NAG Library Routine Document

F08YFF (DTGEXC)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     WANTQ – LOGICALInput

On entry: if $\mathbf{WANTQ}=\mathrm{.TRUE.}$, update the left transformation matrix $Q$.

If $\mathbf{WANTQ}=\mathrm{.FALSE.}$, do not update $Q$.

2:     WANTZ – LOGICALInput

On entry: if $\mathbf{WANTZ}=\mathrm{.TRUE.}$, update the right transformation matrix $Z$.

If $\mathbf{WANTZ}=\mathrm{.FALSE.}$, do not update $Z$.

3:     N – INTEGERInput

On entry: $n$, the order of the matrices $S$ and $T$.

Constraint: $\mathbf{N}\ge 0$.

4:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the matrix $S$ in the pair $\left(S,T\right)$.

On exit: the updated matrix $\hat{S}$.

5:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F08YFF (DTGEXC) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

6:     B(LDB,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the matrix $T$, in the pair $\left(S,T\right)$.

On exit: the updated matrix $\hat{T}$ 

7:     LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F08YFF (DTGEXC) is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

8:     Q(LDQ,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array Q must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{WANTQ}=\mathrm{.TRUE.}$, and at least $1$ otherwise.

On entry: if $\mathbf{WANTQ}=\mathrm{.TRUE.}$, the orthogonal matrix $Q$.

On exit: if $\mathbf{WANTQ}=\mathrm{.TRUE.}$, the updated matrix $Q\hat{Q}$.

If $\mathbf{WANTQ}=\mathrm{.FALSE.}$, Q is not referenced.

9:     LDQ – INTEGERInput

On entry: the first dimension of the array Q as declared in the (sub)program from which F08YFF (DTGEXC) is called.

Constraints:

• if $\mathbf{WANTQ}=\mathrm{.TRUE.}$, $\mathbf{LDQ}\ge \max \left(1,\mathbf{N}\right)$;
• otherwise $\mathbf{LDQ}\ge 1$.

10:   Z(LDZ,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array Z must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{WANTZ}=\mathrm{.TRUE.}$, and at least $1$ otherwise.

On entry: if $\mathbf{WANTZ}=\mathrm{.TRUE.}$, the orthogonal matrix $Z$.

On exit: if $\mathbf{WANTZ}=\mathrm{.TRUE.}$, the updated matrix $Z\hat{Z}$.

If $\mathbf{WANTZ}=\mathrm{.FALSE.}$, Z is not referenced.

11:   LDZ – INTEGERInput

On entry: the first dimension of the array Z as declared in the (sub)program from which F08YFF (DTGEXC) is called.

Constraints:

• if $\mathbf{WANTZ}=\mathrm{.TRUE.}$, $\mathbf{LDZ}\ge \max \left(1,\mathbf{N}\right)$;
• otherwise $\mathbf{LDZ}\ge 1$.

12:   IFST – INTEGERInput/Output

13:   ILST – INTEGERInput/Output

On entry: the indices $i_1$ and $i_2$ that specify the reordering of the diagonal blocks of $\left(S,T\right)$. The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks.

On exit: if IFST pointed on entry to the second row of a $2$ by $2$ block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by $+1$ or $-1$).

Constraint: $1\le \mathbf{IFST}\le \mathbf{N}$ and $1\le \mathbf{ILST}\le \mathbf{N}$.

14:   WORK($\max \left(1,\mathbf{LWORK}\right)$) – REAL (KIND=nag_wp) arrayWorkspace

On exit: if $\mathbf{INFO}=\mathbf{0}$, $\mathbf{WORK}\left(1\right)$ contains the minimum value of LWORK required for optimal performance.

15:   LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08YFF (DTGEXC) is called.

If $\mathbf{LWORK}=-1$, a workspace query is assumed; the routine only calculates the minimum size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.

Constraints:

if $\mathbf{LWORK}\ne -1$,

• if $\mathbf{N}\le 1$, $\mathbf{LWORK}\ge 1$;
• otherwise $\mathbf{LWORK}\ge 4\times \mathbf{N}+16$.

16:   INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}=1$

The transformed matrix pair $\left(\hat{S},\hat{T}\right)$ would be too far from generalized Schur form; the problem is ill-conditioned. $\left(S,T\right)$ may have been partially reordered, and ILST points to the first row of the current position of the block being moved.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f08yffe.f90)

9.2  Program Data

Program Data (f08yffe.d)

9.3  Program Results

Program Results (f08yffe.r)