path: root/contrib/libs/clapack/ctgsna.c

/* ctgsna.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
	on Microsoft Windows system, link with libf2c.lib;
	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
	or, if you install libf2c.a in a standard place, with -lf2c -lm
	-- in that order, at the end of the command line, as in
		cc *.o -lf2c -lm
	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

		http://www.netlib.org/f2c/libf2c.zip
*/

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

/* Table of constant values */

static integer c__1 = 1;
static complex c_b19 = {1.f,0.f};
static complex c_b20 = {0.f,0.f};
static logical c_false = FALSE_;
static integer c__3 = 3;

/* Subroutine */ int ctgsna_(char *job, char *howmny, logical *select, 
	integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
	complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real 
	*dif, integer *mm, integer *m, complex *work, integer *lwork, integer 
	*iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
	    vr_offset, i__1;
    real r__1, r__2;
    complex q__1;

    /* Builtin functions */
    double c_abs(complex *);

    /* Local variables */
    integer i__, k, n1, n2, ks;
    real eps, cond;
    integer ierr, ifst;
    real lnrm;
    complex yhax, yhbx;
    integer ilst;
    real rnrm, scale;
    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
	    *, complex *, integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
    integer lwmin;
    logical wants;
    complex dummy[1];
    extern doublereal scnrm2_(integer *, complex *, integer *), slapy2_(real *
, real *);
    complex dummy1[1];
    extern /* Subroutine */ int slabad_(real *, real *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), ctgexc_(logical *, 
	    logical *, integer *, complex *, integer *, complex *, integer *, 
	    complex *, integer *, complex *, integer *, integer *, integer *, 
	    integer *), xerbla_(char *, integer *);
    real bignum;
    logical wantbh, wantdf, somcon;
    extern /* Subroutine */ int ctgsyl_(char *, integer *, integer *, integer 
	    *, complex *, integer *, complex *, integer *, complex *, integer 
	    *, complex *, integer *, complex *, integer *, complex *, integer 
	    *, real *, real *, complex *, integer *, integer *, integer *);
    real smlnum;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  CTGSNA estimates reciprocal condition numbers for specified */
/*  eigenvalues and/or eigenvectors of a matrix pair (A, B). */

/*  (A, B) must be in generalized Schur canonical form, that is, A and */
/*  B are both upper triangular. */

/*  Arguments */
/*  ========= */

/*  JOB     (input) CHARACTER*1 */
/*          Specifies whether condition numbers are required for */
/*          eigenvalues (S) or eigenvectors (DIF): */
/*          = 'E': for eigenvalues only (S); */
/*          = 'V': for eigenvectors only (DIF); */
/*          = 'B': for both eigenvalues and eigenvectors (S and DIF). */

/*  HOWMNY  (input) CHARACTER*1 */
/*          = 'A': compute condition numbers for all eigenpairs; */
/*          = 'S': compute condition numbers for selected eigenpairs */
/*                 specified by the array SELECT. */

/*  SELECT  (input) LOGICAL array, dimension (N) */
/*          If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
/*          condition numbers are required. To select condition numbers */
/*          for the corresponding j-th eigenvalue and/or eigenvector, */
/*          SELECT(j) must be set to .TRUE.. */
/*          If HOWMNY = 'A', SELECT is not referenced. */

/*  N       (input) INTEGER */
/*          The order of the square matrix pair (A, B). N >= 0. */

/*  A       (input) COMPLEX array, dimension (LDA,N) */
/*          The upper triangular matrix A in the pair (A,B). */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. LDA >= max(1,N). */

/*  B       (input) COMPLEX array, dimension (LDB,N) */
/*          The upper triangular matrix B in the pair (A, B). */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B. LDB >= max(1,N). */

/*  VL      (input) COMPLEX array, dimension (LDVL,M) */
/*          IF JOB = 'E' or 'B', VL must contain left eigenvectors of */
/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
/*          and SELECT.  The eigenvectors must be stored in consecutive */
/*          columns of VL, as returned by CTGEVC. */
/*          If JOB = 'V', VL is not referenced. */

/*  LDVL    (input) INTEGER */
/*          The leading dimension of the array VL. LDVL >= 1; and */
/*          If JOB = 'E' or 'B', LDVL >= N. */

/*  VR      (input) COMPLEX array, dimension (LDVR,M) */
/*          IF JOB = 'E' or 'B', VR must contain right eigenvectors of */
/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
/*          and SELECT.  The eigenvectors must be stored in consecutive */
/*          columns of VR, as returned by CTGEVC. */
/*          If JOB = 'V', VR is not referenced. */

/*  LDVR    (input) INTEGER */
/*          The leading dimension of the array VR. LDVR >= 1; */
/*          If JOB = 'E' or 'B', LDVR >= N. */

/*  S       (output) REAL array, dimension (MM) */
/*          If JOB = 'E' or 'B', the reciprocal condition numbers of the */
/*          selected eigenvalues, stored in consecutive elements of the */
/*          array. */
/*          If JOB = 'V', S is not referenced. */

/*  DIF     (output) REAL array, dimension (MM) */
/*          If JOB = 'V' or 'B', the estimated reciprocal condition */
/*          numbers of the selected eigenvectors, stored in consecutive */
/*          elements of the array. */
/*          If the eigenvalues cannot be reordered to compute DIF(j), */
/*          DIF(j) is set to 0; this can only occur when the true value */
/*          would be very small anyway. */
/*          For each eigenvalue/vector specified by SELECT, DIF stores */
/*          a Frobenius norm-based estimate of Difl. */
/*          If JOB = 'E', DIF is not referenced. */

/*  MM      (input) INTEGER */
/*          The number of elements in the arrays S and DIF. MM >= M. */

/*  M       (output) INTEGER */
/*          The number of elements of the arrays S and DIF used to store */
/*          the specified condition numbers; for each selected eigenvalue */
/*          one element is used. If HOWMNY = 'A', M is set to N. */

/*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK  (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,N). */
/*          If JOB = 'V' or 'B', LWORK >= max(1,2*N*N). */

/*  IWORK   (workspace) INTEGER array, dimension (N+2) */
/*          If JOB = 'E', IWORK is not referenced. */

/*  INFO    (output) INTEGER */
/*          = 0: Successful exit */
/*          < 0: If INFO = -i, the i-th argument had an illegal value */

/*  Further Details */
/*  =============== */

/*  The reciprocal of the condition number of the i-th generalized */
/*  eigenvalue w = (a, b) is defined as */

/*          S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v)) */

/*  where u and v are the right and left eigenvectors of (A, B) */
/*  corresponding to w; |z| denotes the absolute value of the complex */
/*  number, and norm(u) denotes the 2-norm of the vector u. The pair */
/*  (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the */
/*  matrix pair (A, B). If both a and b equal zero, then (A,B) is */
/*  singular and S(I) = -1 is returned. */

/*  An approximate error bound on the chordal distance between the i-th */
/*  computed generalized eigenvalue w and the corresponding exact */
/*  eigenvalue lambda is */

/*          chord(w, lambda) <=   EPS * norm(A, B) / S(I), */

/*  where EPS is the machine precision. */

/*  The reciprocal of the condition number of the right eigenvector u */
/*  and left eigenvector v corresponding to the generalized eigenvalue w */
/*  is defined as follows. Suppose */

/*                   (A, B) = ( a   *  ) ( b  *  )  1 */
/*                            ( 0  A22 ),( 0 B22 )  n-1 */
/*                              1  n-1     1 n-1 */

/*  Then the reciprocal condition number DIF(I) is */

/*          Difl[(a, b), (A22, B22)]  = sigma-min( Zl ) */

/*  where sigma-min(Zl) denotes the smallest singular value of */

/*         Zl = [ kron(a, In-1) -kron(1, A22) ] */
/*              [ kron(b, In-1) -kron(1, B22) ]. */

/*  Here In-1 is the identity matrix of size n-1 and X' is the conjugate */
/*  transpose of X. kron(X, Y) is the Kronecker product between the */
/*  matrices X and Y. */

/*  We approximate the smallest singular value of Zl with an upper */
/*  bound. This is done by CLATDF. */

/*  An approximate error bound for a computed eigenvector VL(i) or */
/*  VR(i) is given by */

/*                      EPS * norm(A, B) / DIF(i). */

/*  See ref. [2-3] for more details and further references. */

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

/*  References */
/*  ========== */

/*  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/*      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/*      M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/*      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */

/*  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/*      Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/*      Estimation: Theory, Algorithms and Software, Report */
/*      UMINF - 94.04, Department of Computing Science, Umea University, */
/*      S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. */
/*      To appear in Numerical Algorithms, 1996. */

/*  [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/*      for Solving the Generalized Sylvester Equation and Estimating the */
/*      Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/*      Department of Computing Science, Umea University, S-901 87 Umea, */
/*      Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/*      Note 75. */
/*      To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and test the input parameters */

    /* Parameter adjustments */
    --select;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --s;
    --dif;
    --work;
    --iwork;

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

    somcon = lsame_(howmny, "S");

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

    if (! wants && ! wantdf) {
	*info = -1;
    } else if (! lsame_(howmny, "A") && ! somcon) {
	*info = -2;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else if (wants && *ldvl < *n) {
	*info = -10;
    } else if (wants && *ldvr < *n) {
	*info = -12;
    } else {

/*        Set M to the number of eigenpairs for which condition numbers */
/*        are required, and test MM. */

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

	if (*n == 0) {
	    lwmin = 1;
	} else if (lsame_(job, "V") || lsame_(job, 
		"B")) {
	    lwmin = (*n << 1) * *n;
	} else {
	    lwmin = *n;
	}
	work[1].r = (real) lwmin, work[1].i = 0.f;

	if (*mm < *m) {
	    *info = -15;
	} else if (*lwork < lwmin && ! lquery) {
	    *info = -18;
	}
    }

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

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);
    ks = 0;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {

/*        Determine whether condition numbers are required for the k-th */
/*        eigenpair. */

	if (somcon) {
	    if (! select[k]) {
		goto L20;
	    }
	}

	++ks;

	if (wants) {

/*           Compute the reciprocal condition number of the k-th */
/*           eigenvalue. */

	    rnrm = scnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
	    lnrm = scnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
	    cgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 + 1]
, &c__1, &c_b20, &work[1], &c__1);
	    cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
	    yhax.r = q__1.r, yhax.i = q__1.i;
	    cgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 + 1]
, &c__1, &c_b20, &work[1], &c__1);
	    cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
	    yhbx.r = q__1.r, yhbx.i = q__1.i;
	    r__1 = c_abs(&yhax);
	    r__2 = c_abs(&yhbx);
	    cond = slapy2_(&r__1, &r__2);
	    if (cond == 0.f) {
		s[ks] = -1.f;
	    } else {
		s[ks] = cond / (rnrm * lnrm);
	    }
	}

	if (wantdf) {
	    if (*n == 1) {
		r__1 = c_abs(&a[a_dim1 + 1]);
		r__2 = c_abs(&b[b_dim1 + 1]);
		dif[ks] = slapy2_(&r__1, &r__2);
	    } else {

/*              Estimate the reciprocal condition number of the k-th */
/*              eigenvectors. */

/*              Copy the matrix (A, B) to the array WORK and move the */
/*              (k,k)th pair to the (1,1) position. */

		clacpy_("Full", n, n, &a[a_offset], lda, &work[1], n);
		clacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1], 
			n);
		ifst = k;
		ilst = 1;

		ctgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1]
, n, dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &ierr)
			;

		if (ierr > 0) {

/*                 Ill-conditioned problem - swap rejected. */

		    dif[ks] = 0.f;
		} else {

/*                 Reordering successful, solve generalized Sylvester */
/*                 equation for R and L, */
/*                            A22 * R - L * A11 = A12 */
/*                            B22 * R - L * B11 = B12, */
/*                 and compute estimate of Difl[(A11,B11), (A22, B22)]. */

		    n1 = 1;
		    n2 = *n - n1;
		    i__ = *n * *n + 1;
		    ctgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n, 
			    &work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1 
			    + i__], n, &work[i__], n, &work[n1 + i__], n, &
			    scale, &dif[ks], dummy, &c__1, &iwork[1], &ierr);
		}
	    }
	}

L20:
	;
    }
    work[1].r = (real) lwmin, work[1].i = 0.f;
    return 0;

/*     End of CTGSNA */

} /* ctgsna_ */