SRC/strevc3.f(3) Library Functions Manual SRC/strevc3.f(3) NAME SRC/strevc3.f SYNOPSIS Functions/Subroutines subroutine strevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, info) STREVC3 Function/Subroutine Documentation subroutine strevc3 (character side, character howmny, logical, dimension( * ) select, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, real, dimension( * ) work, integer lwork, integer info) STREVC3 Purpose: !> !> STREVC3 computes some or all of the right and/or left eigenvectors of !> a real upper quasi-triangular matrix T. !> Matrices of this type are produced by the Schur factorization of !> a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (y**T)*T = w*(y**T) !> !> where y**T denotes the transpose of the vector y. !> The eigenvalues are not input to this routine, but are read directly !> from the diagonal blocks of T. !> !> This routine returns the matrices X and/or Y of right and left !> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an !> input matrix. If Q is the orthogonal factor that reduces a matrix !> A to Schur form T, then Q*X and Q*Y are the matrices of right and !> left eigenvectors of A. !> !> This uses a Level 3 BLAS version of the back transformation. !> Parameters SIDE !> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors. !> HOWMNY !> HOWMNY is CHARACTER*1 !> = 'A': compute all right and/or left eigenvectors; !> = 'B': compute all right and/or left eigenvectors, !> backtransformed by the matrices in VR and/or VL; !> = 'S': compute selected right and/or left eigenvectors, !> as indicated by the logical array SELECT. !> SELECT !> SELECT is LOGICAL array, dimension (N) !> If HOWMNY = 'S', SELECT specifies the eigenvectors to be !> computed. !> If w(j) is a real eigenvalue, the corresponding real !> eigenvector is computed if SELECT(j) is .TRUE.. !> If w(j) and w(j+1) are the real and imaginary parts of a !> complex eigenvalue, the corresponding complex eigenvector is !> computed if either SELECT(j) or SELECT(j+1) is .TRUE., and !> on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to !> .FALSE.. !> Not referenced if HOWMNY = 'A' or 'B'. !> N !> N is INTEGER !> The order of the matrix T. N >= 0. !> T !> T is REAL array, dimension (LDT,N) !> The upper quasi-triangular matrix T in Schur canonical form. !> LDT !> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !> VL !> VL is REAL array, dimension (LDVL,MM) !> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must !> contain an N-by-N matrix Q (usually the orthogonal matrix Q !> of Schur vectors returned by SHSEQR). !> On exit, if SIDE = 'L' or 'B', VL contains: !> if HOWMNY = 'A', the matrix Y of left eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*Y; !> if HOWMNY = 'S', the left eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VL, in the same order as their !> eigenvalues. !> A complex eigenvector corresponding to a complex eigenvalue !> is stored in two consecutive columns, the first holding the !> real part, and the second the imaginary part. !> Not referenced if SIDE = 'R'. !> LDVL !> LDVL is INTEGER !> The leading dimension of the array VL. !> LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. !> VR !> VR is REAL array, dimension (LDVR,MM) !> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must !> contain an N-by-N matrix Q (usually the orthogonal matrix Q !> of Schur vectors returned by SHSEQR). !> On exit, if SIDE = 'R' or 'B', VR contains: !> if HOWMNY = 'A', the matrix X of right eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*X; !> if HOWMNY = 'S', the right eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VR, in the same order as their !> eigenvalues. !> A complex eigenvector corresponding to a complex eigenvalue !> is stored in two consecutive columns, the first holding the !> real part and the second the imaginary part. !> Not referenced if SIDE = 'L'. !> LDVR !> LDVR is INTEGER !> The leading dimension of the array VR. !> LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. !> MM !> MM is INTEGER !> The number of columns in the arrays VL and/or VR. MM >= M. !> M !> M is INTEGER !> The number of columns in the arrays VL and/or VR actually !> used to store the eigenvectors. !> If HOWMNY = 'A' or 'B', M is set to N. !> Each selected real eigenvector occupies one column and each !> selected complex eigenvector occupies two columns. !> WORK !> WORK is REAL array, dimension (MAX(1,LWORK)) !> LWORK !> LWORK is INTEGER !> The dimension of array WORK. LWORK >= max(1,3*N). !> For optimum performance, LWORK >= N + 2*N*NB, where NB is !> the optimal blocksize. !> !> 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. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: !> !> The algorithm used in this program is basically backward (forward) !> substitution, with scaling to make the the code robust against !> possible overflow. !> !> Each eigenvector is normalized so that the element of largest !> magnitude has magnitude 1; here the magnitude of a complex number !> (x,y) is taken to be |x| + |y|. !> Definition at line 235 of file strevc3.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/strevc3.f(3)