaled.

WORK



          WORK is COMPLEX*16 array, dimension (2*N)

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.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Author

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