text: /* zgbtf2.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 doublecomplex c_b1 = {1.,0.};
  static integer c__1 = 1;
  
  /* Subroutine */ int zgbtf2_(integer *m, integer *n, integer *kl, integer *ku, 
  	 doublecomplex *ab, integer *ldab, integer *ipiv, integer *info)
  {
      /* System generated locals */
      integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
      doublecomplex z__1;
  
      /* Builtin functions */
      void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
  
      /* Local variables */
      integer i__, j, km, jp, ju, kv;
      extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
  	    doublecomplex *, integer *), zgeru_(integer *, integer *, 
  	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
  	    integer *, doublecomplex *, integer *), zswap_(integer *, 
  	    doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
  	    char *, integer *);
      extern integer izamax_(integer *, doublecomplex *, integer *);
  
  
  /*  -- LAPACK routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  ZGBTF2 computes an LU factorization of a complex m-by-n band matrix */
  /*  A using partial pivoting with row interchanges. */
  
  /*  This is the unblocked version of the algorithm, calling Level 2 BLAS. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  M       (input) INTEGER */
  /*          The number of rows of the matrix A.  M >= 0. */
  
  /*  N       (input) INTEGER */
  /*          The number of columns of the matrix A.  N >= 0. */
  
  /*  KL      (input) INTEGER */
  /*          The number of subdiagonals within the band of A.  KL >= 0. */
  
  /*  KU      (input) INTEGER */
  /*          The number of superdiagonals within the band of A.  KU >= 0. */
  
  /*  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N) */
  /*          On entry, the matrix A in band storage, in rows KL+1 to */
  /*          2*KL+KU+1; rows 1 to KL of the array need not be set. */
  /*          The j-th column of A is stored in the j-th column of the */
  /*          array AB as follows: */
  /*          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */
  
  /*          On exit, details of the factorization: U is stored as an */
  /*          upper triangular band matrix with KL+KU superdiagonals in */
  /*          rows 1 to KL+KU+1, and the multipliers used during the */
  /*          factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
  /*          See below for further details. */
  
  /*  LDAB    (input) INTEGER */
  /*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
  
  /*  IPIV    (output) INTEGER array, dimension (min(M,N)) */
  /*          The pivot indices; for 1 <= i <= min(M,N), row i of the */
  /*          matrix was interchanged with row IPIV(i). */
  
  /*  INFO    (output) INTEGER */
  /*          = 0: successful exit */
  /*          < 0: if INFO = -i, the i-th argument had an illegal value */
  /*          > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
  /*               has been completed, but the factor U is exactly */
  /*               singular, and division by zero will occur if it is used */
  /*               to solve a system of equations. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  The band storage scheme is illustrated by the following example, when */
  /*  M = N = 6, KL = 2, KU = 1: */
  
  /*  On entry:                       On exit: */
  
  /*      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
  /*      *    *    +    +    +    +       *    *   u13  u24  u35  u46 */
  /*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
  /*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */
  /*     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
  /*     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */
  
  /*  Array elements marked * are not used by the routine; elements marked */
  /*  + need not be set on entry, but are required by the routine to store */
  /*  elements of U, because of fill-in resulting from the row */
  /*  interchanges. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     KV is the number of superdiagonals in the factor U, allowing for */
  /*     fill-in. */
  
      /* Parameter adjustments */
      ab_dim1 = *ldab;
      ab_offset = 1 + ab_dim1;
      ab -= ab_offset;
      --ipiv;
  
      /* Function Body */
      kv = *ku + *kl;
  
  /*     Test the input parameters. */
  
      *info = 0;
      if (*m < 0) {
  	*info = -1;
      } else if (*n < 0) {
  	*info = -2;
      } else if (*kl < 0) {
  	*info = -3;
      } else if (*ku < 0) {
  	*info = -4;
      } else if (*ldab < *kl + kv + 1) {
  	*info = -6;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("ZGBTF2", &i__1);
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*m == 0 || *n == 0) {
  	return 0;
      }
  
  /*     Gaussian elimination with partial pivoting */
  
  /*     Set fill-in elements in columns KU+2 to KV to zero. */
  
      i__1 = min(kv,*n);
      for (j = *ku + 2; j <= i__1; ++j) {
  	i__2 = *kl;
  	for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
  	    i__3 = i__ + j * ab_dim1;
  	    ab[i__3].r = 0., ab[i__3].i = 0.;
  /* L10: */
  	}
  /* L20: */
      }
  
  /*     JU is the index of the last column affected by the current stage */
  /*     of the factorization. */
  
      ju = 1;
  
      i__1 = min(*m,*n);
      for (j = 1; j <= i__1; ++j) {
  
  /*        Set fill-in elements in column J+KV to zero. */
  
  	if (j + kv <= *n) {
  	    i__2 = *kl;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		i__3 = i__ + (j + kv) * ab_dim1;
  		ab[i__3].r = 0., ab[i__3].i = 0.;
  /* L30: */
  	    }
  	}
  
  /*        Find pivot and test for singularity. KM is the number of */
  /*        subdiagonal elements in the current column. */
  
  /* Computing MIN */
  	i__2 = *kl, i__3 = *m - j;
  	km = min(i__2,i__3);
  	i__2 = km + 1;
  	jp = izamax_(&i__2, &ab[kv + 1 + j * ab_dim1], &c__1);
  	ipiv[j] = jp + j - 1;
  	i__2 = kv + jp + j * ab_dim1;
  	if (ab[i__2].r != 0. || ab[i__2].i != 0.) {
  /* Computing MAX */
  /* Computing MIN */
  	    i__4 = j + *ku + jp - 1;
  	    i__2 = ju, i__3 = min(i__4,*n);
  	    ju = max(i__2,i__3);
  
  /*           Apply interchange to columns J to JU. */
  
  	    if (jp != 1) {
  		i__2 = ju - j + 1;
  		i__3 = *ldab - 1;
  		i__4 = *ldab - 1;
  		zswap_(&i__2, &ab[kv + jp + j * ab_dim1], &i__3, &ab[kv + 1 + 
  			j * ab_dim1], &i__4);
  	    }
  	    if (km > 0) {
  
  /*              Compute multipliers. */
  
  		z_div(&z__1, &c_b1, &ab[kv + 1 + j * ab_dim1]);
  		zscal_(&km, &z__1, &ab[kv + 2 + j * ab_dim1], &c__1);
  
  /*              Update trailing submatrix within the band. */
  
  		if (ju > j) {
  		    i__2 = ju - j;
  		    z__1.r = -1., z__1.i = -0.;
  		    i__3 = *ldab - 1;
  		    i__4 = *ldab - 1;
  		    zgeru_(&km, &i__2, &z__1, &ab[kv + 2 + j * ab_dim1], &
  			    c__1, &ab[kv + (j + 1) * ab_dim1], &i__3, &ab[kv 
  			    + 1 + (j + 1) * ab_dim1], &i__4);
  		}
  	    }
  	} else {
  
  /*           If pivot is zero, set INFO to the index of the pivot */
  /*           unless a zero pivot has already been found. */
  
  	    if (*info == 0) {
  		*info = j;
  	    }
  	}
  /* L40: */
      }
      return 0;
  
  /*     End of ZGBTF2 */
  
  } /* zgbtf2_ */
  