.TH "laexc" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laexc \- laexc: reorder Schur form .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdlaexc\fP (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info)" .br .RI "\fBDLAEXC\fP swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation\&. " .ti -1c .RI "subroutine \fBslaexc\fP (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info)" .br .RI "\fBSLAEXC\fP swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dlaexc (logical wantq, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldq, * ) q, integer ldq, integer j1, integer n1, integer n2, double precision, dimension( * ) work, integer info)" .PP \fBDLAEXC\fP swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation\&. T must be in Schur canonical form, that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf WANTQ is LOGICAL = \&.TRUE\&. : accumulate the transformation in the matrix Q; = \&.FALSE\&.: do not accumulate the transformation\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is DOUBLE PRECISION array, dimension (LDT,N) On entry, the upper quasi-triangular matrix T, in Schur canonical form\&. On exit, the updated matrix T, again in Schur canonical form\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIQ\fP .PP .nf Q is DOUBLE PRECISION array, dimension (LDQ,N) On entry, if WANTQ is \&.TRUE\&., the orthogonal matrix Q\&. On exit, if WANTQ is \&.TRUE\&., the updated matrix Q\&. If WANTQ is \&.FALSE\&., Q is not referenced\&. .fi .PP .br \fILDQ\fP .PP .nf LDQ is INTEGER The leading dimension of the array Q\&. LDQ >= 1; and if WANTQ is \&.TRUE\&., LDQ >= N\&. .fi .PP .br \fIJ1\fP .PP .nf J1 is INTEGER The index of the first row of the first block T11\&. .fi .PP .br \fIN1\fP .PP .nf N1 is INTEGER The order of the first block T11\&. N1 = 0, 1 or 2\&. .fi .PP .br \fIN2\fP .PP .nf N2 is INTEGER The order of the second block T22\&. N2 = 0, 1 or 2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit = 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged\&. .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 .SS "subroutine slaexc (logical wantq, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldq, * ) q, integer ldq, integer j1, integer n1, integer n2, real, dimension( * ) work, integer info)" .PP \fBSLAEXC\fP swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation\&. T must be in Schur canonical form, that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIWANTQ\fP .PP .nf WANTQ is LOGICAL = \&.TRUE\&. : accumulate the transformation in the matrix Q; = \&.FALSE\&.: do not accumulate the transformation\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,N) On entry, the upper quasi-triangular matrix T, in Schur canonical form\&. On exit, the updated matrix T, again in Schur canonical form\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIQ\fP .PP .nf Q is REAL array, dimension (LDQ,N) On entry, if WANTQ is \&.TRUE\&., the orthogonal matrix Q\&. On exit, if WANTQ is \&.TRUE\&., the updated matrix Q\&. If WANTQ is \&.FALSE\&., Q is not referenced\&. .fi .PP .br \fILDQ\fP .PP .nf LDQ is INTEGER The leading dimension of the array Q\&. LDQ >= 1; and if WANTQ is \&.TRUE\&., LDQ >= N\&. .fi .PP .br \fIJ1\fP .PP .nf J1 is INTEGER The index of the first row of the first block T11\&. .fi .PP .br \fIN1\fP .PP .nf N1 is INTEGER The order of the first block T11\&. N1 = 0, 1 or 2\&. .fi .PP .br \fIN2\fP .PP .nf N2 is INTEGER The order of the second block T22\&. N2 = 0, 1 or 2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit = 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged\&. .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.