--- name: "trevc" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/trevc" --- # trevc(3) trevc: eigenvectors of triangular Schur form, old ## NAME trevc - trevc: eigenvectors of triangular Schur form, old ## SYNOPSIS ### Functions subroutine **ctrevc** (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)\ **CTREVC** subroutine **dtrevc** (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)\ **DTREVC** subroutine **strevc** (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)\ **STREVC** subroutine **ztrevc** (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)\ **ZTREVC** ## Detailed Description ## Function Documentation ### subroutine ctrevc (character side, character howmny, logical, dimension( \* ) select, integer n, complex, dimension( ldt, \* ) t, integer ldt, complex, dimension( ldvl, \* ) vl, integer ldvl, complex, dimension( ldvr, \* ) vr, integer ldvr, integer mm, integer m, complex, dimension( \* ) work, real, dimension( \* ) rwork, integer info) **CTREVC** **Purpose:** ``` !> !> CTREVC computes some or all of the right and/or left eigenvectors of !> a complex upper triangular matrix T. !> Matrices of this type are produced by the Schur factorization of !> a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (y**H)*T = w*(y**H) !> !> where y**H denotes the conjugate transpose of the vector y. !> The eigenvalues are not input to this routine, but are read directly !> from the diagonal 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 unitary 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. !> ``` **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 using the matrices supplied 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. !> The eigenvector corresponding to the j-th eigenvalue is !> computed if SELECT(j) = .TRUE.. !> Not referenced if HOWMNY = 'A' or 'B'. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix T. N >= 0. !> ``` *T* ``` !> T is COMPLEX array, dimension (LDT,N) !> The upper triangular matrix T. T is modified, but restored !> on exit. !> ``` *LDT* ``` !> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !> ``` *VL* ``` !> VL is COMPLEX 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 unitary matrix Q of !> Schur vectors returned by CHSEQR). !> 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. !> 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 COMPLEX 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 unitary matrix Q of !> Schur vectors returned by CHSEQR). !> 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. !> 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 eigenvector occupies one !> column. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (2*N) !> ``` *RWORK* ``` !> RWORK is REAL array, dimension (N) !> ``` *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 **216** of file **ctrevc.f**. ### subroutine dtrevc (character side, character howmny, logical, dimension( \* ) select, integer n, double precision, dimension( ldt, \* ) t, integer ldt, double precision, dimension( ldvl, \* ) vl, integer ldvl, double precision, dimension( ldvr, \* ) vr, integer ldvr, integer mm, integer m, double precision, dimension( \* ) work, integer info) **DTREVC** **Purpose:** ``` !> !> DTREVC 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 DHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (y**H)*T = w*(y**H) !> !> where y**H denotes the conjugate transpose of 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. !> ``` **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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DHSEQR). !> 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 DOUBLE PRECISION 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 DHSEQR). !> 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 DOUBLE PRECISION array, dimension (3*N) !> ``` *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 **220** of file **dtrevc.f**. ### subroutine strevc (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 info) **STREVC** **Purpose:** ``` !> !> STREVC 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**H)*T = w*(y**H) !> !> where y**H denotes the conjugate transpose of 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. !> ``` **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 (3*N) !> ``` *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 **220** of file **strevc.f**. ### subroutine ztrevc (character side, character howmny, logical, dimension( \* ) select, integer n, complex\*16, dimension( ldt, \* ) t, integer ldt, complex\*16, dimension( ldvl, \* ) vl, integer ldvl, complex\*16, dimension( ldvr, \* ) vr, integer ldvr, integer mm, integer m, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork, integer info) **ZTREVC** **Purpose:** ``` !> !> ZTREVC computes some or all of the right and/or left eigenvectors of !> a complex upper triangular matrix T. !> Matrices of this type are produced by the Schur factorization of !> a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (y**H)*T = w*(y**H) !> !> where y**H denotes the conjugate transpose of the vector y. !> The eigenvalues are not input to this routine, but are read directly !> from the diagonal 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 unitary 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. !> ``` **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 using the matrices supplied 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. !> The eigenvector corresponding to the j-th eigenvalue is !> computed if SELECT(j) = .TRUE.. !> Not referenced if HOWMNY = 'A' or 'B'. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix T. N >= 0. !> ``` *T* ``` !> T is COMPLEX*16 array, dimension (LDT,N) !> The upper triangular matrix T. T is modified, but restored !> on exit. !> ``` *LDT* ``` !> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !> ``` *VL* ``` !> VL is COMPLEX*16 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 unitary matrix Q of !> Schur vectors returned by ZHSEQR). !> 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. !> 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 COMPLEX*16 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 unitary matrix Q of !> Schur vectors returned by ZHSEQR). !> 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. !> 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 eigenvector occupies one !> column. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (2*N) !> ``` *RWORK* ``` !> RWORK is DOUBLE PRECISION array, dimension (N) !> ``` *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 **216** of file **ztrevc.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.