#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Common Block Declarations */ struct { doublereal ops, itcnt; } latime_; #define latime_1 latime_ /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__1 = 1; /* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer * ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, integer *info) { /* 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; 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 integer ibeg, ieig, iend; static doublereal dmin__; static integer isrc; static doublereal temp; static doublecomplex suma, sumb; static doublereal xmax; static doublecomplex d__; static integer i__, j; static doublereal 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 *); static integer iopst; static doublecomplex ca, cb; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); static logical ilbbad; static doublereal acoefa; static integer je; static doublereal bcoefa, acoeff; static doublecomplex bcoeff; static logical ilback; static integer im; static doublereal ascale, bscale; extern doublereal dlamch_(char *); static integer jr; 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; static doublereal big; static logical lsa, lsb; static doublereal ulp; static doublecomplex 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)] /* -- LAPACK routine (instrumented to count operations, version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 ----------------------- Begin Timing Code ------------------------ Common block to return operation count and iteration count ITCNT is initialized to 0, OPS is only incremented OPST is used to accumulate small contributions to OPS to avoid roundoff error ------------------------ End Timing Code ------------------------- Purpose ======= ZTGEVC 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*16 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*16 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*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 (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*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 (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 leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. 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 */ --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_("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(&b_ref(j, j)) != 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 = a_subscr(1, 1); anorm = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a_ref(1, 1)), abs( d__2)); i__1 = b_subscr(1, 1); bnorm = (d__1 = b[i__1].r, abs(d__1)) + (d__2 = d_imag(&b_ref(1, 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 = a_subscr(i__, j); rwork[j] += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a_ref( i__, j)), abs(d__2)); i__3 = b_subscr(i__, j); rwork[*n + j] += (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(& b_ref(i__, j)), abs(d__2)); /* L30: */ } /* Computing MAX */ i__2 = a_subscr(j, j); d__3 = anorm, d__4 = rwork[j] + ((d__1 = a[i__2].r, abs(d__1)) + ( d__2 = d_imag(&a_ref(j, j)), abs(d__2))); anorm = max(d__3,d__4); /* Computing MAX */ i__2 = b_subscr(j, j); d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = b[i__2].r, abs(d__1)) + (d__2 = d_imag(&b_ref(j, j)), abs(d__2))); bnorm = max(d__3,d__4); /* L40: */ } ascale = 1. / max(anorm,safmin); bscale = 1. / max(bnorm,safmin); /* ---------------------- Begin Timing Code ------------------------- Computing 2nd power */ i__1 = *n; latime_1.ops += (doublereal) ((i__1 * i__1 << 1) + (*n << 1) + 6); /* ----------------------- End Timing Code -------------------------- 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 ((d__2 = a[i__2].r, abs(d__2)) + (d__3 = d_imag(&a_ref(je, je)), abs(d__3)) <= safmin && (d__1 = b[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 = vl_subscr(jr, ieig); vl[i__3].r = 0., vl[i__3].i = 0.; /* L50: */ } i__2 = vl_subscr(ieig, ieig); 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 = a_subscr(je, je); i__3 = b_subscr(je, je); d__4 = ((d__2 = a[i__2].r, abs(d__2)) + (d__3 = d_imag(&a_ref( je, je)), abs(d__3))) * ascale, d__5 = (d__1 = b[i__3] .r, abs(d__1)) * bscale, d__4 = max(d__4,d__5); temp = 1. / max(d__4,safmin); i__2 = a_subscr(je, je); z__2.r = temp * a[i__2].r, z__2.i = temp * a[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 = b_subscr(je, je); sbeta = temp * b[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; } /* ----------------- Begin Timing Code ------------------ Calculation of SALPHA through DMIN */ iopst = 34; } else { iopst = 20; /* ------------------ End Timing Code ------------------- */ } 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*A(k,j) - b*B(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.; /* ---------------- Begin Timing Code ---------------- */ iopst += j - je << 1; /* ----------------- End Timing Code ----------------- */ } 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, &a_ref(jr, j)); 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, &b_ref(jr, j)); 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*A(j,j) - b*B(j,j) ) with scaling and perturbation of the denominator */ i__3 = a_subscr(j, j); z__3.r = acoeff * a[i__3].r, z__3.i = acoeff * a[i__3].i; i__4 = b_subscr(j, j); z__4.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, z__4.i = bcoeff.r * b[i__4].i + bcoeff.i * b[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; /* -------------- Begin Timing Code --------------- */ iopst = iopst + (j - je << 1) + 5; /* --------------- End Timing Code ---------------- */ } } 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_ref(1, je), ldvl, &work[ je], &c__1, &c_b1, &work[*n + 1], &c__1); isrc = 2; ibeg = 1; /* ----------------- Begin Timing Code ------------------ */ iopst += (*n << 3) * (*n + 1 - je); /* ------------------ End Timing Code ------------------- */ } 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 = vl_subscr(jr, ieig); 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 = vl_subscr(jr, ieig); vl[i__3].r = 0., vl[i__3].i = 0.; /* L130: */ } /* ------------------- Begin Timing Code ------------------- */ latime_1.ops += (doublereal) ((*n - je) * 36 + (*n - je << 3) * (*n + 1 - je) + (*n + 1 - ibeg) * 3 + 1) + ( doublereal) iopst; /* -------------------- End Timing Code -------------------- */ } 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 ((d__2 = a[i__1].r, abs(d__2)) + (d__3 = d_imag(&a_ref(je, je)), abs(d__3)) <= safmin && (d__1 = b[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 = vr_subscr(jr, ieig); vr[i__2].r = 0., vr[i__2].i = 0.; /* L150: */ } i__1 = vr_subscr(ieig, ieig); 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 = a_subscr(je, je); i__2 = b_subscr(je, je); d__4 = ((d__2 = a[i__1].r, abs(d__2)) + (d__3 = d_imag(&a_ref( je, je)), abs(d__3))) * ascale, d__5 = (d__1 = b[i__2] .r, abs(d__1)) * bscale, d__4 = max(d__4,d__5); temp = 1. / max(d__4,safmin); i__1 = a_subscr(je, je); z__2.r = temp * a[i__1].r, z__2.i = temp * a[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 = b_subscr(je, je); sbeta = temp * b[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; } /* ----------------- Begin Timing Code ------------------ Calculation of SALPHA through DMIN */ iopst = 34; } else { iopst = 20; /* ------------------ End Timing Code ------------------- */ } 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 = a_subscr(jr, je); z__2.r = acoeff * a[i__3].r, z__2.i = acoeff * a[i__3].i; i__4 = b_subscr(jr, je); z__3.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, z__3.i = bcoeff.r * b[i__4].i + bcoeff.i * b[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 = a_subscr(j, j); z__2.r = acoeff * a[i__1].r, z__2.i = acoeff * a[i__1].i; i__2 = b_subscr(j, j); z__3.r = bcoeff.r * b[i__2].r - bcoeff.i * b[i__2].i, z__3.i = bcoeff.r * b[i__2].i + bcoeff.i * b[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: */ } /* -------------- Begin Timing Code --------------- */ iopst = iopst + (je << 1) + 5; } else { iopst += 3; /* --------------- End Timing Code ---------------- */ } } 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 A(*,j) - b B(*,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: */ } /* ------------- Begin Timing Code ------------- */ iopst = iopst + (je << 1) + 6; } else { iopst += 6; /* -------------- End Timing Code -------------- */ } } 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 = a_subscr(jr, j); z__3.r = ca.r * a[i__4].r - ca.i * a[i__4].i, z__3.i = ca.r * a[i__4].i + ca.i * a[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 = b_subscr(jr, j); z__4.r = cb.r * b[i__5].r - cb.i * b[i__5].i, z__4.i = cb.r * b[i__5].i + cb.i * b[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; /* ----------------- Begin Timing Code ------------------ */ iopst += (*n << 3) * je; /* ------------------ End Timing Code ------------------- */ } 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 = vr_subscr(jr, ieig); 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 = vr_subscr(jr, ieig); vr[i__2].r = 0., vr[i__2].i = 0.; /* L240: */ } /* ------------------- Begin Timing Code ------------------- */ latime_1.ops += (doublereal) ((je - 2) * 30 + (je - 1 << 3) * (je - 2) + iend * 3 + 22) + (doublereal) iopst; /* -------------------- End Timing Code -------------------- */ } L250: ; } } return 0; /* End of ZTGEVC */ } /* ztgevc_ */ #undef vr_ref #undef vr_subscr #undef vl_ref #undef vl_subscr #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr