heequb - Man Page

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

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

Definition at line 131 of file cheequb.f.

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

Definition at line 131 of file csyequb.f.

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

Definition at line 130 of file dsyequb.f.

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

Definition at line 130 of file ssyequb.f.

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

Definition at line 131 of file zheequb.f.

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

Definition at line 131 of file zsyequb.f.