Mercurial > hg > octave-nkf
diff liboctave/fMatrix.cc @ 11586:12df7854fa7c
strip trailing whitespace from source files
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 20 Jan 2011 17:24:59 -0500 |
| parents | a83bad07f7e3 |
| children | 6dfebfa334cb |
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line diff
--- a/liboctave/fMatrix.cc +++ b/liboctave/fMatrix.cc @@ -116,7 +116,7 @@ F77_RET_T F77_FUNC (ssyrk, SSYRK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, const octave_idx_type&, + const octave_idx_type&, const octave_idx_type&, const float&, const float*, const octave_idx_type&, const float&, float*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL @@ -130,7 +130,7 @@ F77_RET_T F77_FUNC (sgetrs, SGETRS) (F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, const octave_idx_type&, + const octave_idx_type&, const octave_idx_type&, const float*, const octave_idx_type&, const octave_idx_type*, float*, const octave_idx_type&, octave_idx_type& @@ -143,8 +143,8 @@ F77_RET_T F77_FUNC (sgecon, SGECON) (F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, float*, - const octave_idx_type&, const float&, float&, + const octave_idx_type&, float*, + const octave_idx_type&, const float&, float&, float*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); @@ -181,34 +181,34 @@ F77_RET_T F77_FUNC (spotrs, SPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, - const float*, const octave_idx_type&, float*, + const float*, const octave_idx_type&, float*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (strtri, STRTRI) (F77_CONST_CHAR_ARG_DECL, - F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, const float*, + F77_CONST_CHAR_ARG_DECL, + const octave_idx_type&, const float*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (strcon, STRCON) (F77_CONST_CHAR_ARG_DECL, - F77_CONST_CHAR_ARG_DECL, + F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const float*, const octave_idx_type&, float&, - float*, octave_idx_type*, octave_idx_type& + float*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (strtrs, STRTRS) (F77_CONST_CHAR_ARG_DECL, - F77_CONST_CHAR_ARG_DECL, + F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, - const octave_idx_type&, const float*, - const octave_idx_type&, float*, + const octave_idx_type&, + const octave_idx_type&, const float*, + const octave_idx_type&, float*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL @@ -234,7 +234,7 @@ const octave_idx_type&, const octave_idx_type&, const float*, const octave_idx_type&, float*, float& - F77_CHAR_ARG_LEN_DECL); + F77_CHAR_ARG_LEN_DECL); } // Matrix class. @@ -670,7 +670,7 @@ } FloatMatrix -FloatMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, float& rcon, +FloatMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatMatrix retval; @@ -690,15 +690,15 @@ F77_XFCN (strtri, STRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), - nr, tmp_data, nr, info + nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; - if (info != 0) + if (info != 0) info = -1; - else if (calc_cond) + else if (calc_cond) { octave_idx_type dtrcon_info = 0; char job = '1'; @@ -709,13 +709,13 @@ F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&job, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), - nr, tmp_data, nr, rcon, - work, iwork, dtrcon_info + nr, tmp_data, nr, rcon, + work, iwork, dtrcon_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - if (dtrcon_info != 0) + if (dtrcon_info != 0) info = -1; } @@ -728,7 +728,7 @@ FloatMatrix -FloatMatrix::finverse (MatrixType &mattype, octave_idx_type& info, float& rcon, +FloatMatrix::finverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatMatrix retval; @@ -750,7 +750,7 @@ octave_idx_type lwork = -1; // Query the optimum work array size. - F77_XFCN (sgetri, SGETRI, (nc, tmp_data, nr, pipvt, + F77_XFCN (sgetri, SGETRI, (nc, tmp_data, nr, pipvt, z.fortran_vec (), lwork, info)); lwork = static_cast<octave_idx_type> (z(0)); @@ -762,16 +762,16 @@ // Calculate the norm of the matrix, for later use. float anorm = 0; - if (calc_cond) + if (calc_cond) anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (sgetrf, SGETRF, (nc, nc, tmp_data, nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; - if (info != 0) + if (info != 0) info = -1; - else if (calc_cond) + else if (calc_cond) { octave_idx_type dgecon_info = 0; @@ -780,11 +780,11 @@ Array<octave_idx_type> iz (dim_vector (nc, 1)); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (sgecon, SGECON, (F77_CONST_CHAR_ARG2 (&job, 1), - nc, tmp_data, nr, anorm, + nc, tmp_data, nr, anorm, rcon, pz, piz, dgecon_info F77_CHAR_ARG_LEN (1))); - if (dgecon_info != 0) + if (dgecon_info != 0) info = -1; } @@ -797,7 +797,7 @@ F77_XFCN (sgetri, SGETRI, (nc, tmp_data, nr, pipvt, pz, lwork, dgetri_info)); - if (dgetri_info != 0) + if (dgetri_info != 0) info = -1; } @@ -809,7 +809,7 @@ } FloatMatrix -FloatMatrix::inverse (MatrixType &mattype, octave_idx_type& info, float& rcon, +FloatMatrix::inverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { int typ = mattype.type (false); @@ -910,7 +910,7 @@ const float *in (fortran_vec ()); FloatComplex *out (retval.fortran_vec ()); - octave_fftw::fft (in, out, npts, nsamples); + octave_fftw::fft (in, out, npts, nsamples); return retval; } @@ -940,7 +940,7 @@ FloatComplex *in (tmp.fortran_vec ()); FloatComplex *out (retval.fortran_vec ()); - octave_fftw::ifft (in, out, npts, nsamples); + octave_fftw::ifft (in, out, npts, nsamples); return retval; } @@ -1259,7 +1259,7 @@ if (typ == MatrixType::Lower || typ == MatrixType::Upper) { - for (octave_idx_type i = 0; i < nc; i++) + for (octave_idx_type i = 0; i < nc; i++) retval *= elem (i,i); } else if (typ == MatrixType::Hermitian) @@ -1273,17 +1273,17 @@ char job = 'L'; - F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, + F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } - else + else { Array<float> z (dim_vector (3 * nc, 1)); float *pz = z.fortran_vec (); @@ -1295,10 +1295,10 @@ rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) rcon = 0.0; - for (octave_idx_type i = 0; i < nc; i++) + for (octave_idx_type i = 0; i < nc; i++) retval *= atmp (i,i); retval = retval.square (); @@ -1325,14 +1325,14 @@ // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; - if (info != 0) + if (info != 0) { info = -1; retval = FloatDET (); - } - else + } + else { - if (calc_cond) + if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; @@ -1342,19 +1342,19 @@ octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (sgecon, SGECON, (F77_CONST_CHAR_ARG2 (&job, 1), - nc, tmp_data, nr, anorm, + nc, tmp_data, nr, anorm, rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); } - if (info != 0) + if (info != 0) { info = -1; retval = FloatDET (); - } - else + } + else { - for (octave_idx_type i = 0; i < nc; i++) + for (octave_idx_type i = 0; i < nc; i++) { float c = atmp(i,i); retval *= (ipvt(i) != (i+1)) ? -c : c; @@ -1406,16 +1406,16 @@ Array<octave_idx_type> iz (dim_vector (nc, 1)); octave_idx_type *piz = iz.fortran_vec (); - F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), - F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), + F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) rcon = 0.0; } else if (typ == MatrixType::Permuted_Upper) @@ -1434,16 +1434,16 @@ Array<octave_idx_type> iz (dim_vector (nc, 1)); octave_idx_type *piz = iz.fortran_vec (); - F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), - F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), + F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) rcon = 0.0; } else if (typ == MatrixType::Permuted_Lower) @@ -1462,17 +1462,17 @@ anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); - F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, + F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } - else + else { Array<float> z (dim_vector (3 * nc, 1)); float *pz = z.fortran_vec (); @@ -1484,7 +1484,7 @@ rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) rcon = 0.0; } } @@ -1507,20 +1507,20 @@ F77_XFCN (sgetrf, SGETRF, (nr, nr, tmp_data, nr, pipvt, info)); - if (info != 0) + if (info != 0) { rcon = 0.0; mattype.mark_as_rectangular (); } - else + else { char job = '1'; F77_XFCN (sgecon, SGECON, (F77_CONST_CHAR_ARG2 (&job, 1), - nc, tmp_data, nr, anorm, + nc, tmp_data, nr, anorm, rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) rcon = 0.0; } } @@ -1578,16 +1578,16 @@ Array<octave_idx_type> iz (dim_vector (nc, 1)); octave_idx_type *piz = iz.fortran_vec (); - F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), - F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), + F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; @@ -1614,9 +1614,9 @@ char trans = get_blas_char (transt); char dia = 'N'; - F77_XFCN (strtrs, STRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&trans, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strtrs, STRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&trans, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) @@ -1678,16 +1678,16 @@ Array<octave_idx_type> iz (dim_vector (nc, 1)); octave_idx_type *piz = iz.fortran_vec (); - F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), - F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strcon, STRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), + F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; @@ -1714,9 +1714,9 @@ char trans = get_blas_char (transt); char dia = 'N'; - F77_XFCN (strtrs, STRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), - F77_CONST_CHAR_ARG2 (&trans, 1), - F77_CONST_CHAR_ARG2 (&dia, 1), + F77_XFCN (strtrs, STRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), + F77_CONST_CHAR_ARG2 (&trans, 1), + F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) @@ -1750,7 +1750,7 @@ else { volatile int typ = mattype.type (); - + // Calculate the norm of the matrix, for later use. float anorm = -1.; @@ -1762,20 +1762,20 @@ float *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); - F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, + F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; - if (info != 0) + if (info != 0) { info = -2; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } - else + else { if (calc_cond) { @@ -1789,7 +1789,7 @@ rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; @@ -1823,7 +1823,7 @@ { mattype.mark_as_unsymmetric (); typ = MatrixType::Full; - } + } } } @@ -1848,7 +1848,7 @@ // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; - if (info != 0) + if (info != 0) { info = -2; @@ -1860,19 +1860,19 @@ mattype.mark_as_rectangular (); } - else + else { if (calc_cond) { - // Now calculate the condition number for + // Now calculate the condition number for // non-singular matrix. char job = '1'; F77_XFCN (sgecon, SGECON, (F77_CONST_CHAR_ARG2 (&job, 1), - nc, tmp_data, nr, anorm, + nc, tmp_data, nr, anorm, rcon, pz, piz, info F77_CHAR_ARG_LEN (1))); - if (info != 0) + if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; @@ -1930,7 +1930,7 @@ } FloatMatrix -FloatMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, +FloatMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); @@ -1981,7 +1981,7 @@ } FloatComplexMatrix -FloatMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, +FloatMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, octave_idx_type& info) const { float rcon; @@ -2040,7 +2040,7 @@ } FloatColumnVector -FloatMatrix::solve (MatrixType &typ, const FloatColumnVector& b, +FloatMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info) const { float rcon; @@ -2071,7 +2071,7 @@ } FloatComplexColumnVector -FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, +FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info) const { FloatComplexMatrix tmp (*this); @@ -2079,7 +2079,7 @@ } FloatComplexColumnVector -FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, +FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon) const { FloatComplexMatrix tmp (*this); @@ -2087,7 +2087,7 @@ } FloatComplexColumnVector -FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, +FloatMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { @@ -2358,7 +2358,7 @@ F77_XFCN (sgelsd, SGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, - work.fortran_vec (), lwork, + work.fortran_vec (), lwork, piwork, info)); if (s.elem (0) == 0.0) @@ -2392,7 +2392,7 @@ } FloatComplexMatrix -FloatMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, +FloatMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { FloatComplexMatrix tmp (*this); @@ -2401,7 +2401,7 @@ } FloatComplexMatrix -FloatMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, +FloatMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { FloatComplexMatrix tmp (*this); @@ -2454,7 +2454,7 @@ volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; - + if (m != n) { retval = FloatColumnVector (maxmn, 0.0); @@ -2512,7 +2512,7 @@ F77_XFCN (sgelsd, SGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, - work.fortran_vec (), lwork, + work.fortran_vec (), lwork, piwork, info)); if (rank < minmn) @@ -2549,7 +2549,7 @@ } FloatComplexColumnVector -FloatMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, +FloatMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { FloatComplexMatrix tmp (*this); @@ -2558,7 +2558,7 @@ } FloatComplexColumnVector -FloatMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, +FloatMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, float &rcon) const { FloatComplexMatrix tmp (*this); @@ -2633,7 +2633,7 @@ retval = FloatMatrix (len, a_len); float *c = retval.fortran_vec (); - + F77_XFCN (sgemm, SGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), len, a_len, 1, 1.0, v.data (), len, @@ -3063,7 +3063,7 @@ FloatSCHUR as (a, "U"); FloatSCHUR bs (b, "U"); - + // Transform c to new coordinates. FloatMatrix ua = as.unitary_matrix (); @@ -3071,9 +3071,9 @@ FloatMatrix ub = bs.unitary_matrix (); FloatMatrix sch_b = bs.schur_matrix (); - + FloatMatrix cx = ua.transpose () * c * ub; - + // Solve the sylvester equation, back-transform, and return the // solution. @@ -3096,7 +3096,7 @@ // FIXME -- check info? - + retval = -ua*cx*ub.transpose (); return retval; @@ -3130,8 +3130,8 @@ // the general GEMM operation -FloatMatrix -xgemm (const FloatMatrix& a, const FloatMatrix& b, +FloatMatrix +xgemm (const FloatMatrix& a, const FloatMatrix& b, blas_trans_type transa, blas_trans_type transb) { FloatMatrix retval; @@ -3362,8 +3362,8 @@ return result; } -FloatMatrix linspace (const FloatColumnVector& x1, - const FloatColumnVector& x2, +FloatMatrix linspace (const FloatColumnVector& x1, + const FloatColumnVector& x2, octave_idx_type n) { @@ -3381,7 +3381,7 @@ retval(i, 0) = x1(i); // The last column is not needed while using delta. - float *delta = &retval(0, n-1); + float *delta = &retval(0, n-1); for (octave_idx_type i = 0; i < m; i++) delta[i] = (x2(i) - x1(i)) / (n - 1);