#include "rb_lapack.h"

extern VOID cgeevx_(char* balanc, char* jobvl, char* jobvr, char* sense, integer* n, complex* a, integer* lda, complex* w, complex* vl, integer* ldvl, complex* vr, integer* ldvr, integer* ilo, integer* ihi, real* scale, real* abnrm, real* rconde, real* rcondv, complex* work, integer* lwork, real* rwork, integer* info);


static VALUE
rblapack_cgeevx(int argc, VALUE *argv, VALUE self){
  VALUE rblapack_balanc;
  char balanc; 
  VALUE rblapack_jobvl;
  char jobvl; 
  VALUE rblapack_jobvr;
  char jobvr; 
  VALUE rblapack_sense;
  char sense; 
  VALUE rblapack_a;
  complex *a; 
  VALUE rblapack_lwork;
  integer lwork; 
  VALUE rblapack_w;
  complex *w; 
  VALUE rblapack_vl;
  complex *vl; 
  VALUE rblapack_vr;
  complex *vr; 
  VALUE rblapack_ilo;
  integer ilo; 
  VALUE rblapack_ihi;
  integer ihi; 
  VALUE rblapack_scale;
  real *scale; 
  VALUE rblapack_abnrm;
  real abnrm; 
  VALUE rblapack_rconde;
  real *rconde; 
  VALUE rblapack_rcondv;
  real *rcondv; 
  VALUE rblapack_work;
  complex *work; 
  VALUE rblapack_info;
  integer info; 
  VALUE rblapack_a_out__;
  complex *a_out__;
  real *rwork;

  integer lda;
  integer n;
  integer ldvl;
  integer ldvr;

  VALUE rblapack_options;
  if (argc > 0 && TYPE(argv[argc-1]) == T_HASH) {
    argc--;
    rblapack_options = argv[argc];
    if (rb_hash_aref(rblapack_options, sHelp) == Qtrue) {
      printf("%s\n", "USAGE:\n  w, vl, vr, ilo, ihi, scale, abnrm, rconde, rcondv, work, info, a = NumRu::Lapack.cgeevx( balanc, jobvl, jobvr, sense, a, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n      SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, LWORK, RWORK, INFO )\n\n*  Purpose\n*  =======\n*\n*  CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the\n*  eigenvalues and, optionally, the left and/or right eigenvectors.\n*\n*  Optionally also, it computes a balancing transformation to improve\n*  the conditioning of the eigenvalues and eigenvectors (ILO, IHI,\n*  SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues\n*  (RCONDE), and reciprocal condition numbers for the right\n*  eigenvectors (RCONDV).\n*\n*  The right eigenvector v(j) of A satisfies\n*                   A * v(j) = lambda(j) * v(j)\n*  where lambda(j) is its eigenvalue.\n*  The left eigenvector u(j) of A satisfies\n*                u(j)**H * A = lambda(j) * u(j)**H\n*  where u(j)**H denotes the conjugate transpose of u(j).\n*\n*  The computed eigenvectors are normalized to have Euclidean norm\n*  equal to 1 and largest component real.\n*\n*  Balancing a matrix means permuting the rows and columns to make it\n*  more nearly upper triangular, and applying a diagonal similarity\n*  transformation D * A * D**(-1), where D is a diagonal matrix, to\n*  make its rows and columns closer in norm and the condition numbers\n*  of its eigenvalues and eigenvectors smaller.  The computed\n*  reciprocal condition numbers correspond to the balanced matrix.\n*  Permuting rows and columns will not change the condition numbers\n*  (in exact arithmetic) but diagonal scaling will.  For further\n*  explanation of balancing, see section 4.10.2 of the LAPACK\n*  Users' Guide.\n*\n\n*  Arguments\n*  =========\n*\n*  BALANC  (input) CHARACTER*1\n*          Indicates how the input matrix should be diagonally scaled\n*          and/or permuted to improve the conditioning of its\n*          eigenvalues.\n*          = 'N': Do not diagonally scale or permute;\n*          = 'P': Perform permutations to make the matrix more nearly\n*                 upper triangular. Do not diagonally scale;\n*          = 'S': Diagonally scale the matrix, ie. replace A by\n*                 D*A*D**(-1), where D is a diagonal matrix chosen\n*                 to make the rows and columns of A more equal in\n*                 norm. Do not permute;\n*          = 'B': Both diagonally scale and permute A.\n*\n*          Computed reciprocal condition numbers will be for the matrix\n*          after balancing and/or permuting. Permuting does not change\n*          condition numbers (in exact arithmetic), but balancing does.\n*\n*  JOBVL   (input) CHARACTER*1\n*          = 'N': left eigenvectors of A are not computed;\n*          = 'V': left eigenvectors of A are computed.\n*          If SENSE = 'E' or 'B', JOBVL must = 'V'.\n*\n*  JOBVR   (input) CHARACTER*1\n*          = 'N': right eigenvectors of A are not computed;\n*          = 'V': right eigenvectors of A are computed.\n*          If SENSE = 'E' or 'B', JOBVR must = 'V'.\n*\n*  SENSE   (input) CHARACTER*1\n*          Determines which reciprocal condition numbers are computed.\n*          = 'N': None are computed;\n*          = 'E': Computed for eigenvalues only;\n*          = 'V': Computed for right eigenvectors only;\n*          = 'B': Computed for eigenvalues and right eigenvectors.\n*\n*          If SENSE = 'E' or 'B', both left and right eigenvectors\n*          must also be computed (JOBVL = 'V' and JOBVR = 'V').\n*\n*  N       (input) INTEGER\n*          The order of the matrix A. N >= 0.\n*\n*  A       (input/output) COMPLEX array, dimension (LDA,N)\n*          On entry, the N-by-N matrix A.\n*          On exit, A has been overwritten.  If JOBVL = 'V' or\n*          JOBVR = 'V', A contains the Schur form of the balanced \n*          version of the matrix A.\n*\n*  LDA     (input) INTEGER\n*          The leading dimension of the array A.  LDA >= max(1,N).\n*\n*  W       (output) COMPLEX array, dimension (N)\n*          W contains the computed eigenvalues.\n*\n*  VL      (output) COMPLEX array, dimension (LDVL,N)\n*          If JOBVL = 'V', the left eigenvectors u(j) are stored one\n*          after another in the columns of VL, in the same order\n*          as their eigenvalues.\n*          If JOBVL = 'N', VL is not referenced.\n*          u(j) = VL(:,j), the j-th column of VL.\n*\n*  LDVL    (input) INTEGER\n*          The leading dimension of the array VL.  LDVL >= 1; if\n*          JOBVL = 'V', LDVL >= N.\n*\n*  VR      (output) COMPLEX array, dimension (LDVR,N)\n*          If JOBVR = 'V', the right eigenvectors v(j) are stored one\n*          after another in the columns of VR, in the same order\n*          as their eigenvalues.\n*          If JOBVR = 'N', VR is not referenced.\n*          v(j) = VR(:,j), the j-th column of VR.\n*\n*  LDVR    (input) INTEGER\n*          The leading dimension of the array VR.  LDVR >= 1; if\n*          JOBVR = 'V', LDVR >= N.\n*\n*  ILO     (output) INTEGER\n*  IHI     (output) INTEGER\n*          ILO and IHI are integer values determined when A was\n*          balanced.  The balanced A(i,j) = 0 if I > J and\n*          J = 1,...,ILO-1 or I = IHI+1,...,N.\n*\n*  SCALE   (output) REAL array, dimension (N)\n*          Details of the permutations and scaling factors applied\n*          when balancing A.  If P(j) is the index of the row and column\n*          interchanged with row and column j, and D(j) is the scaling\n*          factor applied to row and column j, then\n*          SCALE(J) = P(J),    for J = 1,...,ILO-1\n*                   = D(J),    for J = ILO,...,IHI\n*                   = P(J)     for J = IHI+1,...,N.\n*          The order in which the interchanges are made is N to IHI+1,\n*          then 1 to ILO-1.\n*\n*  ABNRM   (output) REAL\n*          The one-norm of the balanced matrix (the maximum\n*          of the sum of absolute values of elements of any column).\n*\n*  RCONDE  (output) REAL array, dimension (N)\n*          RCONDE(j) is the reciprocal condition number of the j-th\n*          eigenvalue.\n*\n*  RCONDV  (output) REAL array, dimension (N)\n*          RCONDV(j) is the reciprocal condition number of the j-th\n*          right eigenvector.\n*\n*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n*\n*  LWORK   (input) INTEGER\n*          The dimension of the array WORK.  If SENSE = 'N' or 'E',\n*          LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',\n*          LWORK >= N*N+2*N.\n*          For good performance, LWORK must generally be larger.\n*\n*          If LWORK = -1, then a workspace query is assumed; the routine\n*          only calculates the optimal size of the WORK array, returns\n*          this value as the first entry of the WORK array, and no error\n*          message related to LWORK is issued by XERBLA.\n*\n*  RWORK   (workspace) REAL array, dimension (2*N)\n*\n*  INFO    (output) INTEGER\n*          = 0:  successful exit\n*          < 0:  if INFO = -i, the i-th argument had an illegal value.\n*          > 0:  if INFO = i, the QR algorithm failed to compute all the\n*                eigenvalues, and no eigenvectors or condition numbers\n*                have been computed; elements 1:ILO-1 and i+1:N of W\n*                contain eigenvalues which have converged.\n*\n\n*  =====================================================================\n*\n\n");
      return Qnil;
    }
    if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
      printf("%s\n", "USAGE:\n  w, vl, vr, ilo, ihi, scale, abnrm, rconde, rcondv, work, info, a = NumRu::Lapack.cgeevx( balanc, jobvl, jobvr, sense, a, [:lwork => lwork, :usage => usage, :help => help])\n");
      return Qnil;
    } 
  } else
    rblapack_options = Qnil;
  if (argc != 5 && argc != 6)
    rb_raise(rb_eArgError,"wrong number of arguments (%d for 5)", argc);
  rblapack_balanc = argv[0];
  rblapack_jobvl = argv[1];
  rblapack_jobvr = argv[2];
  rblapack_sense = argv[3];
  rblapack_a = argv[4];
  if (argc == 6) {
    rblapack_lwork = argv[5];
  } else if (rblapack_options != Qnil) {
    rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
  } else {
    rblapack_lwork = Qnil;
  }

  balanc = StringValueCStr(rblapack_balanc)[0];
  jobvr = StringValueCStr(rblapack_jobvr)[0];
  if (!NA_IsNArray(rblapack_a))
    rb_raise(rb_eArgError, "a (5th argument) must be NArray");
  if (NA_RANK(rblapack_a) != 2)
    rb_raise(rb_eArgError, "rank of a (5th argument) must be %d", 2);
  lda = NA_SHAPE0(rblapack_a);
  n = NA_SHAPE1(rblapack_a);
  if (NA_TYPE(rblapack_a) != NA_SCOMPLEX)
    rblapack_a = na_change_type(rblapack_a, NA_SCOMPLEX);
  a = NA_PTR_TYPE(rblapack_a, complex*);
  ldvr = lsame_(&jobvr,"V") ? n : 1;
  jobvl = StringValueCStr(rblapack_jobvl)[0];
  ldvl = lsame_(&jobvl,"V") ? n : 1;
  sense = StringValueCStr(rblapack_sense)[0];
  if (rblapack_lwork == Qnil)
    lwork = (lsame_(&sense,"N")||lsame_(&sense,"E")) ? 2*n : (lsame_(&sense,"V")||lsame_(&sense,"B")) ? n*n+2*n : 0;
  else {
    lwork = NUM2INT(rblapack_lwork);
  }
  {
    na_shape_t shape[1];
    shape[0] = n;
    rblapack_w = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
  }
  w = NA_PTR_TYPE(rblapack_w, complex*);
  {
    na_shape_t shape[2];
    shape[0] = ldvl;
    shape[1] = n;
    rblapack_vl = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
  }
  vl = NA_PTR_TYPE(rblapack_vl, complex*);
  {
    na_shape_t shape[2];
    shape[0] = ldvr;
    shape[1] = n;
    rblapack_vr = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
  }
  vr = NA_PTR_TYPE(rblapack_vr, complex*);
  {
    na_shape_t shape[1];
    shape[0] = n;
    rblapack_scale = na_make_object(NA_SFLOAT, 1, shape, cNArray);
  }
  scale = NA_PTR_TYPE(rblapack_scale, real*);
  {
    na_shape_t shape[1];
    shape[0] = n;
    rblapack_rconde = na_make_object(NA_SFLOAT, 1, shape, cNArray);
  }
  rconde = NA_PTR_TYPE(rblapack_rconde, real*);
  {
    na_shape_t shape[1];
    shape[0] = n;
    rblapack_rcondv = na_make_object(NA_SFLOAT, 1, shape, cNArray);
  }
  rcondv = NA_PTR_TYPE(rblapack_rcondv, real*);
  {
    na_shape_t shape[1];
    shape[0] = MAX(1,lwork);
    rblapack_work = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
  }
  work = NA_PTR_TYPE(rblapack_work, complex*);
  {
    na_shape_t shape[2];
    shape[0] = lda;
    shape[1] = n;
    rblapack_a_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
  }
  a_out__ = NA_PTR_TYPE(rblapack_a_out__, complex*);
  MEMCPY(a_out__, a, complex, NA_TOTAL(rblapack_a));
  rblapack_a = rblapack_a_out__;
  a = a_out__;
  rwork = ALLOC_N(real, (2*n));

  cgeevx_(&balanc, &jobvl, &jobvr, &sense, &n, a, &lda, w, vl, &ldvl, vr, &ldvr, &ilo, &ihi, scale, &abnrm, rconde, rcondv, work, &lwork, rwork, &info);

  free(rwork);
  rblapack_ilo = INT2NUM(ilo);
  rblapack_ihi = INT2NUM(ihi);
  rblapack_abnrm = rb_float_new((double)abnrm);
  rblapack_info = INT2NUM(info);
  return rb_ary_new3(12, rblapack_w, rblapack_vl, rblapack_vr, rblapack_ilo, rblapack_ihi, rblapack_scale, rblapack_abnrm, rblapack_rconde, rblapack_rcondv, rblapack_work, rblapack_info, rblapack_a);
}

void
init_lapack_cgeevx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
  sHelp = sH;
  sUsage = sU;
  rblapack_ZERO = zero;

  rb_define_module_function(mLapack, "cgeevx", rblapack_cgeevx, -1);
}
