gebal#

sgebal

Functions

void sgebal(
    const char* job,
    const INT   n,
          f32*  A,
    const INT   lda,
          INT*  ilo,
          INT*  ihi,
          f32*  scale,
          INT*  info
);

void sgebal(const char *job, const INT n, f32 *A, const INT lda, INT *ilo, INT *ihi, f32 *scale, INT *info)#

SGEBAL balances a general real matrix A.

This involves, first, permuting A by a similarity transformation to isolate eigenvalues in the first 0 to ILO-1 and last IHI+1 to N-1 elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

in

job

Specifies the operations to be performed on A: = ‘N’: none: simply set ILO = 0, IHI = N-1, SCALE(I) = 1.0 for i = 0,…,N-1; = ‘P’: permute only; = ‘S’: scale only; = ‘B’: both permute and scale.

in

n

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

inout

A

Double precision array, dimension (LDA,N). On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = ‘N’, A is not referenced.

in

lda

The leading dimension of the array A. LDA >= max(1,N).

out

ilo

ILO and IHI are set to integers such that on exit A(i,j) = 0 if i > j and j = 0,…,ILO-1 or I = IHI+1,…,N-1. If JOB = ‘N’ or ‘S’, ILO = 0 and IHI = N-1. Uses 0-based indexing.

out

ihi

See ILO. Uses 0-based indexing.

out

scale

Double precision array, dimension (N). Details of the permutations and scaling factors applied to A. If P(j) is the index of the row and column interchanged with row and column j and D(j) is the scaling factor applied to row and column j, then SCALE(j) = P(j) for j = 0,…,ILO-1 = D(j) for j = ILO,…,IHI = P(j) for j = IHI+1,…,N-1. The order in which the interchanges are made is N-1 to IHI+1, then 0 to ILO-1. Permutation indices are 0-based.

out

info

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

dgebal

Functions

void dgebal(
    const char* job,
    const INT   n,
          f64*  A,
    const INT   lda,
          INT*  ilo,
          INT*  ihi,
          f64*  scale,
          INT*  info
);

void dgebal(const char *job, const INT n, f64 *A, const INT lda, INT *ilo, INT *ihi, f64 *scale, INT *info)#

DGEBAL balances a general real matrix A.

This involves, first, permuting A by a similarity transformation to isolate eigenvalues in the first 0 to ILO-1 and last IHI+1 to N-1 elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

in

job

Specifies the operations to be performed on A: = ‘N’: none: simply set ILO = 0, IHI = N-1, SCALE(I) = 1.0 for i = 0,…,N-1; = ‘P’: permute only; = ‘S’: scale only; = ‘B’: both permute and scale.

in

n

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

inout

A

Double precision array, dimension (LDA,N). On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = ‘N’, A is not referenced.

in

lda

The leading dimension of the array A. LDA >= max(1,N).

out

ilo

ILO and IHI are set to integers such that on exit A(i,j) = 0 if i > j and j = 0,…,ILO-1 or I = IHI+1,…,N-1. If JOB = ‘N’ or ‘S’, ILO = 0 and IHI = N-1. Uses 0-based indexing.

out

ihi

See ILO. Uses 0-based indexing.

out

scale

Double precision array, dimension (N). Details of the permutations and scaling factors applied to A. If P(j) is the index of the row and column interchanged with row and column j and D(j) is the scaling factor applied to row and column j, then SCALE(j) = P(j) for j = 0,…,ILO-1 = D(j) for j = ILO,…,IHI = P(j) for j = IHI+1,…,N-1. The order in which the interchanges are made is N-1 to IHI+1, then 0 to ILO-1. Permutation indices are 0-based.

out

info

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

cgebal

Functions

void cgebal(
    const char* job,
    const INT   n,
          c64*  A,
    const INT   lda,
          INT*  ilo,
          INT*  ihi,
          f32*  scale,
          INT*  info
);

void cgebal(const char *job, const INT n, c64 *A, const INT lda, INT *ilo, INT *ihi, f32 *scale, INT *info)#

CGEBAL balances a general complex matrix A.

This involves, first, permuting A by a similarity transformation to isolate eigenvalues in the first 0 to ILO-1 and last IHI+1 to N-1 elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

in

job

Specifies the operations to be performed on A: = ‘N’: none: simply set ILO = 0, IHI = N-1, SCALE(I) = 1.0 for i = 0,…,N-1; = ‘P’: permute only; = ‘S’: scale only; = ‘B’: both permute and scale.

in

n

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

inout

A

Single complex array, dimension (LDA,N). On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = ‘N’, A is not referenced.

in

lda

The leading dimension of the array A. LDA >= max(1,N).

out

ilo

ILO and IHI are set to integers such that on exit A(i,j) = 0 if i > j and j = 0,…,ILO-1 or I = IHI+1,…,N-1. If JOB = ‘N’ or ‘S’, ILO = 0 and IHI = N-1. Uses 0-based indexing.

out

ihi

See ILO. Uses 0-based indexing.

out

scale

Single precision array, dimension (N). Details of the permutations and scaling factors applied to A. If P(j) is the index of the row and column interchanged with row and column j and D(j) is the scaling factor applied to row and column j, then SCALE(j) = P(j) for j = 0,…,ILO-1 = D(j) for j = ILO,…,IHI = P(j) for j = IHI+1,…,N-1. The order in which the interchanges are made is N-1 to IHI+1, then 0 to ILO-1. Permutation indices are 0-based.

out

info

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

zgebal

Functions

void zgebal(
    const char* job,
    const INT   n,
          c128* A,
    const INT   lda,
          INT*  ilo,
          INT*  ihi,
          f64*  scale,
          INT*  info
);

void zgebal(const char *job, const INT n, c128 *A, const INT lda, INT *ilo, INT *ihi, f64 *scale, INT *info)#

ZGEBAL balances a general complex matrix A.

This involves, first, permuting A by a similarity transformation to isolate eigenvalues in the first 0 to ILO-1 and last IHI+1 to N-1 elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

in

job

Specifies the operations to be performed on A: = ‘N’: none: simply set ILO = 0, IHI = N-1, SCALE(I) = 1.0 for i = 0,…,N-1; = ‘P’: permute only; = ‘S’: scale only; = ‘B’: both permute and scale.

in

n

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

inout

A

Double complex array, dimension (LDA,N). On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = ‘N’, A is not referenced.

in

lda

The leading dimension of the array A. LDA >= max(1,N).

out

ilo

ILO and IHI are set to integers such that on exit A(i,j) = 0 if i > j and j = 0,…,ILO-1 or I = IHI+1,…,N-1. If JOB = ‘N’ or ‘S’, ILO = 0 and IHI = N-1. Uses 0-based indexing.

out

ihi

See ILO. Uses 0-based indexing.

out

scale

Double precision array, dimension (N). Details of the permutations and scaling factors applied to A. If P(j) is the index of the row and column interchanged with row and column j and D(j) is the scaling factor applied to row and column j, then SCALE(j) = P(j) for j = 0,…,ILO-1 = D(j) for j = ILO,…,IHI = P(j) for j = IHI+1,…,N-1. The order in which the interchanges are made is N-1 to IHI+1, then 0 to ILO-1. Permutation indices are 0-based.

out

info

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

gebal#

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