/* Subroutine */
int sgegv_(char *jobvl, char *jobvr, integer *n, real *a, integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, integer *lwork, 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;
    real r__1, r__2, r__3, r__4;
    /* Local variables */
    integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo;
    real eps;
    logical ilv;
    real absb, anrm, bnrm;
    integer itau;
    real temp;
    logical ilvl, ilvr;
    integer lopt;
    real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
    extern logical lsame_(char *, char *);
    integer ileft, iinfo, icols, iwork, irows;
    real salfai;
    extern /* Subroutine */
    int sggbak_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, integer * ), sggbal_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, real *, real *, integer *);
    real salfar;
    extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *);
    real safmin;
    extern /* Subroutine */
    int sgghrd_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , real *, integer *, integer *);
    real safmax;
    char chtemp[1];
    logical ldumma[1];
    extern /* Subroutine */
    int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
    integer ijobvl, iright;
    logical ilimit;
    extern /* Subroutine */
    int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */
    int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), stgevc_( char *, char *, logical *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, integer *);
    real onepls;
    integer lwkmin;
    extern /* Subroutine */
    int shgeqz_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real * , real *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer * , integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */
    int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *);
    /* -- LAPACK driver routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. Local Arrays .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Decode the input arguments */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --work;
    /* Function Body */
    if (lsame_(jobvl, "N"))
    {
        ijobvl = 1;
        ilvl = FALSE_;
    }
    else if (lsame_(jobvl, "V"))
    {
        ijobvl = 2;
        ilvl = TRUE_;
    }
    else
    {
//.........这里部分代码省略.........

//.........这里部分代码省略.........
		    work[j] = 0.f;
		} else {
		    work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
			     (poles[j + (poles_dim1 << 1)] + dj);
		}
		i__2 = j - 1;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    if (z__[i__] == 0.f || poles[i__ + (poles_dim1 << 1)] == 
			    0.f) {
			work[i__] = 0.f;
		    } else {
			work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] 
				/ (slamc3_(&poles[i__ + (poles_dim1 << 1)], &
				dsigj) - diflj) / (poles[i__ + (poles_dim1 << 
				1)] + dj);
		    }
		}
		i__2 = *k;
		for (i__ = j + 1; i__ <= i__2; ++i__) {
		    if (z__[i__] == 0.f || poles[i__ + (poles_dim1 << 1)] == 
			    0.f) {
			work[i__] = 0.f;
		    } else {
			work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] 
				/ (slamc3_(&poles[i__ + (poles_dim1 << 1)], &
				dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
				 1)] + dj);
		    }
		}
		work[1] = -1.f;
		temp = snrm2_(k, &work[1], &c__1);
		sgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
			c__1, &c_b13, &b[j + b_dim1], ldb);
		slascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + 
			b_dim1], ldb, info);
	    }
	}

/*        Move the deflated rows of BX to B also. */

	if (*k < max(m,n)) {
	    i__1 = n - *k;
	    slacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 
		    + b_dim1], ldb);
	}
    } else {

/*        Apply back the right orthogonal transformations. */

/*        Step (1R): apply back the new right singular vector matrix */
/*        to B. */

	if (*k == 1) {
	    scopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
	} else {
	    i__1 = *k;
	    for (j = 1; j <= i__1; ++j) {
		dsigj = poles[j + (poles_dim1 << 1)];
		if (z__[j] == 0.f) {
		    work[j] = 0.f;
		} else {
		    work[j] = -z__[j] / difl[j] / (dsigj + poles[j + 
			    poles_dim1]) / difr[j + (difr_dim1 << 1)];
		}
		i__2 = j - 1;
		for (i__ = 1; i__ <= i__2; ++i__) {

//.........这里部分代码省略.........

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1.f / smlnum;

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    icond = 0;
    anrm = clange_("M", n, n, &a[a_offset], lda, dum);
    scalea = FALSE_;
    if (anrm > 0.f && anrm < smlnum) {
	scalea = TRUE_;
	cscale = smlnum;
    } else if (anrm > bignum) {
	scalea = TRUE_;
	cscale = bignum;
    }
    if (scalea) {
	clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
		ierr);
    }

/*     Balance the matrix and compute ABNRM */

    cgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
    *abnrm = clange_("1", n, n, &a[a_offset], lda, dum);
    if (scalea) {
	dum[0] = *abnrm;
	slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
		ierr);
	*abnrm = dum[0];
    }

/*     Reduce to upper Hessenberg form */
/*     (CWorkspace: need 2*N, prefer N+N*NB) */
/*     (RWorkspace: none) */

    itau = 1;
    iwrk = itau + *n;
    i__1 = *lwork - iwrk + 1;
    cgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
	    ierr);

    if (wantvl) {

/*        Want left eigenvectors */
/*        Copy Householder vectors to VL */

	*(unsigned char *)side = 'L';
	clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
		;

/*        Generate unitary matrix in VL */
/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/*        (RWorkspace: none) */

	i__1 = *lwork - iwrk + 1;
	cunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
		i__1, &ierr);

/*        Perform QR iteration, accumulating Schur vectors in VL */

//.........这里部分代码省略.........
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
	    vsr_dim1, vsr_offset, i__1, i__2;
    real r__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static real anrm, bnrm;
    static integer idum[1], ierr, itau, iwrk;
    static real pvsl, pvsr;
    static integer i__;
    extern logical lsame_(char *, char *);
    static integer ileft, icols;
    static logical cursl, ilvsl, ilvsr;
    static integer irows;
    static logical lst2sl;
    extern /* Subroutine */ int slabad_(real *, real *);
    static integer ip;
    extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, integer *
	    ), sggbal_(char *, integer *, real *, integer *, 
	    real *, integer *, integer *, integer *, real *, real *, real *, 
	    integer *);
    static logical ilascl, ilbscl;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *);
    static real safmin;
    extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , real *, integer *, integer *);
    static real safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static integer ijobvl, iright;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *);
    static integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), slaset_(char *, integer *, 
	    integer *, real *, real *, real *, integer *);
    static real anrmto, bnrmto;
    static logical lastsl;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, integer *, real *
	    , real *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, integer *), stgsen_(integer *, 
	    logical *, logical *, logical *, integer *, real *, integer *, 
	    real *, integer *, real *, real *, real *, real *, integer *, 
	    real *, integer *, integer *, real *, real *, real *, real *, 
	    integer *, integer *, integer *, integer *);
    static integer minwrk, maxwrk;
    static real smlnum;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    static logical wantst, lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);
    static real dif[2];
    static integer ihi, ilo;
    static real eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]

//.........这里部分代码省略.........
	xerbla_("SGEGV ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = slamch_("E") * slamch_("B");
    safmin = slamch_("S");
    safmin += safmin;
    safmax = 1.f / safmin;
    onepls = eps * 4 + 1.f;

/*     Scale A */

    anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
    anrm1 = anrm;
    anrm2 = 1.f;
    if (anrm < 1.f) {
	if (safmax * anrm < 1.f) {
	    anrm1 = safmin;
	    anrm2 = safmax * anrm;
	}
    }

    if (anrm > 0.f) {
	slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 10;
	    return 0;
	}
    }

/*     Scale B */

    bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
    bnrm1 = bnrm;
    bnrm2 = 1.f;
    if (bnrm < 1.f) {
	if (safmax * bnrm < 1.f) {
	    bnrm1 = safmin;
	    bnrm2 = safmax * bnrm;
	}
    }

    if (bnrm > 0.f) {
	slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 10;
	    return 0;
	}
    }

/*     Permute the matrix to make it more nearly triangular */
/*     Workspace layout:  (8*N words -- "work" requires 6*N words) */

    ileft = 1;

/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info)
{
    /* System generated locals */
    integer i__1;
    real r__1, r__2, r__3;

    /* Builtin functions */
    double sqrt(doublereal), r_sign(real *, real *);

    /* Local variables */
    real c__;
    integer i__, l, m;
    real p, r__, s;
    integer l1;
    real bb, rt1, rt2, eps, rte;
    integer lsv;
    real eps2, oldc;
    integer lend, jtot;
    extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)
	    ;
    real gamma, alpha, sigma, anorm;
    extern doublereal slapy2_(real *, real *);
    integer iscale;
    real oldgam;
    extern doublereal slamch_(char *);
    real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real safmax;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    integer lendsv;
    real ssfmin;
    integer nmaxit;
    real ssfmax;
    extern doublereal slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SSTERF computes all eigenvalues of a symmetric tridiagonal matrix */
/*  using the Pal-Walker-Kahan variant of the QL or QR algorithm. */

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

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

/*  D       (input/output) REAL array, dimension (N) */
/*          On entry, the n diagonal elements of the tridiagonal matrix. */
/*          On exit, if INFO = 0, the eigenvalues in ascending order. */

/*  E       (input/output) REAL array, dimension (N-1) */
/*          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/*          matrix. */
/*          On exit, E has been destroyed. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  the algorithm failed to find all of the eigenvalues in */
/*                a total of 30*N iterations; if INFO = i, then i */
/*                elements of E have not converged to zero. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --e;
    --d__;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

//.........这里部分代码省略.........

 int ssbev_(char *jobz, char *uplo, int *n, int *kd, 
	float *ab, int *ldab, float *w, float *z__, int *ldz, float *work, 
	 int *info)
{
    /* System generated locals */
    int ab_dim1, ab_offset, z_dim1, z_offset, i__1;
    float r__1;

    /* Builtin functions */
    double sqrt(double);

    /* Local variables */
    float eps;
    int inde;
    float anrm;
    int imax;
    float rmin, rmax, sigma;
    extern int lsame_(char *, char *);
    int iinfo;
    extern  int sscal_(int *, float *, float *, int *);
    int lower, wantz;
    int iscale;
    extern double slamch_(char *);
    float safmin;
    extern  int xerbla_(char *, int *);
    float bignum;
    extern double slansb_(char *, char *, int *, int *, float *, 
	    int *, float *);
    extern  int slascl_(char *, int *, int *, float *, 
	    float *, int *, int *, float *, int *, int *);
    int indwrk;
    extern  int ssbtrd_(char *, char *, int *, int *, 
	    float *, int *, float *, float *, float *, int *, float *, 
	    int *), ssterf_(int *, float *, float *, 
	    int *);
    float smlnum;
    extern  int ssteqr_(char *, int *, float *, float *, 
	    float *, int *, float *, int *);


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

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

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

/*  SSBEV computes all the eigenvalues and, optionally, eigenvectors of */
/*  a float symmetric band matrix A. */

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

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

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

/*  KD      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */

/*  AB      (input/output) REAL array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=MIN(n,j+kd). */

/*          On exit, AB is overwritten by values generated during the */
/*          reduction to tridiagonal form.  If UPLO = 'U', the first */
/*          superdiagonal and the diagonal of the tridiagonal matrix T */
/*          are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/*          the diagonal and first subdiagonal of T are returned in the */
/*          first two rows of AB. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD + 1. */

/*  W       (output) REAL array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  Z       (output) REAL array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/*          eigenvectors of the matrix A, with the i-th column of Z */
/*          holding the eigenvector associated with W(i). */
/*          If JOBZ = 'N', then Z is not referenced. */

//.........这里部分代码省略.........

/* Subroutine */ int cqrt15_(integer *scale, integer *rksel, integer *m, 
	integer *n, integer *nrhs, complex *a, integer *lda, complex *b, 
	integer *ldb, real *s, integer *rank, real *norma, real *normb, 
	integer *iseed, complex *work, integer *lwork)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    real r__1;

    /* Local variables */
    integer j, mn;
    real eps;
    integer info;
    real temp;
    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
	    integer *, complex *, complex *, integer *, complex *, integer *, 
	    complex *, complex *, integer *), clarf_(char *, 
	    integer *, integer *, complex *, integer *, complex *, complex *, 
	    integer *, complex *);
    extern doublereal sasum_(integer *, real *, integer *);
    real dummy[1];
    extern doublereal scnrm2_(integer *, complex *, integer *);
    extern /* Subroutine */ int slabad_(real *, real *);
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, complex *, integer *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
	    *), claset_(char *, integer *, integer *, complex *, complex *, 
	    complex *, integer *), xerbla_(char *, integer *);
    real bignum;
    extern /* Subroutine */ int claror_(char *, char *, integer *, integer *, 
	    complex *, integer *, integer *, complex *, integer *);
    extern doublereal slarnd_(integer *, integer *);
    extern /* Subroutine */ int slaord_(char *, integer *, real *, integer *), clarnv_(integer *, integer *, integer *, complex *), 
	    slascl_(char *, integer *, integer *, real *, real *, integer *, 
	    integer *, real *, integer *, integer *);
    real smlnum;


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  CQRT15 generates a matrix with full or deficient rank and of various */
/*  norms. */

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

/*  SCALE   (input) INTEGER */
/*          SCALE = 1: normally scaled matrix */
/*          SCALE = 2: matrix scaled up */
/*          SCALE = 3: matrix scaled down */

/*  RKSEL   (input) INTEGER */
/*          RKSEL = 1: full rank matrix */
/*          RKSEL = 2: rank-deficient matrix */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A. */

/*  N       (input) INTEGER */
/*          The number of columns of A. */

/*  NRHS    (input) INTEGER */
/*          The number of columns of B. */

/*  A       (output) COMPLEX array, dimension (LDA,N) */
/*          The M-by-N matrix A. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. */

/*  B       (output) COMPLEX array, dimension (LDB, NRHS) */
/*          A matrix that is in the range space of matrix A. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B. */

/*  S       (output) REAL array, dimension MIN(M,N) */
/*          Singular values of A. */

/*  RANK    (output) INTEGER */
/*          number of nonzero singular values of A. */

/*  NORMA   (output) REAL */
/*          one-norm norm of A. */

/*  NORMB   (output) REAL */
/*          one-norm norm of B. */
//.........这里部分代码省略.........

//.........这里部分代码省略.........
    static integer c__8 = 8;
    static integer c_n1 = -1;
    static integer c__4 = 4;
    
    /* System generated locals */
    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer ibal, maxb;
    static real anrm;
    static integer ierr, itau, iwrk, i, k, icond, ieval;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *), cgebak_(char *, char *, integer *, integer 
	    *, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *, 
	    integer *, integer *, real *, integer *), slabad_(real *, 
	    real *);
    static logical scalea;
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    static real cscale;
    extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *, 
	    complex *, integer *, complex *, complex *, integer *, integer *),
	     clascl_(char *, integer *, integer *, real *, real *, integer *, 
	    integer *, complex *, integer *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), xerbla_(char *, 
	    integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), chseqr_(char *, char *, integer *, integer *, integer *, 
	    complex *, integer *, complex *, complex *, integer *, complex *, 
	    integer *, integer *), cunghr_(integer *, integer 
	    *, integer *, complex *, integer *, complex *, complex *, integer 
	    *, integer *);
    static logical wantsb;
    extern /* Subroutine */ int ctrsen_(char *, char *, logical *, integer *, 
	    complex *, integer *, complex *, integer *, complex *, integer *, 
	    real *, real *, complex *, integer *, integer *);
    static logical wantse;
    static integer minwrk, maxwrk;
    static logical wantsn;
    static real smlnum;
    static integer hswork;
    static logical wantst, wantsv, wantvs;
    static integer ihi, ilo;
    static real dum[1], eps;



#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define BWORK(I) bwork[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define VS(I,J) vs[(I)-1 + ((J)-1)* ( *ldvs)]

    *info = 0;
    wantvs = lsame_(jobvs, "V");
    wantst = lsame_(sort, "S");
    wantsn = lsame_(sense, "N");

doublereal sqrt12_(integer *m, integer *n, real *a, integer *lda, real *s, 
	real *work, integer *lwork)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    real ret_val;

    /* Local variables */
    static integer iscl, info;
    static real anrm;
    extern doublereal snrm2_(integer *, real *, integer *);
    static integer i__, j;
    extern doublereal sasum_(integer *, real *, integer *);
    static real dummy[1];
    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 
	    real *, integer *), sgebd2_(integer *, integer *, real *, integer 
	    *, real *, real *, real *, real *, real *, integer *), slabad_(
	    real *, real *);
    static integer mn;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *), sbdsqr_(char *, integer *, integer *, 
	    integer *, integer *, real *, real *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *);
    static real smlnum, nrmsvl;


#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]


/*  -- LAPACK test routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    SQRT12 computes the singular values `svlues' of the upper trapezoid   
    of A(1:M,1:N) and returns the ratio   

         || s - svlues||/(||svlues||*eps*max(M,N))   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix A.   

    N       (input) INTEGER   
            The number of columns of the matrix A.   

    A       (input) REAL array, dimension (LDA,N)   
            The M-by-N matrix A. Only the upper trapezoid is referenced.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.   

    S       (input) REAL array, dimension (min(M,N))   
            The singular values of the matrix A.   

    WORK    (workspace) REAL array, dimension (LWORK)   

    LWORK   (input) INTEGER   
            The length of the array WORK. LWORK >= M*N + 4*min(M,N) +   
            max(M,N).   

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


       Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --s;
    --work;

    /* Function Body */
    ret_val = 0.f;

/*     Test that enough workspace is supplied */

    if (*lwork < *m * *n + (min(*m,*n) << 2) + max(*m,*n)) {
	xerbla_("SQRT12", &c__7);
	return ret_val;
    }

/*     Quick return if possible */

    mn = min(*m,*n);
    if ((real) mn <= 0.f) {
	return ret_val;
    }

    nrmsvl = snrm2_(&mn, &s[1], &c__1);
//.........这里部分代码省略.........

/* Subroutine */ int ssterf_(integer *n, real *d, real *e, integer *info)
{
/*  -- LAPACK routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    SSTERF computes all eigenvalues of a symmetric tridiagonal matrix   
    using the Pal-Walker-Kahan variant of the QL or QR algorithm.   

    Arguments   
    =========   

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

    D       (input/output) REAL array, dimension (N)   
            On entry, the n diagonal elements of the tridiagonal matrix. 
  
            On exit, if INFO = 0, the eigenvalues in ascending order.   

    E       (input/output) REAL array, dimension (N-1)   
            On entry, the (n-1) subdiagonal elements of the tridiagonal   
            matrix.   
            On exit, E has been destroyed.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  the algorithm failed to find all of the eigenvalues in 
  
                  a total of 30*N iterations; if INFO = i, then i   
                  elements of E have not converged to zero.   

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


       Test the input parameters.   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__0 = 0;
    static integer c__1 = 1;
    static real c_b32 = 1.f;
    
    /* System generated locals */
    integer i__1;
    real r__1, r__2;
    /* Builtin functions */
    double sqrt(doublereal), r_sign(real *, real *);
    /* Local variables */
    static real oldc;
    static integer lend, jtot;
    extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)
	    ;
    static real c;
    static integer i, l, m;
    static real p, gamma, r, s, alpha, sigma, anorm;
    static integer l1, lendm1, lendp1;
    static real bb;
    extern doublereal slapy2_(real *, real *);
    static integer iscale;
    static real oldgam;
    extern doublereal slamch_(char *);
    static real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real safmax;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    static integer lendsv;
    static real ssfmin;
    static integer nmaxit;
    static real ssfmax;
    extern doublereal slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
    static integer lm1, mm1, nm1;
    static real rt1, rt2, eps, rte;
    static integer lsv;
    static real tst, eps2;



#define E(I) e[(I)-1]
#define D(I) d[(I)-1]


    *info = 0;

/*     Quick return if possible */

    if (*n < 0) {
	*info = -1;
	i__1 = -(*info);
//.........这里部分代码省略.........

/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp
                             selctg, char *sense, integer *n, real *a, integer *lda, real *b,
                             integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta,
                             real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde,
                             real *rcondv, real *work, integer *lwork, integer *iwork, integer *
                             liwork, logical *bwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
            vsr_dim1, vsr_offset, i__1, i__2;
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__, ip;
    real pl, pr, dif[2];
    integer ihi, ilo;
    real eps;
    integer ijob;
    real anrm, bnrm;
    integer ierr, itau, iwrk, lwrk;
    extern logical lsame_(char *, char *);
    integer ileft, icols;
    logical cursl, ilvsl, ilvsr;
    integer irows;
    logical lst2sl;
    extern /* Subroutine */ int slabad_(real *, real *), sggbak_(char *, char
            *, integer *, integer *, integer *, real *, real *, integer *,
            real *, integer *, integer *), sggbal_(char *,
                    integer *, real *, integer *, real *, integer *, integer *,
                    integer *, real *, real *, real *, integer *);
    logical ilascl, ilbscl;
    extern doublereal slamch_(char *), slange_(char *, integer *,
            integer *, real *, integer *, real *);
    real safmin;
    extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
                                        integer *, real *, integer *, real *, integer *, real *, integer *
                                        , real *, integer *, integer *);
    real safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
                                        real *, integer *, integer *, real *, integer *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
                           integer *, integer *);
    integer ijobvl, iright;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
                                        *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
                                        integer *, real *, integer *);
    logical wantsb, wantse, lastsl;
    integer liwmin;
    real anrmto, bnrmto;
    integer minwrk, maxwrk;
    logical wantsn;
    real smlnum;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
                                        integer *, integer *, real *, integer *, real *, integer *, real *
                                        , real *, real *, real *, integer *, real *, integer *, real *,
                                        integer *, integer *), slaset_(char *,
                                                integer *, integer *, real *, real *, real *, integer *),
                                                        sorgqr_(integer *, integer *, integer *, real *, integer *, real *
                                                                , real *, integer *, integer *), stgsen_(integer *, logical *,
                                                                        logical *, logical *, integer *, real *, integer *, real *,
                                                                        integer *, real *, real *, real *, real *, integer *, real *,
                                                                        integer *, integer *, real *, real *, real *, real *, integer *,
                                                                        integer *, integer *, integer *);
    logical wantst, lquery, wantsv;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
                                        integer *, real *, integer *, real *, real *, integer *, real *,
                                        integer *, integer *);


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

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

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

    /*  SGGESX computes for a pair of N-by-N real nonsymmetric matrices */
    /*  (A,B), the generalized eigenvalues, the real Schur form (S,T), and, */
    /*  optionally, the left and/or right matrices of Schur vectors (VSL and */
    /*  VSR).  This gives the generalized Schur factorization */

    /*       (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T ) */

    /*  Optionally, it also orders the eigenvalues so that a selected cluster */
    /*  of eigenvalues appears in the leading diagonal blocks of the upper */
    /*  quasi-triangular matrix S and the upper triangular matrix T; computes */
//.........这里部分代码省略.........

/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, 
	integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta, 
	 integer *idxq, integer *perm, integer *givptr, integer *givcol, 
	integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
	difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
	work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, 
	    poles_dim1, poles_offset, i__1;
    real r__1, r__2;

    /* Local variables */
    integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), slasd7_(integer *, integer *, integer *, integer *, 
	    integer *, real *, real *, real *, real *, real *, real *, real *, 
	     real *, real *, real *, integer *, integer *, integer *, integer 
	    *, integer *, integer *, integer *, real *, integer *, real *, 
	    real *, integer *), slasd8_(integer *, integer *, real *, real *, 
	    real *, real *, real *, real *, integer *, real *, real *, 
	    integer *);
    integer isigma;
    extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
, real *, integer *, integer *), slamrg_(integer *, 
	    integer *, real *, integer *, integer *, integer *);
    real orgnrm;


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

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

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

/*  SLASD6 computes the SVD of an updated upper bidiagonal matrix B */
/*  obtained by merging two smaller ones by appending a row. This */
/*  routine is used only for the problem which requires all singular */
/*  values and optionally singular vector matrices in factored form. */
/*  B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
/*  A related subroutine, SLASD1, handles the case in which all singular */
/*  values and singular vectors of the bidiagonal matrix are desired. */

/*  SLASD6 computes the SVD as follows: */

/*                ( D1(in)  0    0     0 ) */
/*    B = U(in) * (   Z1'   a   Z2'    b ) * VT(in) */
/*                (   0     0   D2(in) 0 ) */

/*      = U(out) * ( D(out) 0) * VT(out) */

/*  where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */
/*  with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
/*  elsewhere; and the entry b is empty if SQRE = 0. */

/*  The singular values of B can be computed using D1, D2, the first */
/*  components of all the right singular vectors of the lower block, and */
/*  the last components of all the right singular vectors of the upper */
/*  block. These components are stored and updated in VF and VL, */
/*  respectively, in SLASD6. Hence U and VT are not explicitly */
/*  referenced. */

/*  The singular values are stored in D. The algorithm consists of two */
/*  stages: */

/*        The first stage consists of deflating the size of the problem */
/*        when there are multiple singular values or if there is a zero */
/*        in the Z vector. For each such occurence the dimension of the */
/*        secular equation problem is reduced by one. This stage is */
/*        performed by the routine SLASD7. */

/*        The second stage consists of calculating the updated */
/*        singular values. This is done by finding the roots of the */
/*        secular equation via the routine SLASD4 (as called by SLASD8). */
/*        This routine also updates VF and VL and computes the distances */
/*        between the updated singular values and the old singular */
/*        values. */

/*  SLASD6 is called from SLASDA. */

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

/*  ICOMPQ (input) INTEGER */
/*         Specifies whether singular vectors are to be computed in */
/*         factored form: */
/*         = 0: Compute singular values only. */
/*         = 1: Compute singular vectors in factored form as well. */

/*  NL     (input) INTEGER */
/*         The row dimension of the upper block.  NL >= 1. */

/*  NR     (input) INTEGER */
//.........这里部分代码省略.........

doublereal sqrt17_(char *trans, integer *iresid, integer *m, integer *n, 
	integer *nrhs, real *a, integer *lda, real *x, integer *ldx, real *b, 
	integer *ldb, real *c__, real *work, integer *lwork)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, x_dim1, 
	    x_offset, i__1;
    real ret_val;

    /* Local variables */
    static integer iscl, info;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    static real norma, normb;
    static integer ncols;
    static real normx, rwork[1];
    static integer nrows;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, 
	    real *, integer *);
    static real smlnum, normrs, err;


/*  -- LAPACK test 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   
    =======   

    SQRT17 computes the ratio   

       || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)   

    where R = op(A)*X - B, op(A) is A or A', and   

       alpha = ||B|| if IRESID = 1 (zero-residual problem)   
       alpha = ||R|| if IRESID = 2 (otherwise).   

    Arguments   
    =========   

    TRANS   (input) CHARACTER*1   
            Specifies whether or not the transpose of A is used.   
            = 'N':  No transpose, op(A) = A.   
            = 'T':  Transpose, op(A) = A'.   

    IRESID  (input) INTEGER   
            IRESID = 1 indicates zero-residual problem.   
            IRESID = 2 indicates non-zero residual.   

    M       (input) INTEGER   
            The number of rows of the matrix A.   
            If TRANS = 'N', the number of rows of the matrix B.   
            If TRANS = 'T', the number of rows of the matrix X.   

    N       (input) INTEGER   
            The number of columns of the matrix  A.   
            If TRANS = 'N', the number of rows of the matrix X.   
            If TRANS = 'T', the number of rows of the matrix B.   

    NRHS    (input) INTEGER   
            The number of columns of the matrices X and B.   

    A       (input) REAL array, dimension (LDA,N)   
            The m-by-n matrix A.   

    LDA     (input) INTEGER   
            The leading dimension of the array A. LDA >= M.   

    X       (input) REAL array, dimension (LDX,NRHS)   
            If TRANS = 'N', the n-by-nrhs matrix X.   
            If TRANS = 'T', the m-by-nrhs matrix X.   

    LDX     (input) INTEGER   
            The le