Mercurial > octave
view liboctave/array/fCRowVector.cc @ 21724:aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
* configure.ac, Doxyfile.in, make_int.cc, Backend.cc, BaseControl.cc,
ButtonControl.cc, Canvas.cc, CheckBoxControl.cc, Container.cc,
ContextMenu.cc, EditControl.cc, Figure.cc, FigureWindow.cc,
GLCanvas.cc, KeyMap.cc, ListBoxControl.cc, Logger.cc, Menu.cc,
MouseModeActionGroup.cc, Object.cc, ObjectFactory.cc,
ObjectProxy.cc, Panel.cc, PopupMenuControl.cc, PushButtonControl.cc,
PushTool.cc, QtHandlesUtils.cc, RadioButtonControl.cc,
SliderControl.cc, TextControl.cc, TextEdit.cc,
ToggleButtonControl.cc, ToggleTool.cc, ToolBar.cc, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, color-picker.cc,
dialog.cc, documentation-dock-widget.cc, files-dock-widget.cc,
find-files-dialog.cc, find-files-model.cc, history-dock-widget.cc,
liboctgui-build-info.in.cc, file-editor-tab.cc, file-editor.cc,
find-dialog.cc, marker.cc, marker.h, octave-qscintilla.cc,
octave-txt-lexer.cc, main-window.cc, octave-cmd.cc,
octave-dock-widget.cc, octave-gui.cc, octave-interpreter.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, shortcut-manager.cc, terminal-dock-widget.cc,
thread-manager.cc, welcome-wizard.cc, workspace-model.cc,
workspace-view.cc, build-env.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc,
__lin_interpn__.cc, __luinc__.cc, __magick_read__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc,
bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
cdisplay.c, cdisplay.h, cellfun.cc, coct-hdf5-types.c, colloc.cc,
comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defaults.in.h, defun.cc, det.cc, dirfns.cc,
display.cc, dlmread.cc, dot.cc, dynamic-ld.cc, eig.cc, ellipj.cc,
error.cc, errwarn.cc, event-queue.cc, fft.cc, fft2.cc, fftn.cc,
file-io.cc, filter.cc, find.cc, ft-text-renderer.cc, gammainc.cc,
gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
gl-render.cc, gl2ps-print.cc, graphics.cc, gripes.cc, hash.cc,
help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, jit-ir.cc, jit-ir.h,
jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, kron.cc,
load-path.cc, load-save.cc, lookup.cc, ls-ascii-helper.cc,
ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc,
ls-oct-binary.cc, ls-oct-text.cc, ls-oct-text.h, ls-utils.cc,
lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mex.h,
mexproto.h, mgorth.cc, nproc.cc, oct-errno.in.cc, oct-fstrm.cc,
oct-hdf5-types.cc, oct-hdf5-types.h, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc,
oct-stdstrm.h, oct-stream.cc, oct-strstrm.cc, oct-tex-lexer.in.ll,
oct-tex-parser.in.yy, octave-link.cc, ordschur.cc, pager.cc,
pinv.cc, pr-output.cc, procstream.cc, profiler.cc, psi.cc,
pt-jit.cc, pt-jit.h, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, siglist.c,
siglist.h, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc, spparms.cc,
sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, text-renderer.cc,
time.cc, toplev.cc, tril.cc, tsearch.cc, txt-eng.cc, typecast.cc,
urlwrite.cc, utils.cc, variables.cc, xdiv.cc, xgl2ps.c, xnorm.cc,
xpow.cc, zfstream.cc, zfstream.h, __delaunayn__.cc, __eigs__.cc,
__fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc,
audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc,
convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc,
liboctinterp-build-info.in.cc, mkbuiltins, mkops, ov-base.cc,
ov-bool-mat.cc, ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc,
ov-cell.cc, ov-ch-mat.cc, ov-class.cc, ov-classdef.cc, ov-colon.cc,
ov-complex.cc, ov-cs-list.cc, ov-cx-diag.cc, ov-cx-mat.cc,
ov-cx-sparse.cc, ov-dld-fcn.cc, ov-fcn-handle.cc, ov-fcn-inline.cc,
ov-fcn.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc,
ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-lazy-idx.cc,
ov-mex-fcn.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-perm.cc,
ov-range.cc, ov-re-diag.cc, ov-re-mat.cc, ov-re-sparse.cc,
ov-scalar.cc, ov-str-mat.cc, ov-struct.cc, ov-typeinfo.cc,
ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc,
ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ovl.cc, octave.cc, octave.h,
op-b-b.cc, op-b-bm.cc, op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc,
op-bm-sbm.cc, op-cdm-cdm.cc, op-cdm-cm.cc, op-cdm-dm.cc,
op-cdm-m.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cdm.cc,
op-cm-cm.cc, op-cm-cs.cc, op-cm-dm.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc,
op-cs-s.cc, op-cs-scm.cc, op-cs-sm.cc, op-dm-cdm.cc, op-dm-cm.cc,
op-dm-dm.cc, op-dm-m.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-double-conv.cc,
op-fcdm-fcdm.cc, op-fcdm-fcm.cc, op-fcdm-fdm.cc, op-fcdm-fm.cc,
op-fcm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fdm.cc,
op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc,
op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fcdm.cc, op-fdm-fcm.cc,
op-fdm-fdm.cc, op-fdm-fm.cc, op-float-conv.cc, op-fm-fcdm.cc,
op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fdm.cc, op-fm-fm.cc, op-fm-fs.cc,
op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc,
op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc,
op-int-conv.cc, op-m-cdm.cc, op-m-cm.cc, op-m-cs.cc, op-m-dm.cc,
op-m-m.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.cc, op-pm-pm.cc,
op-pm-scm.cc, op-pm-sm.cc, op-pm-template.cc, op-range.cc,
op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc,
op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc,
op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc,
op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc,
lex.ll, oct-parse.in.yy, pt-arg-list.cc, pt-array-list.cc,
pt-assign.cc, pt-binop.cc, pt-bp.cc, pt-cbinop.cc, pt-cell.cc,
pt-check.cc, pt-classdef.cc, pt-cmd.cc, pt-colon.cc, pt-const.cc,
pt-decl.cc, pt-eval.cc, pt-except.cc, pt-exp.cc, pt-fcn-handle.cc,
pt-funcall.cc, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-loop.cc,
pt-loop.h, pt-mat.cc, pt-misc.cc, pt-pr-code.cc, pt-select.cc,
pt-stmt.cc, pt-unop.cc, pt.cc, token.cc, Array-jit.cc, Array-tc.cc,
version.cc, Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc,
Array-f.cc, Array-fC.cc, Array-i.cc, Array-idx-vec.cc, Array-s.cc,
Array-str.cc, Array-util.cc, Array-voidp.cc, Array.cc,
CColVector.cc, CDiagMatrix.cc, CMatrix.cc, CNDArray.cc,
CRowVector.cc, CSparse.cc, MArray-C.cc, MArray-d.cc, MArray-f.cc,
MArray-fC.cc, MArray-i.cc, MArray-s.cc, MSparse-C.cc, MSparse-d.cc,
MatrixType.cc, PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc,
Sparse-d.cc, boolMatrix.cc, boolNDArray.cc, boolSparse.cc,
chMatrix.cc, chNDArray.cc, dColVector.cc, dDiagMatrix.cc,
dMatrix.cc, dNDArray.cc, dRowVector.cc, dSparse.cc, dim-vector.cc,
dim-vector.h, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc,
fCNDArray.cc, fCRowVector.cc, fColVector.cc, fDiagMatrix.cc,
fMatrix.cc, fNDArray.cc, fRowVector.cc, idx-vector.cc,
int16NDArray.cc, int32NDArray.cc, int64NDArray.cc, int8NDArray.cc,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc,
uint8NDArray.cc, Faddeeva.cc, blaswrap.c, cquit.c, f77-extern.cc,
f77-fcn.c, f77-fcn.h, lo-error.c, lo-error.h, quit.cc, quit.h,
liboctave-build-info.in.cc, CollocWt.cc, DASPK.cc, DASRT.cc,
DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, aepbalance.cc,
chol.cc, eigs-base.cc, fEIG.cc, gepbalance.cc, hess.cc,
lo-mappers.cc, lo-specfun.cc, lu.cc, oct-convn.cc, oct-fftw.cc,
oct-norm.cc, oct-rand.cc, oct-spparms.cc, qr.cc, qrp.cc,
randmtzig.cc, randpoisson.cc, schur.cc, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc, mk-ops.awk,
mx-defs.h, dir-ops.cc, file-ops.cc, file-stat.cc, lo-sysdep.cc,
mach-info.cc, oct-env.cc, oct-group.cc, oct-passwd.cc,
oct-syscalls.cc, oct-time.cc, oct-uname.cc, pathlen.h, syswait.h,
cmd-edit.cc, cmd-hist.cc, data-conv.cc, f2c-main.c, glob-match.cc,
kpse.cc, lo-array-errwarn.cc, lo-array-gripes.cc, lo-cutils.c,
lo-cutils.h, lo-ieee.cc, lo-ieee.h, lo-regexp.cc, lo-utils.cc,
oct-base64.cc, oct-glob.cc, oct-inttypes.cc, oct-inttypes.h,
oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-edit.h,
oct-rl-hist.c, oct-rl-hist.h, oct-shlib.cc, oct-sort.cc,
pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc, sparse-util.cc,
statdefs.h, str-vec.cc, unwind-prot.cc, url-transfer.cc,
acinclude.m4, display-available.c, display-available.h, main-cli.cc,
main-gui.cc, main.in.cc, mkoctfile.in.cc, octave-build-info.in.cc,
octave-config.in.cc, shared-fcns.h:
Use "#if ..." consistently instead of "#ifdef" and "#ifndef".
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 17 May 2016 12:09:30 -0400 |
parents | 40de9f8f23a6 |
children | 59cadee1c74b |
line wrap: on
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// RowVector manipulations. /* Copyright (C) 1994-2015 John W. Eaton This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <iostream> #include "Array-util.h" #include "f77-fcn.h" #include "functor.h" #include "lo-error.h" #include "mx-base.h" #include "mx-inlines.cc" #include "oct-cmplx.h" // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (cgemv, CGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xcdotu, XCDOTU) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex&); } // FloatComplex Row Vector class bool FloatComplexRowVector::operator == (const FloatComplexRowVector& a) const { octave_idx_type len = numel (); if (len != a.numel ()) return 0; return mx_inline_equal (len, data (), a.data ()); } bool FloatComplexRowVector::operator != (const FloatComplexRowVector& a) const { return !(*this == a); } // destructive insert/delete/reorder operations FloatComplexRowVector& FloatComplexRowVector::insert (const FloatRowVector& a, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (c < 0 || c + a_len > numel ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (c+i) = a.elem (i); } return *this; } FloatComplexRowVector& FloatComplexRowVector::insert (const FloatComplexRowVector& a, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (c < 0 || c + a_len > numel ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (c+i) = a.elem (i); } return *this; } FloatComplexRowVector& FloatComplexRowVector::fill (float val) { octave_idx_type len = numel (); if (len > 0) { make_unique (); for (octave_idx_type i = 0; i < len; i++) xelem (i) = val; } return *this; } FloatComplexRowVector& FloatComplexRowVector::fill (const FloatComplex& val) { octave_idx_type len = numel (); if (len > 0) { make_unique (); for (octave_idx_type i = 0; i < len; i++) xelem (i) = val; } return *this; } FloatComplexRowVector& FloatComplexRowVector::fill (float val, octave_idx_type c1, octave_idx_type c2) { octave_idx_type len = numel (); if (c1 < 0 || c2 < 0 || c1 >= len || c2 >= len) (*current_liboctave_error_handler) ("range error for fill"); if (c1 > c2) { std::swap (c1, c2); } if (c2 >= c1) { make_unique (); for (octave_idx_type i = c1; i <= c2; i++) xelem (i) = val; } return *this; } FloatComplexRowVector& FloatComplexRowVector::fill (const FloatComplex& val, octave_idx_type c1, octave_idx_type c2) { octave_idx_type len = numel (); if (c1 < 0 || c2 < 0 || c1 >= len || c2 >= len) (*current_liboctave_error_handler) ("range error for fill"); if (c1 > c2) { std::swap (c1, c2); } if (c2 >= c1) { make_unique (); for (octave_idx_type i = c1; i <= c2; i++) xelem (i) = val; } return *this; } FloatComplexRowVector FloatComplexRowVector::append (const FloatRowVector& a) const { octave_idx_type len = numel (); octave_idx_type nc_insert = len; FloatComplexRowVector retval (len + a.numel ()); retval.insert (*this, 0); retval.insert (a, nc_insert); return retval; } FloatComplexRowVector FloatComplexRowVector::append (const FloatComplexRowVector& a) const { octave_idx_type len = numel (); octave_idx_type nc_insert = len; FloatComplexRowVector retval (len + a.numel ()); retval.insert (*this, 0); retval.insert (a, nc_insert); return retval; } FloatComplexColumnVector FloatComplexRowVector::hermitian (void) const { return MArray<FloatComplex>::hermitian (std::conj); } FloatComplexColumnVector FloatComplexRowVector::transpose (void) const { return MArray<FloatComplex>::transpose (); } FloatComplexRowVector conj (const FloatComplexRowVector& a) { return do_mx_unary_map<FloatComplex, FloatComplex, std::conj<float> > (a); } // resize is the destructive equivalent for this one FloatComplexRowVector FloatComplexRowVector::extract (octave_idx_type c1, octave_idx_type c2) const { if (c1 > c2) { std::swap (c1, c2); } octave_idx_type new_c = c2 - c1 + 1; FloatComplexRowVector result (new_c); for (octave_idx_type i = 0; i < new_c; i++) result.elem (i) = elem (c1+i); return result; } FloatComplexRowVector FloatComplexRowVector::extract_n (octave_idx_type r1, octave_idx_type n) const { FloatComplexRowVector result (n); for (octave_idx_type i = 0; i < n; i++) result.elem (i) = elem (r1+i); return result; } // row vector by row vector -> row vector operations FloatComplexRowVector& FloatComplexRowVector::operator += (const FloatRowVector& a) { octave_idx_type len = numel (); octave_idx_type a_len = a.numel (); if (len != a_len) err_nonconformant ("operator +=", len, a_len); if (len == 0) return *this; FloatComplex *d = fortran_vec (); // Ensures only 1 reference to my privates! mx_inline_add2 (len, d, a.data ()); return *this; } FloatComplexRowVector& FloatComplexRowVector::operator -= (const FloatRowVector& a) { octave_idx_type len = numel (); octave_idx_type a_len = a.numel (); if (len != a_len) err_nonconformant ("operator -=", len, a_len); if (len == 0) return *this; FloatComplex *d = fortran_vec (); // Ensures only 1 reference to my privates! mx_inline_sub2 (len, d, a.data ()); return *this; } // row vector by matrix -> row vector FloatComplexRowVector operator * (const FloatComplexRowVector& v, const FloatComplexMatrix& a) { FloatComplexRowVector retval; octave_idx_type len = v.numel (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (a_nr != len) err_nonconformant ("operator *", 1, len, a_nr, a_nc); if (len == 0) retval.resize (a_nc, 0.0); else { // Transpose A to form A'*x == (x'*A)' octave_idx_type ld = a_nr; retval.resize (a_nc); FloatComplex *y = retval.fortran_vec (); F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 ("T", 1), a_nr, a_nc, 1.0, a.data (), ld, v.data (), 1, 0.0, y, 1 F77_CHAR_ARG_LEN (1))); } return retval; } FloatComplexRowVector operator * (const FloatRowVector& v, const FloatComplexMatrix& a) { FloatComplexRowVector tmp (v); return tmp * a; } // other operations FloatComplex FloatComplexRowVector::min (void) const { octave_idx_type len = numel (); if (len == 0) return FloatComplex (0.0); FloatComplex res = elem (0); float absres = std::abs (res); for (octave_idx_type i = 1; i < len; i++) if (std::abs (elem (i)) < absres) { res = elem (i); absres = std::abs (res); } return res; } FloatComplex FloatComplexRowVector::max (void) const { octave_idx_type len = numel (); if (len == 0) return FloatComplex (0.0); FloatComplex res = elem (0); float absres = std::abs (res); for (octave_idx_type i = 1; i < len; i++) if (std::abs (elem (i)) > absres) { res = elem (i); absres = std::abs (res); } return res; } // i/o std::ostream& operator << (std::ostream& os, const FloatComplexRowVector& a) { // int field_width = os.precision () + 7; for (octave_idx_type i = 0; i < a.numel (); i++) os << " " /* setw (field_width) */ << a.elem (i); return os; } std::istream& operator >> (std::istream& is, FloatComplexRowVector& a) { octave_idx_type len = a.numel (); if (len > 0) { FloatComplex tmp; for (octave_idx_type i = 0; i < len; i++) { is >> tmp; if (is) a.elem (i) = tmp; else break; } } return is; } // row vector by column vector -> scalar // row vector by column vector -> scalar FloatComplex operator * (const FloatComplexRowVector& v, const FloatColumnVector& a) { FloatComplexColumnVector tmp (a); return v * tmp; } FloatComplex operator * (const FloatComplexRowVector& v, const FloatComplexColumnVector& a) { FloatComplex retval (0.0, 0.0); octave_idx_type len = v.numel (); octave_idx_type a_len = a.numel (); if (len != a_len) err_nonconformant ("operator *", len, a_len); if (len != 0) F77_FUNC (xcdotu, XCDOTU) (len, v.data (), 1, a.data (), 1, retval); return retval; } // other operations FloatComplexRowVector linspace (const FloatComplex& x1, const FloatComplex& x2, octave_idx_type n) { NoAlias<FloatComplexRowVector> retval; if (n < 1) return retval; else retval.clear (n); retval(0) = x1; FloatComplex delta = (x2 - x1) / (n - 1.0f); for (octave_idx_type i = 1; i < n-1; i++) retval(i) = x1 + static_cast<float> (i)*delta; retval(n-1) = x2; return retval; }