Specifies whether matrix storage layout is row major (

LAPACK_ROW_MAJOR

) or column major (

LAPACK_COL_MAJOR

).

Specifies whether condition numbers are required for eigenvalues or eigenvectors. Must be

'E'

or

'V'

or

'B'

.

If

job

=

'E'

, for eigenvalues only (compute

s

).

If

job

=

'V'

, for eigenvectors only (compute

dif

).

If

job

=

'B'

, for both eigenvalues and eigenvectors (compute both

s

and

dif

).

Must be

'A'

or

'S'

.

If

howmny

=

'A'

, compute condition numbers for all eigenpairs.

If

howmny

=

'S'

, compute condition numbers for selected eigenpairs specified by the logical array

select

.

Array, size at least max (1,

n

).

If

howmny

=

'S'

,

select

specifies the eigenpairs for which condition numbers are required.

If

howmny

=

'A'

,

select

is not referenced.

For real flavors

:

To select condition numbers for the eigenpair corresponding to a real eigenvalue

ω

j

,

select

[

j

- 1]

must be set to

1

; to select condition numbers corresponding to a complex conjugate pair of eigenvalues

ω

j

and

ω

j

+ 1

, either

select

[

j

- 1]

or

select

[

j

]

must be set to

1.

To select condition numbers for the corresponding

j

-th eigenvalue and/or eigenvector,

select

[

j

- 1]

must be set to

1

.

The order of the square matrix pair (

A

,

B

)

(

n

≥

0).

Arrays:

a

(size max(1,

lda

*

n

))

contains the upper quasi-triangular (for real flavors) or upper triangular (for complex flavors) matrix

A

in the pair (

A

,

B

).

b

(size max(1,

ldb

*

n

))

contains the upper triangular matrix

B

in the pair (

A

,

B

).

If

job

=

'E'

or

'B'

,

vl

(size max(1,

ldvl

*

m

) for column major layout and max(1,

ldvl

*

n

) for row major layout)

must contain left eigenvectors of (

A

,

B

), corresponding to the eigenpairs specified by

howmny

and

select

. The eigenvectors must be stored in consecutive columns of

vl

, as returned by

?tgevc

.

If

job

=

'V'

,

vl

is not referenced.

If

job

=

'E'

or

'B'

,

vr

(size max(1,

ldvr

*

m

) for column major layout and max(1,

ldvr

*

n

) for row major layout)

must contain right eigenvectors of (

A

,

B

), corresponding to the eigenpairs specified by

howmny

and

select

. The eigenvectors must be stored in consecutive columns of

vr

, as returned by

?tgevc

.

If

job

=

'V'

,

vr

is not referenced.

The leading dimension of

a

; at least max(1,

n

).

The leading dimension of

b

; at least max(1,

n

).

The leading dimension of

vl

;

ldvl

≥

1

.

If

job

=

'E'

or

'B'

, then

ldvl

≥

max(1,

n

)

for column major layout and

ldvl

≥

max(1,

m

) for row major layout

.

The leading dimension of

vr

;

ldvr

≥

1

.

If

job

=

'E'

or

'B'

, then

ldvr

≥

max(1,

n

)

for column major layout and

ldvr

≥

max(1,

m

) for row major layout

.

The number of elements in the arrays

s

and

dif

(

mm

≥

m

).

Array,

size

mm

.

If

job

=

'E'

or

'B'

, contains the reciprocal condition numbers of the selected eigenvalues, stored in consecutive elements of the array.

If

job

=

'V'

,

s

is not referenced.

For real flavors

:

For a complex conjugate pair of eigenvalues two consecutive elements of

s

are set to the same value. Thus,

s

[

j

- 1]

,

dif

[

j

- 1]

, and the

j

-th columns of

vl

and

vr

all correspond to the same eigenpair (but not in general the

j

-th eigenpair, unless all eigenpairs are selected).

Array,

size

mm

.

If

job

=

'V'

or

'B'

, contains the estimated reciprocal condition numbers of the selected eigenvectors, stored in consecutive elements of the array.

If the eigenvalues cannot be reordered to compute

dif

[

j

]

,

dif

[

j

]

is set to 0; this can only occur when the true value would be very small anyway.

If

job

=

'E'

,

dif

is not referenced.

For real flavors

:

For a complex eigenvector, two consecutive elements of

dif

are set to the same value.

For complex flavors

:

For each eigenvalue/vector specified by

select

,

dif

stores a Frobenius norm-based estimate of Difl.

The number of elements in the arrays

s

and

dif

used to store the specified condition numbers; for each selected eigenvalue one element is used.

If

howmny

=

'A'

,

m

is set to

n

.