.TH "tgexc" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME tgexc \- tgexc: reorder generalized Schur form .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctgexc\fP (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)" .br .RI "\fBCTGEXC\fP " .ti -1c .RI "subroutine \fBdtgexc\fP (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)" .br .RI "\fBDTGEXC\fP " .ti -1c .RI "subroutine \fBstgexc\fP (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)" .br .RI "\fBSTGEXC\fP " .ti -1c .RI "subroutine \fBztgexc\fP (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)" .br .RI "\fBZTGEXC\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctgexc (logical wantq, logical wantz, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( ldz, * ) z, integer ldz, integer ifst, integer ilst, integer info)" .PP \fBCTGEXC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CTGEXC reorders the generalized Schur decomposition of a complex !> matrix pair (A,B), using an unitary equivalence transformation !> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with !> row index IFST is moved to row ILST\&. !> !> (A, B) must be in generalized Schur canonical form, that is, A and !> B are both upper triangular\&. !> !> Optionally, the matrices Q and Z of generalized Schur vectors are !> updated\&. !> !> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H !> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf !> WANTQ is LOGICAL !> \&.TRUE\&. : update the left transformation matrix Q; !> \&.FALSE\&.: do not update Q\&. !> .fi .PP .br \fIWANTZ\fP .PP .nf !> WANTZ is LOGICAL !> \&.TRUE\&. : update the right transformation matrix Z; !> \&.FALSE\&.: do not update Z\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the upper triangular matrix A in the pair (A, B)\&. !> On exit, the updated matrix A\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX array, dimension (LDB,N) !> On entry, the upper triangular matrix B in the pair (A, B)\&. !> On exit, the updated matrix B\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIQ\fP .PP .nf !> Q is COMPLEX array, dimension (LDQ,N) !> On entry, if WANTQ = \&.TRUE\&., the unitary matrix Q\&. !> On exit, the updated matrix Q\&. !> If WANTQ = \&.FALSE\&., Q is not referenced\&. !> .fi .PP .br \fILDQ\fP .PP .nf !> LDQ is INTEGER !> The leading dimension of the array Q\&. LDQ >= 1; !> If WANTQ = \&.TRUE\&., LDQ >= N\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is COMPLEX array, dimension (LDZ,N) !> On entry, if WANTZ = \&.TRUE\&., the unitary matrix Z\&. !> On exit, the updated matrix Z\&. !> If WANTZ = \&.FALSE\&., Z is not referenced\&. !> .fi .PP .br \fILDZ\fP .PP .nf !> LDZ is INTEGER !> The leading dimension of the array Z\&. LDZ >= 1; !> If WANTZ = \&.TRUE\&., LDZ >= N\&. !> .fi .PP .br \fIIFST\fP .PP .nf !> IFST is INTEGER !> .fi .PP .br \fIILST\fP .PP .nf !> ILST is INTEGER !> Specify the reordering of the diagonal blocks of (A, B)\&. !> The block with row index IFST is moved to row ILST, by a !> sequence of swapping between adjacent blocks\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> =0: Successful exit\&. !> <0: if INFO = -i, the i-th argument had an illegal value\&. !> =1: The transformed matrix pair (A, B) would be too far !> from generalized Schur form; the problem is ill- !> conditioned\&. (A, B) may have been partially reordered, !> and ILST points to the first row of the current !> position of the block being moved\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. .RE .PP \fBReferences:\fP .RS 4 [1] B\&. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M\&.S\&. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ\&. 1993, pp 195-218\&. .br [2] B\&. Kagstrom and P\&. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF - 94\&.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994\&. Also as LAPACK Working Note 87\&. To appear in Numerical Algorithms, 1996\&. .br [3] B\&. Kagstrom and P\&. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93\&.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75\&. To appear in ACM Trans\&. on Math\&. Software, Vol 22, No 1, 1996\&. .RE .PP .PP Definition at line \fB198\fP of file \fBctgexc\&.f\fP\&. .SS "subroutine dtgexc (logical wantq, logical wantz, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( ldz, * ) z, integer ldz, integer ifst, integer ilst, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fBDTGEXC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DTGEXC reorders the generalized real Schur decomposition of a real !> matrix pair (A,B) using an orthogonal equivalence transformation !> !> (A, B) = Q * (A, B) * Z**T, !> !> so that the diagonal block of (A, B) with row index IFST is moved !> to row ILST\&. !> !> (A, B) must be in generalized real Schur canonical form (as returned !> by DGGES), i\&.e\&. A is block upper triangular with 1-by-1 and 2-by-2 !> diagonal blocks\&. B is upper triangular\&. !> !> Optionally, the matrices Q and Z of generalized Schur vectors are !> updated\&. !> !> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T !> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T !> !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf !> WANTQ is LOGICAL !> \&.TRUE\&. : update the left transformation matrix Q; !> \&.FALSE\&.: do not update Q\&. !> .fi .PP .br \fIWANTZ\fP .PP .nf !> WANTZ is LOGICAL !> \&.TRUE\&. : update the right transformation matrix Z; !> \&.FALSE\&.: do not update Z\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the matrix A in generalized real Schur canonical !> form\&. !> On exit, the updated matrix A, again in generalized !> real Schur canonical form\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is DOUBLE PRECISION array, dimension (LDB,N) !> On entry, the matrix B in generalized real Schur canonical !> form (A,B)\&. !> On exit, the updated matrix B, again in generalized !> real Schur canonical form (A,B)\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIQ\fP .PP .nf !> Q is DOUBLE PRECISION array, dimension (LDQ,N) !> On entry, if WANTQ = \&.TRUE\&., the orthogonal matrix Q\&. !> On exit, the updated matrix Q\&. !> If WANTQ = \&.FALSE\&., Q is not referenced\&. !> .fi .PP .br \fILDQ\fP .PP .nf !> LDQ is INTEGER !> The leading dimension of the array Q\&. LDQ >= 1\&. !> If WANTQ = \&.TRUE\&., LDQ >= N\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is DOUBLE PRECISION array, dimension (LDZ,N) !> On entry, if WANTZ = \&.TRUE\&., the orthogonal matrix Z\&. !> On exit, the updated matrix Z\&. !> If WANTZ = \&.FALSE\&., Z is not referenced\&. !> .fi .PP .br \fILDZ\fP .PP .nf !> LDZ is INTEGER !> The leading dimension of the array Z\&. LDZ >= 1\&. !> If WANTZ = \&.TRUE\&., LDZ >= N\&. !> .fi .PP .br \fIIFST\fP .PP .nf !> IFST is INTEGER !> .fi .PP .br \fIILST\fP .PP .nf !> ILST is INTEGER !> Specify the reordering of the diagonal blocks of (A, B)\&. !> 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)\&. 1 <= IFST, ILST <= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal 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 by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> =0: successful exit\&. !> <0: if INFO = -i, the i-th argument had an illegal value\&. !> =1: The transformed matrix pair (A, B) would be too far !> from generalized Schur form; the problem is ill- !> conditioned\&. (A, B) may have been partially reordered, !> and ILST points to the first row of the current !> position of the block being moved\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. .RE .PP \fBReferences:\fP .RS 4 .PP .nf !> !> [1] B\&. Kagstrom; A Direct Method for Reordering Eigenvalues in the !> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in !> M\&.S\&. Moonen et al (eds), Linear Algebra for Large Scale and !> Real-Time Applications, Kluwer Academic Publ\&. 1993, pp 195-218\&. !> .fi .PP .RE .PP .PP Definition at line \fB218\fP of file \fBdtgexc\&.f\fP\&. .SS "subroutine stgexc (logical wantq, logical wantz, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldq, * ) q, integer ldq, real, dimension( ldz, * ) z, integer ldz, integer ifst, integer ilst, real, dimension( * ) work, integer lwork, integer info)" .PP \fBSTGEXC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> STGEXC reorders the generalized real Schur decomposition of a real !> matrix pair (A,B) using an orthogonal equivalence transformation !> !> (A, B) = Q * (A, B) * Z**T, !> !> so that the diagonal block of (A, B) with row index IFST is moved !> to row ILST\&. !> !> (A, B) must be in generalized real Schur canonical form (as returned !> by SGGES), i\&.e\&. A is block upper triangular with 1-by-1 and 2-by-2 !> diagonal blocks\&. B is upper triangular\&. !> !> Optionally, the matrices Q and Z of generalized Schur vectors are !> updated\&. !> !> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T !> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T !> !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf !> WANTQ is LOGICAL !> \&.TRUE\&. : update the left transformation matrix Q; !> \&.FALSE\&.: do not update Q\&. !> .fi .PP .br \fIWANTZ\fP .PP .nf !> WANTZ is LOGICAL !> \&.TRUE\&. : update the right transformation matrix Z; !> \&.FALSE\&.: do not update Z\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the matrix A in generalized real Schur canonical !> form\&. !> On exit, the updated matrix A, again in generalized !> real Schur canonical form\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is REAL array, dimension (LDB,N) !> On entry, the matrix B in generalized real Schur canonical !> form (A,B)\&. !> On exit, the updated matrix B, again in generalized !> real Schur canonical form (A,B)\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIQ\fP .PP .nf !> Q is REAL array, dimension (LDQ,N) !> On entry, if WANTQ = \&.TRUE\&., the orthogonal matrix Q\&. !> On exit, the updated matrix Q\&. !> If WANTQ = \&.FALSE\&., Q is not referenced\&. !> .fi .PP .br \fILDQ\fP .PP .nf !> LDQ is INTEGER !> The leading dimension of the array Q\&. LDQ >= 1\&. !> If WANTQ = \&.TRUE\&., LDQ >= N\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is REAL array, dimension (LDZ,N) !> On entry, if WANTZ = \&.TRUE\&., the orthogonal matrix Z\&. !> On exit, the updated matrix Z\&. !> If WANTZ = \&.FALSE\&., Z is not referenced\&. !> .fi .PP .br \fILDZ\fP .PP .nf !> LDZ is INTEGER !> The leading dimension of the array Z\&. LDZ >= 1\&. !> If WANTZ = \&.TRUE\&., LDZ >= N\&. !> .fi .PP .br \fIIFST\fP .PP .nf !> IFST is INTEGER !> .fi .PP .br \fIILST\fP .PP .nf !> ILST is INTEGER !> Specify the reordering of the diagonal blocks of (A, B)\&. !> 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)\&. 1 <= IFST, ILST <= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal 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 by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> =0: successful exit\&. !> <0: if INFO = -i, the i-th argument had an illegal value\&. !> =1: The transformed matrix pair (A, B) would be too far !> from generalized Schur form; the problem is ill- !> conditioned\&. (A, B) may have been partially reordered, !> and ILST points to the first row of the current !> position of the block being moved\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. .RE .PP \fBReferences:\fP .RS 4 .PP .nf !> !> [1] B\&. Kagstrom; A Direct Method for Reordering Eigenvalues in the !> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in !> M\&.S\&. Moonen et al (eds), Linear Algebra for Large Scale and !> Real-Time Applications, Kluwer Academic Publ\&. 1993, pp 195-218\&. !> .fi .PP .RE .PP .PP Definition at line \fB218\fP of file \fBstgexc\&.f\fP\&. .SS "subroutine ztgexc (logical wantq, logical wantz, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( ldz, * ) z, integer ldz, integer ifst, integer ilst, integer info)" .PP \fBZTGEXC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZTGEXC reorders the generalized Schur decomposition of a complex !> matrix pair (A,B), using an unitary equivalence transformation !> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with !> row index IFST is moved to row ILST\&. !> !> (A, B) must be in generalized Schur canonical form, that is, A and !> B are both upper triangular\&. !> !> Optionally, the matrices Q and Z of generalized Schur vectors are !> updated\&. !> !> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H !> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf !> WANTQ is LOGICAL !> \&.TRUE\&. : update the left transformation matrix Q; !> \&.FALSE\&.: do not update Q\&. !> .fi .PP .br \fIWANTZ\fP .PP .nf !> WANTZ is LOGICAL !> \&.TRUE\&. : update the right transformation matrix Z; !> \&.FALSE\&.: do not update Z\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the upper triangular matrix A in the pair (A, B)\&. !> On exit, the updated matrix A\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX*16 array, dimension (LDB,N) !> On entry, the upper triangular matrix B in the pair (A, B)\&. !> On exit, the updated matrix B\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIQ\fP .PP .nf !> Q is COMPLEX*16 array, dimension (LDQ,N) !> On entry, if WANTQ = \&.TRUE\&., the unitary matrix Q\&. !> On exit, the updated matrix Q\&. !> If WANTQ = \&.FALSE\&., Q is not referenced\&. !> .fi .PP .br \fILDQ\fP .PP .nf !> LDQ is INTEGER !> The leading dimension of the array Q\&. LDQ >= 1; !> If WANTQ = \&.TRUE\&., LDQ >= N\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is COMPLEX*16 array, dimension (LDZ,N) !> On entry, if WANTZ = \&.TRUE\&., the unitary matrix Z\&. !> On exit, the updated matrix Z\&. !> If WANTZ = \&.FALSE\&., Z is not referenced\&. !> .fi .PP .br \fILDZ\fP .PP .nf !> LDZ is INTEGER !> The leading dimension of the array Z\&. LDZ >= 1; !> If WANTZ = \&.TRUE\&., LDZ >= N\&. !> .fi .PP .br \fIIFST\fP .PP .nf !> IFST is INTEGER !> .fi .PP .br \fIILST\fP .PP .nf !> ILST is INTEGER !> Specify the reordering of the diagonal blocks of (A, B)\&. !> The block with row index IFST is moved to row ILST, by a !> sequence of swapping between adjacent blocks\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> =0: Successful exit\&. !> <0: if INFO = -i, the i-th argument had an illegal value\&. !> =1: The transformed matrix pair (A, B) would be too far !> from generalized Schur form; the problem is ill- !> conditioned\&. (A, B) may have been partially reordered, !> and ILST points to the first row of the current !> position of the block being moved\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. .RE .PP \fBReferences:\fP .RS 4 [1] B\&. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M\&.S\&. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ\&. 1993, pp 195-218\&. .br [2] B\&. Kagstrom and P\&. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF - 94\&.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994\&. Also as LAPACK Working Note 87\&. To appear in Numerical Algorithms, 1996\&. .br [3] B\&. Kagstrom and P\&. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93\&.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75\&. To appear in ACM Trans\&. on Math\&. Software, Vol 22, No 1, 1996\&. .RE .PP .PP Definition at line \fB198\fP of file \fBztgexc\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.