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#include "rb_lapack.h"
extern VOID zgeevx_(char* balanc, char* jobvl, char* jobvr, char* sense, integer* n, doublecomplex* a, integer* lda, doublecomplex* w, doublecomplex* vl, integer* ldvl, doublecomplex* vr, integer* ldvr, integer* ilo, integer* ihi, doublereal* scale, doublereal* abnrm, doublereal* rconde, doublereal* rcondv, doublecomplex* work, integer* lwork, doublereal* rwork, integer* info);
static VALUE
rblapack_zgeevx(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;
doublecomplex *a;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_w;
doublecomplex *w;
VALUE rblapack_vl;
doublecomplex *vl;
VALUE rblapack_vr;
doublecomplex *vr;
VALUE rblapack_ilo;
integer ilo;
VALUE rblapack_ihi;
integer ihi;
VALUE rblapack_scale;
doublereal *scale;
VALUE rblapack_abnrm;
doublereal abnrm;
VALUE rblapack_rconde;
doublereal *rconde;
VALUE rblapack_rcondv;
doublereal *rcondv;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
doublereal *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.zgeevx( balanc, jobvl, jobvr, sense, a, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGEEVX( 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* ZGEEVX 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*16 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*16 array, dimension (N)\n* W contains the computed eigenvalues.\n*\n* VL (output) COMPLEX*16 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*16 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) DOUBLE PRECISION 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) DOUBLE PRECISION\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) DOUBLE PRECISION array, dimension (N)\n* RCONDE(j) is the reciprocal condition number of the j-th\n* eigenvalue.\n*\n* RCONDV (output) DOUBLE PRECISION array, dimension (N)\n* RCONDV(j) is the reciprocal condition number of the j-th\n* right eigenvector.\n*\n* WORK (workspace/output) COMPLEX*16 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) DOUBLE PRECISION 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.zgeevx( 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_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
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_DCOMPLEX, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldvl;
shape[1] = n;
rblapack_vl = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
vl = NA_PTR_TYPE(rblapack_vl, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldvr;
shape[1] = n;
rblapack_vr = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
vr = NA_PTR_TYPE(rblapack_vr, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_scale = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
scale = NA_PTR_TYPE(rblapack_scale, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_rconde = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
rconde = NA_PTR_TYPE(rblapack_rconde, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_rcondv = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
rcondv = NA_PTR_TYPE(rblapack_rcondv, doublereal*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublecomplex*);
MEMCPY(a_out__, a, doublecomplex, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
rwork = ALLOC_N(doublereal, (2*n));
zgeevx_(&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_zgeevx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zgeevx", rblapack_zgeevx, -1);
}
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