#include "f2c.h" #include "blaswrap.h" /* 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; /* Subroutine */ int ctgevc_(char *side, char *howmny, logical *select, integer *n, complex *s, integer *lds, complex *p, integer *ldp, complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, integer *m, complex *work, real *rwork, integer *info) { /* 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; 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 */ complex d__; integer i__, j; complex ca, cb; integer je, im, jr; real big; logical lsa, lsb; real ulp; complex sum; integer ibeg, ieig, iend; real dmin__; integer isrc; real temp; complex suma, sumb; real xmax, scale; logical ilall; integer iside; real sbeta; extern logical lsame_(char *, char *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); real small; logical compl; real anorm, bnorm; logical compr, ilbbad; real acoefa, bcoefa, acoeff; complex bcoeff; logical ilback; extern /* Subroutine */ int slabad_(real *, real *); real ascale, bscale; extern /* Complex */ VOID cladiv_(complex *, complex *, complex *); extern doublereal slamch_(char *); complex salpha; real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); real bignum; logical ilcomp; integer ihwmny; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CTGEVC 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 CGGHRD + CHGEQZ. */ /* 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 array, dimension (LDS,N) */ /* The upper triangular matrix S from a generalized Schur */ /* factorization, as computed by CHGEQZ. */ /* LDS (input) INTEGER */ /* The leading dimension of array S. LDS >= max(1,N). */ /* P (input) COMPLEX array, dimension (LDP,N) */ /* The upper triangular matrix P from a generalized Schur */ /* factorization, as computed by CHGEQZ. P must have real */ /* diagonal elements. */ /* LDP (input) INTEGER */ /* The leading dimension of array P. LDP >= 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 (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 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 (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 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function definitions .. */ /* .. */ /* .. Executable Statements .. */ /* Decode and Test the input parameters */ /* Parameter adjustments */ --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_("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(&p[j + j * p_dim1]) != 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 = s_dim1 + 1; anorm = (r__1 = s[i__1].r, dabs(r__1)) + (r__2 = r_imag(&s[s_dim1 + 1]), dabs(r__2)); i__1 = p_dim1 + 1; bnorm = (r__1 = p[i__1].r, dabs(r__1)) + (r__2 = r_imag(&p[p_dim1 + 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 = i__ + j * s_dim1; rwork[j] += (r__1 = s[i__3].r, dabs(r__1)) + (r__2 = r_imag(&s[ i__ + j * s_dim1]), dabs(r__2)); i__3 = i__ + j * p_dim1; rwork[*n + j] += (r__1 = p[i__3].r, dabs(r__1)) + (r__2 = r_imag(& p[i__ + j * p_dim1]), dabs(r__2)); /* L30: */ } /* Computing MAX */ i__2 = j + j * s_dim1; r__3 = anorm, r__4 = rwork[j] + ((r__1 = s[i__2].r, dabs(r__1)) + ( r__2 = r_imag(&s[j + j * s_dim1]), dabs(r__2))); anorm = dmax(r__3,r__4); /* Computing MAX */ i__2 = j + j * p_dim1; r__3 = bnorm, r__4 = rwork[*n + j] + ((r__1 = p[i__2].r, dabs(r__1)) + (r__2 = r_imag(&p[j + j * p_dim1]), 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 = je + je * s_dim1; i__3 = je + je * p_dim1; if ((r__2 = s[i__2].r, dabs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), dabs(r__3)) <= safmin && (r__1 = p[ 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 = jr + ieig * vl_dim1; vl[i__3].r = 0.f, vl[i__3].i = 0.f; /* L50: */ } i__2 = ieig + ieig * vl_dim1; 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 = je + je * s_dim1; i__3 = je + je * p_dim1; r__4 = ((r__2 = s[i__2].r, dabs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), dabs(r__3))) * ascale, r__5 = (r__1 = p[i__3].r, dabs(r__1)) * bscale, r__4 = max(r__4, r__5); temp = 1.f / dmax(r__4,safmin); i__2 = je + je * s_dim1; q__2.r = temp * s[i__2].r, q__2.i = temp * s[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 = je + je * p_dim1; sbeta = temp * p[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*S(k,j) - b*P(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, &s[jr + j * s_dim1]); 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, &p[jr + j * p_dim1]); 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*S(j,j) - b*P(j,j) ) */ /* with scaling and perturbation of the denominator */ i__3 = j + j * s_dim1; q__3.r = acoeff * s[i__3].r, q__3.i = acoeff * s[i__3].i; i__4 = j + j * p_dim1; q__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, q__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[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[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.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 = jr + ieig * vl_dim1; 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 = jr + ieig * vl_dim1; 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 = je + je * s_dim1; i__2 = je + je * p_dim1; if ((r__2 = s[i__1].r, dabs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), dabs(r__3)) <= safmin && (r__1 = p[ 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 = jr + ieig * vr_dim1; vr[i__2].r = 0.f, vr[i__2].i = 0.f; /* L150: */ } i__1 = ieig + ieig * vr_dim1; 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 = je + je * s_dim1; i__2 = je + je * p_dim1; r__4 = ((r__2 = s[i__1].r, dabs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), dabs(r__3))) * ascale, r__5 = (r__1 = p[i__2].r, dabs(r__1)) * bscale, r__4 = max(r__4, r__5); temp = 1.f / dmax(r__4,safmin); i__1 = je + je * s_dim1; q__2.r = temp * s[i__1].r, q__2.i = temp * s[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 = je + je * p_dim1; sbeta = temp * p[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 = jr + je * s_dim1; q__2.r = acoeff * s[i__3].r, q__2.i = acoeff * s[i__3].i; i__4 = jr + je * p_dim1; q__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, q__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[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 = j + j * s_dim1; q__2.r = acoeff * s[i__1].r, q__2.i = acoeff * s[i__1].i; i__2 = j + j * p_dim1; q__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i, q__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[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 S(*,j) - b P(*,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 = jr + j * s_dim1; q__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i, q__3.i = ca.r * s[i__4].i + ca.i * s[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 = jr + j * p_dim1; q__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i, q__4.i = cb.r * p[i__5].i + cb.i * p[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 = jr + ieig * vr_dim1; 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 = jr + ieig * vr_dim1; vr[i__2].r = 0.f, vr[i__2].i = 0.f; /* L240: */ } } L250: ; } } return 0; /* End of CTGEVC */ } /* ctgevc_ */