text: /* dlasy2.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__4 = 4;
  static integer c__1 = 1;
  static integer c__16 = 16;
  static integer c__0 = 0;
  
  /* Subroutine */ int dlasy2_(logical *ltranl, logical *ltranr, integer *isgn, 
  	integer *n1, integer *n2, doublereal *tl, integer *ldtl, doublereal *
  	tr, integer *ldtr, doublereal *b, integer *ldb, doublereal *scale, 
  	doublereal *x, integer *ldx, doublereal *xnorm, integer *info)
  {
      /* Initialized data */
  
      static integer locu12[4] = { 3,4,1,2 };
      static integer locl21[4] = { 2,1,4,3 };
      static integer locu22[4] = { 4,3,2,1 };
      static logical xswpiv[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
      static logical bswpiv[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
  
      /* System generated locals */
      integer b_dim1, b_offset, tl_dim1, tl_offset, tr_dim1, tr_offset, x_dim1, 
  	    x_offset;
      doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8;
  
      /* Local variables */
      integer i__, j, k;
      doublereal x2[2], l21, u11, u12;
      integer ip, jp;
      doublereal u22, t16[16]	/* was [4][4] */, gam, bet, eps, sgn, tmp[4], 
  	    tau1, btmp[4], smin;
      integer ipiv;
      doublereal temp;
      integer jpiv[4];
      doublereal xmax;
      integer ipsv, jpsv;
      logical bswap;
      extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
  	    doublereal *, integer *), dswap_(integer *, doublereal *, integer 
  	    *, doublereal *, integer *);
      logical xswap;
      extern doublereal dlamch_(char *);
      extern integer idamax_(integer *, doublereal *, integer *);
      doublereal smlnum;
  
  
  /*  -- LAPACK auxiliary routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in */
  
  /*         op(TL)*X + ISGN*X*op(TR) = SCALE*B, */
  
  /*  where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or */
  /*  -1.  op(T) = T or T', where T' denotes the transpose of T. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  LTRANL  (input) LOGICAL */
  /*          On entry, LTRANL specifies the op(TL): */
  /*             = .FALSE., op(TL) = TL, */
  /*             = .TRUE., op(TL) = TL'. */
  
  /*  LTRANR  (input) LOGICAL */
  /*          On entry, LTRANR specifies the op(TR): */
  /*            = .FALSE., op(TR) = TR, */
  /*            = .TRUE., op(TR) = TR'. */
  
  /*  ISGN    (input) INTEGER */
  /*          On entry, ISGN specifies the sign of the equation */
  /*          as described before. ISGN may only be 1 or -1. */
  
  /*  N1      (input) INTEGER */
  /*          On entry, N1 specifies the order of matrix TL. */
  /*          N1 may only be 0, 1 or 2. */
  
  /*  N2      (input) INTEGER */
  /*          On entry, N2 specifies the order of matrix TR. */
  /*          N2 may only be 0, 1 or 2. */
  
  /*  TL      (input) DOUBLE PRECISION array, dimension (LDTL,2) */
  /*          On entry, TL contains an N1 by N1 matrix. */
  
  /*  LDTL    (input) INTEGER */
  /*          The leading dimension of the matrix TL. LDTL >= max(1,N1). */
  
  /*  TR      (input) DOUBLE PRECISION array, dimension (LDTR,2) */
  /*          On entry, TR contains an N2 by N2 matrix. */
  
  /*  LDTR    (input) INTEGER */
  /*          The leading dimension of the matrix TR. LDTR >= max(1,N2). */
  
  /*  B       (input) DOUBLE PRECISION array, dimension (LDB,2) */
  /*          On entry, the N1 by N2 matrix B contains the right-hand */
  /*          side of the equation. */
  
  /*  LDB     (input) INTEGER */
  /*          The leading dimension of the matrix B. LDB >= max(1,N1). */
  
  /*  SCALE   (output) DOUBLE PRECISION */
  /*          On exit, SCALE contains the scale factor. SCALE is chosen */
  /*          less than or equal to 1 to prevent the solution overflowing. */
  
  /*  X       (output) DOUBLE PRECISION array, dimension (LDX,2) */
  /*          On exit, X contains the N1 by N2 solution. */
  
  /*  LDX     (input) INTEGER */
  /*          The leading dimension of the matrix X. LDX >= max(1,N1). */
  
  /*  XNORM   (output) DOUBLE PRECISION */
  /*          On exit, XNORM is the infinity-norm of the solution. */
  
  /*  INFO    (output) INTEGER */
  /*          On exit, INFO is set to */
  /*             0: successful exit. */
  /*             1: TL and TR have too close eigenvalues, so TL or */
  /*                TR is perturbed to get a nonsingular equation. */
  /*          NOTE: In the interests of speed, this routine does not */
  /*                check the inputs for errors. */
  
  /* ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. Local Arrays .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Data statements .. */
      /* Parameter adjustments */
      tl_dim1 = *ldtl;
      tl_offset = 1 + tl_dim1;
      tl -= tl_offset;
      tr_dim1 = *ldtr;
      tr_offset = 1 + tr_dim1;
      tr -= tr_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1;
      b -= b_offset;
      x_dim1 = *ldx;
      x_offset = 1 + x_dim1;
      x -= x_offset;
  
      /* Function Body */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Do not check the input parameters for errors */
  
      *info = 0;
  
  /*     Quick return if possible */
  
      if (*n1 == 0 || *n2 == 0) {
  	return 0;
      }
  
  /*     Set constants to control overflow */
  
      eps = dlamch_("P");
      smlnum = dlamch_("S") / eps;
      sgn = (doublereal) (*isgn);
  
      k = *n1 + *n1 + *n2 - 2;
      switch (k) {
  	case 1:  goto L10;
  	case 2:  goto L20;
  	case 3:  goto L30;
  	case 4:  goto L50;
      }
  
  /*     1 by 1: TL11*X + SGN*X*TR11 = B11 */
  
  L10:
      tau1 = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
      bet = abs(tau1);
      if (bet <= smlnum) {
  	tau1 = smlnum;
  	bet = smlnum;
  	*info = 1;
      }
  
      *scale = 1.;
      gam = (d__1 = b[b_dim1 + 1], abs(d__1));
      if (smlnum * gam > bet) {
  	*scale = 1. / gam;
      }
  
      x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / tau1;
      *xnorm = (d__1 = x[x_dim1 + 1], abs(d__1));
      return 0;
  
  /*     1 by 2: */
  /*     TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12]  = [B11 B12] */
  /*                                       [TR21 TR22] */
  
  L20:
  
  /* Computing MAX */
  /* Computing MAX */
      d__7 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__8 = (d__2 = tr[tr_dim1 + 1]
  	    , abs(d__2)), d__7 = max(d__7,d__8), d__8 = (d__3 = tr[(tr_dim1 <<
  	     1) + 1], abs(d__3)), d__7 = max(d__7,d__8), d__8 = (d__4 = tr[
  	    tr_dim1 + 2], abs(d__4)), d__7 = max(d__7,d__8), d__8 = (d__5 = 
  	    tr[(tr_dim1 << 1) + 2], abs(d__5));
      d__6 = eps * max(d__7,d__8);
      smin = max(d__6,smlnum);
      tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
      tmp[3] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
      if (*ltranr) {
  	tmp[1] = sgn * tr[tr_dim1 + 2];
  	tmp[2] = sgn * tr[(tr_dim1 << 1) + 1];
      } else {
  	tmp[1] = sgn * tr[(tr_dim1 << 1) + 1];
  	tmp[2] = sgn * tr[tr_dim1 + 2];
      }
      btmp[0] = b[b_dim1 + 1];
      btmp[1] = b[(b_dim1 << 1) + 1];
      goto L40;
  
  /*     2 by 1: */
  /*          op[TL11 TL12]*[X11] + ISGN* [X11]*TR11  = [B11] */
  /*            [TL21 TL22] [X21]         [X21]         [B21] */
  
  L30:
  /* Computing MAX */
  /* Computing MAX */
      d__7 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__8 = (d__2 = tl[tl_dim1 + 1]
  	    , abs(d__2)), d__7 = max(d__7,d__8), d__8 = (d__3 = tl[(tl_dim1 <<
  	     1) + 1], abs(d__3)), d__7 = max(d__7,d__8), d__8 = (d__4 = tl[
  	    tl_dim1 + 2], abs(d__4)), d__7 = max(d__7,d__8), d__8 = (d__5 = 
  	    tl[(tl_dim1 << 1) + 2], abs(d__5));
      d__6 = eps * max(d__7,d__8);
      smin = max(d__6,smlnum);
      tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
      tmp[3] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
      if (*ltranl) {
  	tmp[1] = tl[(tl_dim1 << 1) + 1];
  	tmp[2] = tl[tl_dim1 + 2];
      } else {
  	tmp[1] = tl[tl_dim1 + 2];
  	tmp[2] = tl[(tl_dim1 << 1) + 1];
      }
      btmp[0] = b[b_dim1 + 1];
      btmp[1] = b[b_dim1 + 2];
  L40:
  
  /*     Solve 2 by 2 system using complete pivoting. */
  /*     Set pivots less than SMIN to SMIN. */
  
      ipiv = idamax_(&c__4, tmp, &c__1);
      u11 = tmp[ipiv - 1];
      if (abs(u11) <= smin) {
  	*info = 1;
  	u11 = smin;
      }
      u12 = tmp[locu12[ipiv - 1] - 1];
      l21 = tmp[locl21[ipiv - 1] - 1] / u11;
      u22 = tmp[locu22[ipiv - 1] - 1] - u12 * l21;
      xswap = xswpiv[ipiv - 1];
      bswap = bswpiv[ipiv - 1];
      if (abs(u22) <= smin) {
  	*info = 1;
  	u22 = smin;
      }
      if (bswap) {
  	temp = btmp[1];
  	btmp[1] = btmp[0] - l21 * temp;
  	btmp[0] = temp;
      } else {
  	btmp[1] -= l21 * btmp[0];
      }
      *scale = 1.;
      if (smlnum * 2. * abs(btmp[1]) > abs(u22) || smlnum * 2. * abs(btmp[0]) > 
  	    abs(u11)) {
  /* Computing MAX */
  	d__1 = abs(btmp[0]), d__2 = abs(btmp[1]);
  	*scale = .5 / max(d__1,d__2);
  	btmp[0] *= *scale;
  	btmp[1] *= *scale;
      }
      x2[1] = btmp[1] / u22;
      x2[0] = btmp[0] / u11 - u12 / u11 * x2[1];
      if (xswap) {
  	temp = x2[1];
  	x2[1] = x2[0];
  	x2[0] = temp;
      }
      x[x_dim1 + 1] = x2[0];
      if (*n1 == 1) {
  	x[(x_dim1 << 1) + 1] = x2[1];
  	*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1)) + (d__2 = x[(x_dim1 << 1) 
  		+ 1], abs(d__2));
      } else {
  	x[x_dim1 + 2] = x2[1];
  /* Computing MAX */
  	d__3 = (d__1 = x[x_dim1 + 1], abs(d__1)), d__4 = (d__2 = x[x_dim1 + 2]
  		, abs(d__2));
  	*xnorm = max(d__3,d__4);
      }
      return 0;
  
  /*     2 by 2: */
  /*     op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12] */
  /*       [TL21 TL22] [X21 X22]        [X21 X22]   [TR21 TR22]   [B21 B22] */
  
  /*     Solve equivalent 4 by 4 system using complete pivoting. */
  /*     Set pivots less than SMIN to SMIN. */
  
  L50:
  /* Computing MAX */
      d__5 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__6 = (d__2 = tr[(tr_dim1 << 
  	    1) + 1], abs(d__2)), d__5 = max(d__5,d__6), d__6 = (d__3 = tr[
  	    tr_dim1 + 2], abs(d__3)), d__5 = max(d__5,d__6), d__6 = (d__4 = 
  	    tr[(tr_dim1 << 1) + 2], abs(d__4));
      smin = max(d__5,d__6);
  /* Computing MAX */
      d__5 = smin, d__6 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__5 = max(d__5,
  	    d__6), d__6 = (d__2 = tl[(tl_dim1 << 1) + 1], abs(d__2)), d__5 = 
  	    max(d__5,d__6), d__6 = (d__3 = tl[tl_dim1 + 2], abs(d__3)), d__5 =
  	     max(d__5,d__6), d__6 = (d__4 = tl[(tl_dim1 << 1) + 2], abs(d__4))
  	    ;
      smin = max(d__5,d__6);
  /* Computing MAX */
      d__1 = eps * smin;
      smin = max(d__1,smlnum);
      btmp[0] = 0.;
      dcopy_(&c__16, btmp, &c__0, t16, &c__1);
      t16[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
      t16[5] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
      t16[10] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
      t16[15] = tl[(tl_dim1 << 1) + 2] + sgn * tr[(tr_dim1 << 1) + 2];
      if (*ltranl) {
  	t16[4] = tl[tl_dim1 + 2];
  	t16[1] = tl[(tl_dim1 << 1) + 1];
  	t16[14] = tl[tl_dim1 + 2];
  	t16[11] = tl[(tl_dim1 << 1) + 1];
      } else {
  	t16[4] = tl[(tl_dim1 << 1) + 1];
  	t16[1] = tl[tl_dim1 + 2];
  	t16[14] = tl[(tl_dim1 << 1) + 1];
  	t16[11] = tl[tl_dim1 + 2];
      }
      if (*ltranr) {
  	t16[8] = sgn * tr[(tr_dim1 << 1) + 1];
  	t16[13] = sgn * tr[(tr_dim1 << 1) + 1];
  	t16[2] = sgn * tr[tr_dim1 + 2];
  	t16[7] = sgn * tr[tr_dim1 + 2];
      } else {
  	t16[8] = sgn * tr[tr_dim1 + 2];
  	t16[13] = sgn * tr[tr_dim1 + 2];
  	t16[2] = sgn * tr[(tr_dim1 << 1) + 1];
  	t16[7] = sgn * tr[(tr_dim1 << 1) + 1];
      }
      btmp[0] = b[b_dim1 + 1];
      btmp[1] = b[b_dim1 + 2];
      btmp[2] = b[(b_dim1 << 1) + 1];
      btmp[3] = b[(b_dim1 << 1) + 2];
  
  /*     Perform elimination */
  
      for (i__ = 1; i__ <= 3; ++i__) {
  	xmax = 0.;
  	for (ip = i__; ip <= 4; ++ip) {
  	    for (jp = i__; jp <= 4; ++jp) {
  		if ((d__1 = t16[ip + (jp << 2) - 5], abs(d__1)) >= xmax) {
  		    xmax = (d__1 = t16[ip + (jp << 2) - 5], abs(d__1));
  		    ipsv = ip;
  		    jpsv = jp;
  		}
  /* L60: */
  	    }
  /* L70: */
  	}
  	if (ipsv != i__) {
  	    dswap_(&c__4, &t16[ipsv - 1], &c__4, &t16[i__ - 1], &c__4);
  	    temp = btmp[i__ - 1];
  	    btmp[i__ - 1] = btmp[ipsv - 1];
  	    btmp[ipsv - 1] = temp;
  	}
  	if (jpsv != i__) {
  	    dswap_(&c__4, &t16[(jpsv << 2) - 4], &c__1, &t16[(i__ << 2) - 4], 
  		    &c__1);
  	}
  	jpiv[i__ - 1] = jpsv;
  	if ((d__1 = t16[i__ + (i__ << 2) - 5], abs(d__1)) < smin) {
  	    *info = 1;
  	    t16[i__ + (i__ << 2) - 5] = smin;
  	}
  	for (j = i__ + 1; j <= 4; ++j) {
  	    t16[j + (i__ << 2) - 5] /= t16[i__ + (i__ << 2) - 5];
  	    btmp[j - 1] -= t16[j + (i__ << 2) - 5] * btmp[i__ - 1];
  	    for (k = i__ + 1; k <= 4; ++k) {
  		t16[j + (k << 2) - 5] -= t16[j + (i__ << 2) - 5] * t16[i__ + (
  			k << 2) - 5];
  /* L80: */
  	    }
  /* L90: */
  	}
  /* L100: */
      }
      if (abs(t16[15]) < smin) {
  	t16[15] = smin;
      }
      *scale = 1.;
      if (smlnum * 8. * abs(btmp[0]) > abs(t16[0]) || smlnum * 8. * abs(btmp[1])
  	     > abs(t16[5]) || smlnum * 8. * abs(btmp[2]) > abs(t16[10]) || 
  	    smlnum * 8. * abs(btmp[3]) > abs(t16[15])) {
  /* Computing MAX */
  	d__1 = abs(btmp[0]), d__2 = abs(btmp[1]), d__1 = max(d__1,d__2), d__2 
  		= abs(btmp[2]), d__1 = max(d__1,d__2), d__2 = abs(btmp[3]);
  	*scale = .125 / max(d__1,d__2);
  	btmp[0] *= *scale;
  	btmp[1] *= *scale;
  	btmp[2] *= *scale;
  	btmp[3] *= *scale;
      }
      for (i__ = 1; i__ <= 4; ++i__) {
  	k = 5 - i__;
  	temp = 1. / t16[k + (k << 2) - 5];
  	tmp[k - 1] = btmp[k - 1] * temp;
  	for (j = k + 1; j <= 4; ++j) {
  	    tmp[k - 1] -= temp * t16[k + (j << 2) - 5] * tmp[j - 1];
  /* L110: */
  	}
  /* L120: */
      }
      for (i__ = 1; i__ <= 3; ++i__) {
  	if (jpiv[4 - i__ - 1] != 4 - i__) {
  	    temp = tmp[4 - i__ - 1];
  	    tmp[4 - i__ - 1] = tmp[jpiv[4 - i__ - 1] - 1];
  	    tmp[jpiv[4 - i__ - 1] - 1] = temp;
  	}
  /* L130: */
      }
      x[x_dim1 + 1] = tmp[0];
      x[x_dim1 + 2] = tmp[1];
      x[(x_dim1 << 1) + 1] = tmp[2];
      x[(x_dim1 << 1) + 2] = tmp[3];
  /* Computing MAX */
      d__1 = abs(tmp[0]) + abs(tmp[2]), d__2 = abs(tmp[1]) + abs(tmp[3]);
      *xnorm = max(d__1,d__2);
      return 0;
  
  /*     End of DLASY2 */
  
  } /* dlasy2_ */
  