#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer * ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZTGEVC computes some or all of the right and/or left eigenvectors of a pair of complex matrices (S,P), where S and P are upper triangular. Matrix pairs of this type are produced by the generalized Schur factorization of a complex matrix pair (A,B): A = Q*S*Z**H, B = Q*P*Z**H as computed by ZGGHRD + ZHGEQZ. The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by: S*x = w*P*x, (y**H)*S = w*(y**H)*P, where y**H denotes the conjugate tranpose of y. The eigenvalues are not input to this routine, but are computed directly from the diagonal elements of S and P. This routine returns the matrices X and/or Y of right and left eigenvectors of (S,P), or the products Z*X and/or Q*Y, where Z and Q are input matrices. If Q and Z are the unitary factors from the generalized Schur factorization of a matrix pair (A,B), then Z*X and Q*Y are the matrices of right and left eigenvectors of (A,B). 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, backtransformed by the matrices 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. The eigenvector corresponding to the j-th eigenvalue is computed if SELECT(j) = .TRUE.. Not referenced if HOWMNY = 'A' or 'B'. N (input) INTEGER The order of the matrices S and P. N >= 0. S (input) COMPLEX*16 array, dimension (LDS,N) The upper triangular matrix S from a generalized Schur factorization, as computed by ZHGEQZ. LDS (input) INTEGER The leading dimension of array S. LDS >= max(1,N). P (input) COMPLEX*16 array, dimension (LDP,N) The upper triangular matrix P from a generalized Schur factorization, as computed by ZHGEQZ. P must have real diagonal elements. LDP (input) INTEGER The leading dimension of array P. LDP >= max(1,N). VL (input/output) 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 left Schur vectors returned by ZHGEQZ). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of (S,P) specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. Not referenced if SIDE = 'R'. LDVL (input) INTEGER The leading dimension of array VL. LDVL >= 1, and if SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. VR (input/output) 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 Z of right Schur vectors returned by ZHGEQZ). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the right eigenvectors of (S,P) specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. Not referenced if SIDE = 'L'. LDVR (input) INTEGER The leading dimension of the array VR. LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. 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*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION 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 doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__1 = 1; /* System generated locals */ integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2, d__3, d__4, d__5, d__6; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ double d_imag(doublecomplex *); void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static doublecomplex d__; static integer i__, j; static doublecomplex ca, cb; static integer je, im, jr; static doublereal big; static logical lsa, lsb; static doublereal ulp; static doublecomplex sum; static integer ibeg, ieig, iend; static doublereal dmin__; static integer isrc; static doublereal temp; static doublecomplex suma, sumb; static doublereal xmax, scale; static logical ilall; static integer iside; static doublereal sbeta; extern logical lsame_(char *, char *); static doublereal small; static logical compl; static doublereal anorm, bnorm; static logical compr; extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *); static logical ilbbad; static doublereal acoefa, bcoefa, acoeff; static doublecomplex bcoeff; static logical ilback; static doublereal ascale, bscale; extern doublereal dlamch_(char *); static doublecomplex salpha; static doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum; static logical ilcomp; extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *); static integer ihwmny; --select; s_dim1 = *lds; s_offset = 1 + s_dim1; s -= s_offset; p_dim1 = *ldp; p_offset = 1 + p_dim1; p -= p_offset; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1; 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")) { 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 (*lds < max(1,*n)) { *info = -6; } else if (*ldp < max(1,*n)) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTGEVC", &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 (d_imag(&p[j + j * p_dim1]) != 0.) { 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_("ZTGEVC", &i__1); return 0; } /* Quick return if possible */ *m = im; if (*n == 0) { return 0; } /* Machine Constants */ safmin = dlamch_("Safe minimum"); big = 1. / safmin; dlabad_(&safmin, &big); ulp = dlamch_("Epsilon") * dlamch_("Base"); small = safmin * *n / ulp; big = 1. / small; bignum = 1. / (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 = s_dim1 + 1; anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]), abs(d__2)); i__1 = p_dim1 + 1; bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]), abs(d__2)); rwork[1] = 0.; rwork[*n + 1] = 0.; i__1 = *n; for (j = 2; j <= i__1; ++j) { rwork[j] = 0.; rwork[*n + j] = 0.; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * s_dim1; rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__ + j * s_dim1]), abs(d__2)); i__3 = i__ + j * p_dim1; rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(& p[i__ + j * p_dim1]), abs(d__2)); /* L30: */ } /* Computing MAX */ i__2 = j + j * s_dim1; d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + ( d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2))); anorm = max(d__3,d__4); /* Computing MAX */ i__2 = j + j * p_dim1; d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) + (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2))); bnorm = max(d__3,d__4); /* L40: */ } ascale = 1. / max(anorm,safmin); bscale = 1. / max(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 = je + je * s_dim1; i__3 = je + je * p_dim1; if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r, abs(d__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; vl[i__3].r = 0., vl[i__3].i = 0.; /* L50: */ } i__2 = ieig + ieig * vl_dim1; vl[i__2].r = 1., vl[i__2].i = 0.; goto L140; } /* Non-singular eigenvalue: Compute coefficients a and b in H y ( a A - b B ) = 0 Computing MAX */ i__2 = je + je * s_dim1; i__3 = je + je * p_dim1; d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = p[i__3].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5); temp = 1. / max(d__4,safmin); i__2 = je + je * s_dim1; z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i; z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i; salpha.r = z__1.r, salpha.i = z__1.i; i__2 = je + je * p_dim1; sbeta = temp * p[i__2].r * bscale; acoeff = sbeta * ascale; z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; /* Scale to avoid underflow */ lsa = abs(sbeta) >= safmin && abs(acoeff) < small; lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) + (d__4 = d_imag(&bcoeff), abs(d__4)) < small; scale = 1.; if (lsa) { scale = small / abs(sbeta) * min(anorm,big); } if (lsb) { /* Computing MAX */ d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2))) * min( bnorm,big); scale = max(d__3,d__4); } if (lsa || lsb) { /* Computing MIN Computing MAX */ d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6), d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&bcoeff), abs(d__2)); d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6)); scale = min(d__3,d__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { z__2.r = scale * salpha.r, z__2.i = scale * salpha.i; z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } else { z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } } acoefa = abs(acoeff); bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(& bcoeff), abs(d__2)); xmax = 1.; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr; work[i__3].r = 0., work[i__3].i = 0.; /* L60: */ } i__2 = je; work[i__2].r = 1., work[i__2].i = 0.; /* Computing MAX */ d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = max(d__1,d__2); dmin__ = max(d__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*S(k,j) - b*P(k,j) )*x(k) k=je (Scale if necessary) */ temp = 1. / 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; z__1.r = temp * work[i__5].r, z__1.i = temp * work[i__5].i; work[i__4].r = z__1.r, work[i__4].i = z__1.i; /* L70: */ } xmax = 1.; } suma.r = 0., suma.i = 0.; sumb.r = 0., sumb.i = 0.; i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { d_cnjg(&z__3, &s[jr + j * s_dim1]); i__4 = jr; z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4] .i, z__2.i = z__3.r * work[i__4].i + z__3.i * work[i__4].r; z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i; suma.r = z__1.r, suma.i = z__1.i; d_cnjg(&z__3, &p[jr + j * p_dim1]); i__4 = jr; z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4] .i, z__2.i = z__3.r * work[i__4].i + z__3.i * work[i__4].r; z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i; sumb.r = z__1.r, sumb.i = z__1.i; /* L80: */ } z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i; d_cnjg(&z__4, &bcoeff); z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i = z__4.r * sumb.i + z__4.i * sumb.r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; sum.r = z__1.r, sum.i = z__1.i; /* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) with scaling and perturbation of the denominator */ i__3 = j + j * s_dim1; z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i; i__4 = j + j * p_dim1; z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; d_cnjg(&z__1, &z__2); d__.r = z__1.r, d__.i = z__1.i; if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) <= dmin__) { z__1.r = dmin__, z__1.i = 0.; d__.r = z__1.r, d__.i = z__1.i; } if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) < 1.) { if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum), abs(d__2)) >= bignum * ((d__3 = d__.r, abs( d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) { temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum), abs(d__2))); i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { i__4 = jr; i__5 = jr; z__1.r = temp * work[i__5].r, z__1.i = temp * work[i__5].i; work[i__4].r = z__1.r, work[i__4].i = z__1.i; /* L90: */ } xmax = temp * xmax; z__1.r = temp * sum.r, z__1.i = temp * sum.i; sum.r = z__1.r, sum.i = z__1.i; } } i__3 = j; z__2.r = -sum.r, z__2.i = -sum.i; zladiv_(&z__1, &z__2, &d__); work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* Computing MAX */ i__3 = j; d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__2)); xmax = max(d__3,d__4); /* L100: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { i__2 = *n + 1 - je; zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], 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.; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { /* Computing MAX */ i__3 = (isrc - 1) * *n + jr; d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + ( d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs( d__2)); xmax = max(d__3,d__4); /* L110: */ } if (xmax > safmin) { temp = 1. / xmax; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; i__4 = (isrc - 1) * *n + jr; z__1.r = temp * work[i__4].r, z__1.i = temp * work[ i__4].i; vl[i__3].r = z__1.r, vl[i__3].i = z__1.i; /* L120: */ } } else { ibeg = *n + 1; } i__2 = ibeg - 1; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; vl[i__3].r = 0., vl[i__3].i = 0.; /* 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 = je + je * s_dim1; i__2 = je + je * p_dim1; if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r, abs(d__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; vr[i__2].r = 0., vr[i__2].i = 0.; /* L150: */ } i__1 = ieig + ieig * vr_dim1; vr[i__1].r = 1., vr[i__1].i = 0.; goto L250; } /* Non-singular eigenvalue: Compute coefficients a and b in ( a A - b B ) x = 0 Computing MAX */ i__1 = je + je * s_dim1; i__2 = je + je * p_dim1; d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = p[i__2].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5); temp = 1. / max(d__4,safmin); i__1 = je + je * s_dim1; z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i; z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i; salpha.r = z__1.r, salpha.i = z__1.i; i__1 = je + je * p_dim1; sbeta = temp * p[i__1].r * bscale; acoeff = sbeta * ascale; z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; /* Scale to avoid underflow */ lsa = abs(sbeta) >= safmin && abs(acoeff) < small; lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) + (d__4 = d_imag(&bcoeff), abs(d__4)) < small; scale = 1.; if (lsa) { scale = small / abs(sbeta) * min(anorm,big); } if (lsb) { /* Computing MAX */ d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2))) * min( bnorm,big); scale = max(d__3,d__4); } if (lsa || lsb) { /* Computing MIN Computing MAX */ d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6), d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&bcoeff), abs(d__2)); d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6)); scale = min(d__3,d__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { z__2.r = scale * salpha.r, z__2.i = scale * salpha.i; z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } else { z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } } acoefa = abs(acoeff); bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(& bcoeff), abs(d__2)); xmax = 1.; i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; work[i__2].r = 0., work[i__2].i = 0.; /* L160: */ } i__1 = je; work[i__1].r = 1., work[i__1].i = 0.; /* Computing MAX */ d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = max(d__1,d__2); dmin__ = max(d__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 = jr + je * s_dim1; z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i; i__4 = jr + je * p_dim1; z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L170: */ } i__1 = je; work[i__1].r = 1., work[i__1].i = 0.; for (j = je - 1; j >= 1; --j) { /* Form x(j) := - w(j) / d with scaling and perturbation of the denominator */ i__1 = j + j * s_dim1; z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i; i__2 = j + j * p_dim1; z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i, z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2] .r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; d__.r = z__1.r, d__.i = z__1.i; if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) <= dmin__) { z__1.r = dmin__, z__1.i = 0.; d__.r = z__1.r, d__.i = z__1.i; } if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) < 1.) { i__1 = j; if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag( &work[j]), abs(d__2)) >= bignum * ((d__3 = d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs( d__4)))) { i__1 = j; temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__2))); i__1 = je; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; z__1.r = temp * work[i__3].r, z__1.i = temp * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L180: */ } } } i__1 = j; i__2 = j; z__2.r = -work[i__2].r, z__2.i = -work[i__2].i; zladiv_(&z__1, &z__2, &d__); work[i__1].r = z__1.r, work[i__1].i = z__1.i; if (j > 1) { /* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */ i__1 = j; if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag( &work[j]), abs(d__2)) > 1.) { i__1 = j; temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__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; z__1.r = temp * work[i__3].r, z__1.i = temp * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L190: */ } } } i__1 = j; z__1.r = acoeff * work[i__1].r, z__1.i = acoeff * work[i__1].i; ca.r = z__1.r, ca.i = z__1.i; i__1 = j; z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[ i__1].i, z__1.i = bcoeff.r * work[i__1].i + bcoeff.i * work[i__1].r; cb.r = z__1.r, cb.i = z__1.i; i__1 = j - 1; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; i__4 = jr + j * s_dim1; z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i, z__3.i = ca.r * s[i__4].i + ca.i * s[i__4] .r; z__2.r = work[i__3].r + z__3.r, z__2.i = work[ i__3].i + z__3.i; i__5 = jr + j * p_dim1; z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i, z__4.i = cb.r * p[i__5].i + cb.i * p[i__5] .r; z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L200: */ } } /* L210: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { zgemv_("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.; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { /* Computing MAX */ i__2 = (isrc - 1) * *n + jr; d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + ( d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs( d__2)); xmax = max(d__3,d__4); /* L220: */ } if (xmax > safmin) { temp = 1. / xmax; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; i__3 = (isrc - 1) * *n + jr; z__1.r = temp * work[i__3].r, z__1.i = temp * work[ i__3].i; vr[i__2].r = z__1.r, vr[i__2].i = z__1.i; /* L230: */ } } else { iend = 0; } i__1 = *n; for (jr = iend + 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; vr[i__2].r = 0., vr[i__2].i = 0.; /* L240: */ } } L250: ; } } return 0; /* End of ZTGEVC */ } /* ztgevc_ */