#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctgevc_(char *side, char *howmny, logical *select, integer *n, complex *a, integer *lda, complex *b, integer *ldb, complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, integer *m, complex *work, real *rwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CTGEVC computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B). The right generalized eigenvector x and the left generalized eigenvector y of (A,B) corresponding to a generalized eigenvalue w are defined by: (A - wB) * x = 0 and y**H * (A - wB) = 0 where y**H denotes the conjugate tranpose of y. If an eigenvalue w is determined by zero diagonal elements of both A and B, a unit vector is returned as the corresponding eigenvector. If all eigenvectors are requested, the routine may either return the matrices X and/or Y of right or left eigenvectors of (A,B), or the products Z*X and/or Q*Y, where Z and Q are input unitary matrices. If (A,B) was obtained from the generalized Schur factorization of an original pair of matrices (A0,B0) = (Q*A*Z**H,Q*B*Z**H), then Z*X and Q*Y are the matrices of right or left eigenvectors of A. Arguments ========= SIDE (input) CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. HOWMNY (input) CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, and backtransform them using the input matrices supplied in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, specified by the logical array SELECT. SELECT (input) LOGICAL array, dimension (N) If HOWMNY='S', SELECT specifies the eigenvectors to be computed. If HOWMNY='A' or 'B', SELECT is not referenced. To select the eigenvector corresponding to the j-th eigenvalue, SELECT(j) must be set to .TRUE.. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input) COMPLEX array, dimension (LDA,N) The upper triangular matrix A. LDA (input) INTEGER The leading dimension of array A. LDA >= max(1,N). B (input) COMPLEX array, dimension (LDB,N) The upper triangular matrix B. B must have real diagonal elements. LDB (input) INTEGER The leading dimension of array B. LDB >= max(1,N). VL (input/output) 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 left Schur vectors returned by CHGEQZ). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of (A,B) specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. If SIDE = 'R', VL is not referenced. LDVL (input) INTEGER The leading dimension of array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. VR (input/output) 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 Z of right Schur vectors returned by CHGEQZ). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the right eigenvectors of (A,B) specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. If SIDE = 'L', VR is not referenced. LDVR (input) INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. MM (input) INTEGER The number of columns in the arrays VL and/or VR. MM >= M. M (output) 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 (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (2*N) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. ===================================================================== Decode and Test the input parameters Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {0.f,0.f}; static complex c_b2 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2, r__3, r__4, r__5, r__6; complex q__1, q__2, q__3, q__4; /* Builtin functions */ double r_imag(complex *); void r_cnjg(complex *, complex *); /* Local variables */ static integer ibeg, ieig, iend; static real dmin__; static integer isrc; static real temp; static complex suma, sumb; static real xmax; static complex d__; static integer i__, j; static real scale; static logical ilall; static integer iside; static real sbeta; extern logical lsame_(char *, char *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); static real small; static logical compl; static real anorm, bnorm; static logical compr; static complex ca, cb; static logical ilbbad; static real acoefa; static integer je; static real bcoefa, acoeff; static complex bcoeff; static logical ilback; static integer im; extern /* Subroutine */ int slabad_(real *, real *); static real ascale, bscale; static integer jr; extern /* Complex */ VOID cladiv_(complex *, complex *, complex *); extern doublereal slamch_(char *); static complex salpha; static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static real bignum; static logical ilcomp; static integer ihwmny; static real big; static logical lsa, lsb; static real ulp; static complex sum; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] #define vl_subscr(a_1,a_2) (a_2)*vl_dim1 + a_1 #define vl_ref(a_1,a_2) vl[vl_subscr(a_1,a_2)] #define vr_subscr(a_1,a_2) (a_2)*vr_dim1 + a_1 #define vr_ref(a_1,a_2) vr[vr_subscr(a_1,a_2)] --select; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --work; --rwork; /* Function Body */ if (lsame_(howmny, "A")) { ihwmny = 1; ilall = TRUE_; ilback = FALSE_; } else if (lsame_(howmny, "S")) { ihwmny = 2; ilall = FALSE_; ilback = FALSE_; } else if (lsame_(howmny, "B") || lsame_(howmny, "T")) { ihwmny = 3; ilall = TRUE_; ilback = TRUE_; } else { ihwmny = -1; } if (lsame_(side, "R")) { iside = 1; compl = FALSE_; compr = TRUE_; } else if (lsame_(side, "L")) { iside = 2; compl = TRUE_; compr = FALSE_; } else if (lsame_(side, "B")) { iside = 3; compl = TRUE_; compr = TRUE_; } else { iside = -1; } *info = 0; if (iside < 0) { *info = -1; } else if (ihwmny < 0) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldb < max(1,*n)) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("CTGEVC", &i__1); return 0; } /* Count the number of eigenvectors */ if (! ilall) { im = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (select[j]) { ++im; } /* L10: */ } } else { im = *n; } /* Check diagonal of B */ ilbbad = FALSE_; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (r_imag(&b_ref(j, j)) != 0.f) { ilbbad = TRUE_; } /* L20: */ } if (ilbbad) { *info = -7; } else if (compl && *ldvl < *n || *ldvl < 1) { *info = -10; } else if (compr && *ldvr < *n || *ldvr < 1) { *info = -12; } else if (*mm < im) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("CTGEVC", &i__1); return 0; } /* Quick return if possible */ *m = im; if (*n == 0) { return 0; } /* Machine Constants */ safmin = slamch_("Safe minimum"); big = 1.f / safmin; slabad_(&safmin, &big); ulp = slamch_("Epsilon") * slamch_("Base"); small = safmin * *n / ulp; big = 1.f / small; bignum = 1.f / (safmin * *n); /* Compute the 1-norm of each column of the strictly upper triangular part of A and B to check for possible overflow in the triangular solver. */ i__1 = a_subscr(1, 1); anorm = (r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a_ref(1, 1)), dabs(r__2)); i__1 = b_subscr(1, 1); bnorm = (r__1 = b[i__1].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(1, 1)), dabs(r__2)); rwork[1] = 0.f; rwork[*n + 1] = 0.f; i__1 = *n; for (j = 2; j <= i__1; ++j) { rwork[j] = 0.f; rwork[*n + j] = 0.f; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); rwork[j] += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(& a_ref(i__, j)), dabs(r__2)); i__3 = b_subscr(i__, j); rwork[*n + j] += (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(& b_ref(i__, j)), dabs(r__2)); /* L30: */ } /* Computing MAX */ i__2 = a_subscr(j, j); r__3 = anorm, r__4 = rwork[j] + ((r__1 = a[i__2].r, dabs(r__1)) + ( r__2 = r_imag(&a_ref(j, j)), dabs(r__2))); anorm = dmax(r__3,r__4); /* Computing MAX */ i__2 = b_subscr(j, j); r__3 = bnorm, r__4 = rwork[*n + j] + ((r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(j, j)), dabs(r__2))); bnorm = dmax(r__3,r__4); /* L40: */ } ascale = 1.f / dmax(anorm,safmin); bscale = 1.f / dmax(bnorm,safmin); /* Left eigenvectors */ if (compl) { ieig = 0; /* Main loop over eigenvalues */ i__1 = *n; for (je = 1; je <= i__1; ++je) { if (ilall) { ilcomp = TRUE_; } else { ilcomp = select[je]; } if (ilcomp) { ++ieig; i__2 = a_subscr(je, je); i__3 = b_subscr(je, je); if ((r__2 = a[i__2].r, dabs(r__2)) + (r__3 = r_imag(&a_ref(je, je)), dabs(r__3)) <= safmin && (r__1 = b[i__3].r, dabs(r__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = vl_subscr(jr, ieig); vl[i__3].r = 0.f, vl[i__3].i = 0.f; /* L50: */ } i__2 = vl_subscr(ieig, ieig); vl[i__2].r = 1.f, vl[i__2].i = 0.f; goto L140; } /* Non-singular eigenvalue: Compute coefficients a and b in H y ( a A - b B ) = 0 Computing MAX */ i__2 = a_subscr(je, je); i__3 = b_subscr(je, je); r__4 = ((r__2 = a[i__2].r, dabs(r__2)) + (r__3 = r_imag(& a_ref(je, je)), dabs(r__3))) * ascale, r__5 = (r__1 = b[i__3].r, dabs(r__1)) * bscale, r__4 = max(r__4,r__5) ; temp = 1.f / dmax(r__4,safmin); i__2 = a_subscr(je, je); q__2.r = temp * a[i__2].r, q__2.i = temp * a[i__2].i; q__1.r = ascale * q__2.r, q__1.i = ascale * q__2.i; salpha.r = q__1.r, salpha.i = q__1.i; i__2 = b_subscr(je, je); sbeta = temp * b[i__2].r * bscale; acoeff = sbeta * ascale; q__1.r = bscale * salpha.r, q__1.i = bscale * salpha.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; /* Scale to avoid underflow */ lsa = dabs(sbeta) >= safmin && dabs(acoeff) < small; lsb = (r__1 = salpha.r, dabs(r__1)) + (r__2 = r_imag(&salpha), dabs(r__2)) >= safmin && (r__3 = bcoeff.r, dabs(r__3) ) + (r__4 = r_imag(&bcoeff), dabs(r__4)) < small; scale = 1.f; if (lsa) { scale = small / dabs(sbeta) * dmin(anorm,big); } if (lsb) { /* Computing MAX */ r__3 = scale, r__4 = small / ((r__1 = salpha.r, dabs(r__1) ) + (r__2 = r_imag(&salpha), dabs(r__2))) * dmin( bnorm,big); scale = dmax(r__3,r__4); } if (lsa || lsb) { /* Computing MIN Computing MAX */ r__5 = 1.f, r__6 = dabs(acoeff), r__5 = max(r__5,r__6), r__6 = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = r_imag(&bcoeff), dabs(r__2)); r__3 = scale, r__4 = 1.f / (safmin * dmax(r__5,r__6)); scale = dmin(r__3,r__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { q__2.r = scale * salpha.r, q__2.i = scale * salpha.i; q__1.r = bscale * q__2.r, q__1.i = bscale * q__2.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; } else { q__1.r = scale * bcoeff.r, q__1.i = scale * bcoeff.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; } } acoefa = dabs(acoeff); bcoefa = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = r_imag(& bcoeff), dabs(r__2)); xmax = 1.f; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr; work[i__3].r = 0.f, work[i__3].i = 0.f; /* L60: */ } i__2 = je; work[i__2].r = 1.f, work[i__2].i = 0.f; /* Computing MAX */ r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, r__1 = max(r__1,r__2); dmin__ = dmax(r__1,safmin); /* H Triangular solve of (a A - b B) y = 0 H (rowwise in (a A - b B) , or columnwise in a A - b B) */ i__2 = *n; for (j = je + 1; j <= i__2; ++j) { /* Compute j-1 SUM = sum conjg( a*A(k,j) - b*B(k,j) )*x(k) k=je (Scale if necessary) */ temp = 1.f / xmax; if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum * temp) { i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { i__4 = jr; i__5 = jr; q__1.r = temp * work[i__5].r, q__1.i = temp * work[i__5].i; work[i__4].r = q__1.r, work[i__4].i = q__1.i; /* L70: */ } xmax = 1.f; } suma.r = 0.f, suma.i = 0.f; sumb.r = 0.f, sumb.i = 0.f; i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { r_cnjg(&q__3, &a_ref(jr, j)); i__4 = jr; q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4] .i, q__2.i = q__3.r * work[i__4].i + q__3.i * work[i__4].r; q__1.r = suma.r + q__2.r, q__1.i = suma.i + q__2.i; suma.r = q__1.r, suma.i = q__1.i; r_cnjg(&q__3, &b_ref(jr, j)); i__4 = jr; q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4] .i, q__2.i = q__3.r * work[i__4].i + q__3.i * work[i__4].r; q__1.r = sumb.r + q__2.r, q__1.i = sumb.i + q__2.i; sumb.r = q__1.r, sumb.i = q__1.i; /* L80: */ } q__2.r = acoeff * suma.r, q__2.i = acoeff * suma.i; r_cnjg(&q__4, &bcoeff); q__3.r = q__4.r * sumb.r - q__4.i * sumb.i, q__3.i = q__4.r * sumb.i + q__4.i * sumb.r; q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i; sum.r = q__1.r, sum.i = q__1.i; /* Form x(j) = - SUM / conjg( a*A(j,j) - b*B(j,j) ) with scaling and perturbation of the denominator */ i__3 = a_subscr(j, j); q__3.r = acoeff * a[i__3].r, q__3.i = acoeff * a[i__3].i; i__4 = b_subscr(j, j); q__4.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, q__4.i = bcoeff.r * b[i__4].i + bcoeff.i * b[i__4] .r; q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i; r_cnjg(&q__1, &q__2); d__.r = q__1.r, d__.i = q__1.i; if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), dabs(r__2)) <= dmin__) { q__1.r = dmin__, q__1.i = 0.f; d__.r = q__1.r, d__.i = q__1.i; } if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), dabs(r__2)) < 1.f) { if ((r__1 = sum.r, dabs(r__1)) + (r__2 = r_imag(&sum), dabs(r__2)) >= bignum * ((r__3 = d__.r, dabs( r__3)) + (r__4 = r_imag(&d__), dabs(r__4)))) { temp = 1.f / ((r__1 = sum.r, dabs(r__1)) + (r__2 = r_imag(&sum), dabs(r__2))); i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { i__4 = jr; i__5 = jr; q__1.r = temp * work[i__5].r, q__1.i = temp * work[i__5].i; work[i__4].r = q__1.r, work[i__4].i = q__1.i; /* L90: */ } xmax = temp * xmax; q__1.r = temp * sum.r, q__1.i = temp * sum.i; sum.r = q__1.r, sum.i = q__1.i; } } i__3 = j; q__2.r = -sum.r, q__2.i = -sum.i; cladiv_(&q__1, &q__2, &d__); work[i__3].r = q__1.r, work[i__3].i = q__1.i; /* Computing MAX */ i__3 = j; r__3 = xmax, r__4 = (r__1 = work[i__3].r, dabs(r__1)) + ( r__2 = r_imag(&work[j]), dabs(r__2)); xmax = dmax(r__3,r__4); /* L100: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { i__2 = *n + 1 - je; cgemv_("N", n, &i__2, &c_b2, &vl_ref(1, je), ldvl, &work[ je], &c__1, &c_b1, &work[*n + 1], &c__1); isrc = 2; ibeg = 1; } else { isrc = 1; ibeg = je; } /* Copy and scale eigenvector into column of VL */ xmax = 0.f; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { /* Computing MAX */ i__3 = (isrc - 1) * *n + jr; r__3 = xmax, r__4 = (r__1 = work[i__3].r, dabs(r__1)) + ( r__2 = r_imag(&work[(isrc - 1) * *n + jr]), dabs( r__2)); xmax = dmax(r__3,r__4); /* L110: */ } if (xmax > safmin) { temp = 1.f / xmax; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { i__3 = vl_subscr(jr, ieig); i__4 = (isrc - 1) * *n + jr; q__1.r = temp * work[i__4].r, q__1.i = temp * work[ i__4].i; vl[i__3].r = q__1.r, vl[i__3].i = q__1.i; /* L120: */ } } else { ibeg = *n + 1; } i__2 = ibeg - 1; for (jr = 1; jr <= i__2; ++jr) { i__3 = vl_subscr(jr, ieig); vl[i__3].r = 0.f, vl[i__3].i = 0.f; /* L130: */ } } L140: ; } } /* Right eigenvectors */ if (compr) { ieig = im + 1; /* Main loop over eigenvalues */ for (je = *n; je >= 1; --je) { if (ilall) { ilcomp = TRUE_; } else { ilcomp = select[je]; } if (ilcomp) { --ieig; i__1 = a_subscr(je, je); i__2 = b_subscr(je, je); if ((r__2 = a[i__1].r, dabs(r__2)) + (r__3 = r_imag(&a_ref(je, je)), dabs(r__3)) <= safmin && (r__1 = b[i__2].r, dabs(r__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = vr_subscr(jr, ieig); vr[i__2].r = 0.f, vr[i__2].i = 0.f; /* L150: */ } i__1 = vr_subscr(ieig, ieig); vr[i__1].r = 1.f, vr[i__1].i = 0.f; goto L250; } /* Non-singular eigenvalue: Compute coefficients a and b in ( a A - b B ) x = 0 Computing MAX */ i__1 = a_subscr(je, je); i__2 = b_subscr(je, je); r__4 = ((r__2 = a[i__1].r, dabs(r__2)) + (r__3 = r_imag(& a_ref(je, je)), dabs(r__3))) * ascale, r__5 = (r__1 = b[i__2].r, dabs(r__1)) * bscale, r__4 = max(r__4,r__5) ; temp = 1.f / dmax(r__4,safmin); i__1 = a_subscr(je, je); q__2.r = temp * a[i__1].r, q__2.i = temp * a[i__1].i; q__1.r = ascale * q__2.r, q__1.i = ascale * q__2.i; salpha.r = q__1.r, salpha.i = q__1.i; i__1 = b_subscr(je, je); sbeta = temp * b[i__1].r * bscale; acoeff = sbeta * ascale; q__1.r = bscale * salpha.r, q__1.i = bscale * salpha.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; /* Scale to avoid underflow */ lsa = dabs(sbeta) >= safmin && dabs(acoeff) < small; lsb = (r__1 = salpha.r, dabs(r__1)) + (r__2 = r_imag(&salpha), dabs(r__2)) >= safmin && (r__3 = bcoeff.r, dabs(r__3) ) + (r__4 = r_imag(&bcoeff), dabs(r__4)) < small; scale = 1.f; if (lsa) { scale = small / dabs(sbeta) * dmin(anorm,big); } if (lsb) { /* Computing MAX */ r__3 = scale, r__4 = small / ((r__1 = salpha.r, dabs(r__1) ) + (r__2 = r_imag(&salpha), dabs(r__2))) * dmin( bnorm,big); scale = dmax(r__3,r__4); } if (lsa || lsb) { /* Computing MIN Computing MAX */ r__5 = 1.f, r__6 = dabs(acoeff), r__5 = max(r__5,r__6), r__6 = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = r_imag(&bcoeff), dabs(r__2)); r__3 = scale, r__4 = 1.f / (safmin * dmax(r__5,r__6)); scale = dmin(r__3,r__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { q__2.r = scale * salpha.r, q__2.i = scale * salpha.i; q__1.r = bscale * q__2.r, q__1.i = bscale * q__2.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; } else { q__1.r = scale * bcoeff.r, q__1.i = scale * bcoeff.i; bcoeff.r = q__1.r, bcoeff.i = q__1.i; } } acoefa = dabs(acoeff); bcoefa = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = r_imag(& bcoeff), dabs(r__2)); xmax = 1.f; i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; work[i__2].r = 0.f, work[i__2].i = 0.f; /* L160: */ } i__1 = je; work[i__1].r = 1.f, work[i__1].i = 0.f; /* Computing MAX */ r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, r__1 = max(r__1,r__2); dmin__ = dmax(r__1,safmin); /* Triangular solve of (a A - b B) x = 0 (columnwise) WORK(1:j-1) contains sums w, WORK(j+1:JE) contains x */ i__1 = je - 1; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = a_subscr(jr, je); q__2.r = acoeff * a[i__3].r, q__2.i = acoeff * a[i__3].i; i__4 = b_subscr(jr, je); q__3.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, q__3.i = bcoeff.r * b[i__4].i + bcoeff.i * b[i__4] .r; q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; /* L170: */ } i__1 = je; work[i__1].r = 1.f, work[i__1].i = 0.f; for (j = je - 1; j >= 1; --j) { /* Form x(j) := - w(j) / d with scaling and perturbation of the denominator */ i__1 = a_subscr(j, j); q__2.r = acoeff * a[i__1].r, q__2.i = acoeff * a[i__1].i; i__2 = b_subscr(j, j); q__3.r = bcoeff.r * b[i__2].r - bcoeff.i * b[i__2].i, q__3.i = bcoeff.r * b[i__2].i + bcoeff.i * b[i__2] .r; q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i; d__.r = q__1.r, d__.i = q__1.i; if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), dabs(r__2)) <= dmin__) { q__1.r = dmin__, q__1.i = 0.f; d__.r = q__1.r, d__.i = q__1.i; } if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), dabs(r__2)) < 1.f) { i__1 = j; if ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(&work[j]), dabs(r__2)) >= bignum * (( r__3 = d__.r, dabs(r__3)) + (r__4 = r_imag(& d__), dabs(r__4)))) { i__1 = j; temp = 1.f / ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(&work[j]), dabs(r__2))); i__1 = je; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; q__1.r = temp * work[i__3].r, q__1.i = temp * work[i__3].i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; /* L180: */ } } } i__1 = j; i__2 = j; q__2.r = -work[i__2].r, q__2.i = -work[i__2].i; cladiv_(&q__1, &q__2, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; if (j > 1) { /* w = w + x(j)*(a A(*,j) - b B(*,j) ) with scaling */ i__1 = j; if ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(&work[j]), dabs(r__2)) > 1.f) { i__1 = j; temp = 1.f / ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(&work[j]), dabs(r__2))); if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >= bignum * temp) { i__1 = je; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; q__1.r = temp * work[i__3].r, q__1.i = temp * work[i__3].i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; /* L190: */ } } } i__1 = j; q__1.r = acoeff * work[i__1].r, q__1.i = acoeff * work[i__1].i; ca.r = q__1.r, ca.i = q__1.i; i__1 = j; q__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[ i__1].i, q__1.i = bcoeff.r * work[i__1].i + bcoeff.i * work[i__1].r; cb.r = q__1.r, cb.i = q__1.i; i__1 = j - 1; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; i__4 = a_subscr(jr, j); q__3.r = ca.r * a[i__4].r - ca.i * a[i__4].i, q__3.i = ca.r * a[i__4].i + ca.i * a[i__4] .r; q__2.r = work[i__3].r + q__3.r, q__2.i = work[ i__3].i + q__3.i; i__5 = b_subscr(jr, j); q__4.r = cb.r * b[i__5].r - cb.i * b[i__5].i, q__4.i = cb.r * b[i__5].i + cb.i * b[i__5] .r; q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; /* L200: */ } } /* L210: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { cgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1); isrc = 2; iend = *n; } else { isrc = 1; iend = je; } /* Copy and scale eigenvector into column of VR */ xmax = 0.f; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { /* Computing MAX */ i__2 = (isrc - 1) * *n + jr; r__3 = xmax, r__4 = (r__1 = work[i__2].r, dabs(r__1)) + ( r__2 = r_imag(&work[(isrc - 1) * *n + jr]), dabs( r__2)); xmax = dmax(r__3,r__4); /* L220: */ } if (xmax > safmin) { temp = 1.f / xmax; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { i__2 = vr_subscr(jr, ieig); i__3 = (isrc - 1) * *n + jr; q__1.r = temp * work[i__3].r, q__1.i = temp * work[ i__3].i; vr[i__2].r = q__1.r, vr[i__2].i = q__1.i; /* L230: */ } } else { iend = 0; } i__1 = *n; for (jr = iend + 1; jr <= i__1; ++jr) { i__2 = vr_subscr(jr, ieig); vr[i__2].r = 0.f, vr[i__2].i = 0.f; /* L240: */ } } L250: ; } } return 0; /* End of CTGEVC */ } /* ctgevc_ */ #undef vr_ref #undef vr_subscr #undef vl_ref #undef vl_subscr #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr