#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int ctrsen_(char *job, char *compq, logical *select, integer 
	*n, complex *t, integer *ldt, complex *q, integer *ldq, complex *w, 
	integer *m, real *s, real *sep, complex *work, integer *lwork, 
	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   
    =======   

    CTRSEN reorders the Schur factorization of a complex matrix   
    A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in   
    the leading positions on the diagonal of the upper triangular matrix   
    T, and the leading columns of Q form an orthonormal basis of the   
    corresponding right invariant subspace.   

    Optionally the routine computes the reciprocal condition numbers of   
    the cluster of eigenvalues and/or the invariant subspace.   

    Arguments   
    =========   

    JOB     (input) CHARACTER*1   
            Specifies whether condition numbers are required for the   
            cluster of eigenvalues (S) or the invariant subspace (SEP):   
            = 'N': none;   
            = 'E': for eigenvalues only (S);   
            = 'V': for invariant subspace only (SEP);   
            = 'B': for both eigenvalues and invariant subspace (S and   
                   SEP).   

    COMPQ   (input) CHARACTER*1   
            = 'V': update the matrix Q of Schur vectors;   
            = 'N': do not update Q.   

    SELECT  (input) LOGICAL array, dimension (N)   
            SELECT specifies the eigenvalues in the selected cluster. To   
            select the j-th eigenvalue, SELECT(j) must be set to .TRUE..   

    N       (input) INTEGER   
            The order of the matrix T. N >= 0.   

    T       (input/output) COMPLEX array, dimension (LDT,N)   
            On entry, the upper triangular matrix T.   
            On exit, T is overwritten by the reordered matrix T, with the   
            selected eigenvalues as the leading diagonal elements.   

    LDT     (input) INTEGER   
            The leading dimension of the array T. LDT >= max(1,N).   

    Q       (input/output) COMPLEX array, dimension (LDQ,N)   
            On entry, if COMPQ = 'V', the matrix Q of Schur vectors.   
            On exit, if COMPQ = 'V', Q has been postmultiplied by the   
            unitary transformation matrix which reorders T; the leading M   
            columns of Q form an orthonormal basis for the specified   
            invariant subspace.   
            If COMPQ = 'N', Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q.   
            LDQ >= 1; and if COMPQ = 'V', LDQ >= N.   

    W       (output) COMPLEX array, dimension (N)   
            The reordered eigenvalues of T, in the same order as they   
            appear on the diagonal of T.   

    M       (output) INTEGER   
            The dimension of the specified invariant subspace.   
            0 <= M <= N.   

    S       (output) REAL   
            If JOB = 'E' or 'B', S is a lower bound on the reciprocal   
            condition number for the selected cluster of eigenvalues.   
            S cannot underestimate the true reciprocal condition number   
            by more than a factor of sqrt(N). If M = 0 or N, S = 1.   
            If JOB = 'N' or 'V', S is not referenced.   

    SEP     (output) REAL   
            If JOB = 'V' or 'B', SEP is the estimated reciprocal   
            condition number of the specified invariant subspace. If   
            M = 0 or N, SEP = norm(T).   
            If JOB = 'N' or 'E', SEP is not referenced.   

    WORK    (workspace/output) COMPLEX array, dimension (LWORK)   
            If JOB = 'N', WORK is not referenced.  Otherwise,   
            on exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   
            If JOB = 'N', LWORK >= 1;   
            if JOB = 'E', LWORK = M*(N-M);   
            if JOB = 'V' or 'B', LWORK >= 2*M*(N-M).   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   

    Further Details   
    ===============   

    CTRSEN first collects the selected eigenvalues by computing a unitary   
    transformation Z to move them to the top left corner of T. In other   
    words, the selected eigenvalues are the eigenvalues of T11 in:   

                  Z'*T*Z = ( T11 T12 ) n1   
                           (  0  T22 ) n2   
                              n1  n2   

    where N = n1+n2 and Z' means the conjugate transpose of Z. The first   
    n1 columns of Z span the specified invariant subspace of T.   

    If T has been obtained from the Schur factorization of a matrix   
    A = Q*T*Q', then the reordered Schur factorization of A is given by   
    A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span the   
    corresponding invariant subspace of A.   

    The reciprocal condition number of the average of the eigenvalues of   
    T11 may be returned in S. S lies between 0 (very badly conditioned)   
    and 1 (very well conditioned). It is computed as follows. First we   
    compute R so that   

                           P = ( I  R ) n1   
                               ( 0  0 ) n2   
                                 n1 n2   

    is the projector on the invariant subspace associated with T11.   
    R is the solution of the Sylvester equation:   

                          T11*R - R*T22 = T12.   

    Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote   
    the two-norm of M. Then S is computed as the lower bound   

                        (1 + F-norm(R)**2)**(-1/2)   

    on the reciprocal of 2-norm(P), the true reciprocal condition number.   
    S cannot underestimate 1 / 2-norm(P) by more than a factor of   
    sqrt(N).   

    An approximate error bound for the computed average of the   
    eigenvalues of T11 is   

                           EPS * norm(T) / S   

    where EPS is the machine precision.   

    The reciprocal condition number of the right invariant subspace   
    spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP.   
    SEP is defined as the separation of T11 and T22:   

                       sep( T11, T22 ) = sigma-min( C )   

    where sigma-min(C) is the smallest singular value of the   
    n1*n2-by-n1*n2 matrix   

       C  = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) )   

    I(m) is an m by m identity matrix, and kprod denotes the Kronecker   
    product. We estimate sigma-min(C) by the reciprocal of an estimate of   
    the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C)   
    cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2).   

    When SEP is small, small changes in T can cause large changes in   
    the invariant subspace. An approximate bound on the maximum angular   
    error in the computed right invariant subspace is   

                        EPS * norm(T) / SEP   

    =====================================================================   


       Decode and test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer q_dim1, q_offset, t_dim1, t_offset, i__1, i__2, i__3;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer kase, ierr, k;
    static real scale;
    extern logical lsame_(char *, char *);
    static integer lwmin;
    static logical wantq, wants;
    static real rnorm;
    static integer n1, n2;
    static real rwork[1];
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    static integer nn, ks;
    extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real 
	    *, integer *), clacpy_(char *, integer *, integer *, complex *, 
	    integer *, complex *, integer *), xerbla_(char *, integer 
	    *);
    static logical wantbh;
    extern /* Subroutine */ int ctrexc_(char *, integer *, complex *, integer 
	    *, complex *, integer *, integer *, integer *, integer *);
    static logical wantsp;
    extern /* Subroutine */ int ctrsyl_(char *, char *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, integer *, complex *, 
	    integer *, real *, integer *);
    static logical lquery;
    static real est;
#define t_subscr(a_1,a_2) (a_2)*t_dim1 + a_1
#define t_ref(a_1,a_2) t[t_subscr(a_1,a_2)]


    --select;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1 * 1;
    t -= t_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --w;
    --work;

    /* Function Body */
    wantbh = lsame_(job, "B");
    wants = lsame_(job, "E") || wantbh;
    wantsp = lsame_(job, "V") || wantbh;
    wantq = lsame_(compq, "V");

/*     Set M to the number of selected eigenvalues. */

    *m = 0;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (select[k]) {
	    ++(*m);
	}
/* L10: */
    }

    n1 = *m;
    n2 = *n - *m;
    nn = n1 * n2;

    *info = 0;
    lquery = *lwork == -1;

    if (wantsp) {
/* Computing MAX */
	i__1 = 1, i__2 = nn << 1;
	lwmin = max(i__1,i__2);
    } else if (lsame_(job, "N")) {
	lwmin = 1;
    } else if (lsame_(job, "E")) {
	lwmin = max(1,nn);
    }

    if (! lsame_(job, "N") && ! wants && ! wantsp) {
	*info = -1;
    } else if (! lsame_(compq, "N") && ! wantq) {
	*info = -2;
    } else if (*n < 0) {
	*info = -4;
    } else if (*ldt < max(1,*n)) {
	*info = -6;
    } else if (*ldq < 1 || wantq && *ldq < *n) {
	*info = -8;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -14;
    }

    if (*info == 0) {
	work[1].r = (real) lwmin, work[1].i = 0.f;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CTRSEN", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*m == *n || *m == 0) {
	if (wants) {
	    *s = 1.f;
	}
	if (wantsp) {
	    *sep = clange_("1", n, n, &t[t_offset], ldt, rwork);
	}
	goto L40;
    }

/*     Collect the selected eigenvalues at the top left corner of T. */

    ks = 0;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (select[k]) {
	    ++ks;

/*           Swap the K-th eigenvalue to position KS. */

	    if (k != ks) {
		ctrexc_(compq, n, &t[t_offset], ldt, &q[q_offset], ldq, &k, &
			ks, &ierr);
	    }
	}
/* L20: */
    }

    if (wants) {

/*        Solve the Sylvester equation for R:   

             T11*R - R*T22 = scale*T12 */

	clacpy_("F", &n1, &n2, &t_ref(1, n1 + 1), ldt, &work[1], &n1);
	ctrsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t_ref(n1 + 1, 
		n1 + 1), ldt, &work[1], &n1, &scale, &ierr);

/*        Estimate the reciprocal of the condition number of the cluster   
          of eigenvalues. */

	rnorm = clange_("F", &n1, &n2, &work[1], &n1, rwork);
	if (rnorm == 0.f) {
	    *s = 1.f;
	} else {
	    *s = scale / (sqrt(scale * scale / rnorm + rnorm) * sqrt(rnorm));
	}
    }

    if (wantsp) {

/*        Estimate sep(T11,T22). */

	est = 0.f;
	kase = 0;
L30:
	clacon_(&nn, &work[nn + 1], &work[1], &est, &kase);
	if (kase != 0) {
	    if (kase == 1) {

/*              Solve T11*R - R*T22 = scale*X. */

		ctrsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t_ref(
			n1 + 1, n1 + 1), ldt, &work[1], &n1, &scale, &ierr);
	    } else {

/*              Solve T11'*R - R*T22' = scale*X. */

		ctrsyl_("C", "C", &c_n1, &n1, &n2, &t[t_offset], ldt, &t_ref(
			n1 + 1, n1 + 1), ldt, &work[1], &n1, &scale, &ierr);
	    }
	    goto L30;
	}

	*sep = scale / est;
    }

L40:

/*     Copy reordered eigenvalues to W. */

    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	i__2 = k;
	i__3 = t_subscr(k, k);
	w[i__2].r = t[i__3].r, w[i__2].i = t[i__3].i;
/* L50: */
    }

    work[1].r = (real) lwmin, work[1].i = 0.f;

    return 0;

/*     End of CTRSEN */

} /* ctrsen_ */

#undef t_ref
#undef t_subscr


