From eda5bc26f44ee9a6f83dcf8c91f17296d7fc509d Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Mon, 12 Feb 2024 14:52:43 +0100 Subject: Move into version control --- .../include/armadillo_bits/def_lapack.hpp | 1178 ++++++++++++++++++++ 1 file changed, 1178 insertions(+) create mode 100644 src/armadillo/include/armadillo_bits/def_lapack.hpp (limited to 'src/armadillo/include/armadillo_bits/def_lapack.hpp') diff --git a/src/armadillo/include/armadillo_bits/def_lapack.hpp b/src/armadillo/include/armadillo_bits/def_lapack.hpp new file mode 100644 index 0000000..00854ab --- /dev/null +++ b/src/armadillo/include/armadillo_bits/def_lapack.hpp @@ -0,0 +1,1178 @@ +// SPDX-License-Identifier: Apache-2.0 +// +// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au) +// Copyright 2008-2016 National ICT Australia (NICTA) +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +// ------------------------------------------------------------------------ + + + +#if defined(ARMA_USE_LAPACK) + +#if defined(dgetrf) || defined(DGETRF) + #pragma message ("WARNING: detected possible interference with definitions of LAPACK functions;") + #pragma message ("WARNING: include the armadillo header before any other header as a workaround") +#endif + + +#if defined(ARMA_LAPACK_NOEXCEPT) + #undef ARMA_NOEXCEPT + #define ARMA_NOEXCEPT noexcept +#else + #undef ARMA_NOEXCEPT + #define ARMA_NOEXCEPT +#endif + + +#if !defined(ARMA_BLAS_CAPITALS) + #define arma_sgetrf sgetrf + #define arma_dgetrf dgetrf + #define arma_cgetrf cgetrf + #define arma_zgetrf zgetrf + + #define arma_sgetrs sgetrs + #define arma_dgetrs dgetrs + #define arma_cgetrs cgetrs + #define arma_zgetrs zgetrs + + #define arma_sgetri sgetri + #define arma_dgetri dgetri + #define arma_cgetri cgetri + #define arma_zgetri zgetri + + #define arma_strtri strtri + #define arma_dtrtri dtrtri + #define arma_ctrtri ctrtri + #define arma_ztrtri ztrtri + + #define arma_sgeev sgeev + #define arma_dgeev dgeev + #define arma_cgeev cgeev + #define arma_zgeev zgeev + + #define arma_sgeevx sgeevx + #define arma_dgeevx dgeevx + #define arma_cgeevx cgeevx + #define arma_zgeevx zgeevx + + #define arma_ssyev ssyev + #define arma_dsyev dsyev + + #define arma_cheev cheev + #define arma_zheev zheev + + #define arma_ssyevd ssyevd + #define arma_dsyevd dsyevd + + #define arma_cheevd cheevd + #define arma_zheevd zheevd + + #define arma_sggev sggev + #define arma_dggev dggev + + #define arma_cggev cggev + #define arma_zggev zggev + + #define arma_spotrf spotrf + #define arma_dpotrf dpotrf + #define arma_cpotrf cpotrf + #define arma_zpotrf zpotrf + + #define arma_spotrs spotrs + #define arma_dpotrs dpotrs + #define arma_cpotrs cpotrs + #define arma_zpotrs zpotrs + + #define arma_spbtrf spbtrf + #define arma_dpbtrf dpbtrf + #define arma_cpbtrf cpbtrf + #define arma_zpbtrf zpbtrf + + #define arma_spotri spotri + #define arma_dpotri dpotri + #define arma_cpotri cpotri + #define arma_zpotri zpotri + + #define arma_sgeqrf sgeqrf + #define arma_dgeqrf dgeqrf + #define arma_cgeqrf cgeqrf + #define arma_zgeqrf zgeqrf + + #define arma_sgeqp3 sgeqp3 + #define arma_dgeqp3 dgeqp3 + #define arma_cgeqp3 cgeqp3 + #define arma_zgeqp3 zgeqp3 + + #define arma_sorgqr sorgqr + #define arma_dorgqr dorgqr + + #define arma_cungqr cungqr + #define arma_zungqr zungqr + + #define arma_sgesvd sgesvd + #define arma_dgesvd dgesvd + + #define arma_cgesvd cgesvd + #define arma_zgesvd zgesvd + + #define arma_sgesdd sgesdd + #define arma_dgesdd dgesdd + #define arma_cgesdd cgesdd + #define arma_zgesdd zgesdd + + #define arma_sgesv sgesv + #define arma_dgesv dgesv + #define arma_cgesv cgesv + #define arma_zgesv zgesv + + #define arma_sgesvx sgesvx + #define arma_dgesvx dgesvx + #define arma_cgesvx cgesvx + #define arma_zgesvx zgesvx + + #define arma_sposv sposv + #define arma_dposv dposv + #define arma_cposv cposv + #define arma_zposv zposv + + #define arma_sposvx sposvx + #define arma_dposvx dposvx + #define arma_cposvx cposvx + #define arma_zposvx zposvx + + #define arma_sgels sgels + #define arma_dgels dgels + #define arma_cgels cgels + #define arma_zgels zgels + + #define arma_sgelsd sgelsd + #define arma_dgelsd dgelsd + #define arma_cgelsd cgelsd + #define arma_zgelsd zgelsd + + #define arma_strtrs strtrs + #define arma_dtrtrs dtrtrs + #define arma_ctrtrs ctrtrs + #define arma_ztrtrs ztrtrs + + #define arma_sgbtrf sgbtrf + #define arma_dgbtrf dgbtrf + #define arma_cgbtrf cgbtrf + #define arma_zgbtrf zgbtrf + + #define arma_sgbtrs sgbtrs + #define arma_dgbtrs dgbtrs + #define arma_cgbtrs cgbtrs + #define arma_zgbtrs zgbtrs + + #define arma_sgbsv sgbsv + #define arma_dgbsv dgbsv + #define arma_cgbsv cgbsv + #define arma_zgbsv zgbsv + + #define arma_sgbsvx sgbsvx + #define arma_dgbsvx dgbsvx + #define arma_cgbsvx cgbsvx + #define arma_zgbsvx zgbsvx + + #define arma_sgtsv sgtsv + #define arma_dgtsv dgtsv + #define arma_cgtsv cgtsv + #define arma_zgtsv zgtsv + + #define arma_sgtsvx sgtsvx + #define arma_dgtsvx dgtsvx + #define arma_cgtsvx cgtsvx + #define arma_zgtsvx zgtsvx + + #define arma_sgees sgees + #define arma_dgees dgees + #define arma_cgees cgees + #define arma_zgees zgees + + #define arma_strsyl strsyl + #define arma_dtrsyl dtrsyl + #define arma_ctrsyl ctrsyl + #define arma_ztrsyl ztrsyl + + #define arma_sgges sgges + #define arma_dgges dgges + #define arma_cgges cgges + #define arma_zgges zgges + + #define arma_slange slange + #define arma_dlange dlange + #define arma_clange clange + #define arma_zlange zlange + + #define arma_slansy slansy + #define arma_dlansy dlansy + #define arma_clansy clansy + #define arma_zlansy zlansy + + #define arma_clanhe clanhe + #define arma_zlanhe zlanhe + + #define arma_slangb slangb + #define arma_dlangb dlangb + #define arma_clangb clangb + #define arma_zlangb zlangb + + #define arma_sgecon sgecon + #define arma_dgecon dgecon + #define arma_cgecon cgecon + #define arma_zgecon zgecon + + #define arma_spocon spocon + #define arma_dpocon dpocon + #define arma_cpocon cpocon + #define arma_zpocon zpocon + + #define arma_strcon strcon + #define arma_dtrcon dtrcon + #define arma_ctrcon ctrcon + #define arma_ztrcon ztrcon + + #define arma_sgbcon sgbcon + #define arma_dgbcon dgbcon + #define arma_cgbcon cgbcon + #define arma_zgbcon zgbcon + + #define arma_ilaenv ilaenv + + #define arma_slahqr slahqr + #define arma_dlahqr dlahqr + + #define arma_sstedc sstedc + #define arma_dstedc dstedc + + #define arma_strevc strevc + #define arma_dtrevc dtrevc + + #define arma_sgehrd sgehrd + #define arma_dgehrd dgehrd + #define arma_cgehrd cgehrd + #define arma_zgehrd zgehrd + + #define arma_spstrf spstrf + #define arma_dpstrf dpstrf + #define arma_cpstrf cpstrf + #define arma_zpstrf zpstrf + +#else + + #define arma_sgetrf SGETRF + #define arma_dgetrf DGETRF + #define arma_cgetrf CGETRF + #define arma_zgetrf ZGETRF + + #define arma_sgetrs SGETRS + #define arma_dgetrs DGETRS + #define arma_cgetrs CGETRS + #define arma_zgetrs ZGETRS + + #define arma_sgetri SGETRI + #define arma_dgetri DGETRI + #define arma_cgetri CGETRI + #define arma_zgetri ZGETRI + + #define arma_strtri STRTRI + #define arma_dtrtri DTRTRI + #define arma_ctrtri CTRTRI + #define arma_ztrtri ZTRTRI + + #define arma_sgeev SGEEV + #define arma_dgeev DGEEV + #define arma_cgeev CGEEV + #define arma_zgeev ZGEEV + + #define arma_sgeevx SGEEVX + #define arma_dgeevx DGEEVX + #define arma_cgeevx CGEEVX + #define arma_zgeevx ZGEEVX + + #define arma_ssyev SSYEV + #define arma_dsyev DSYEV + + #define arma_cheev CHEEV + #define arma_zheev ZHEEV + + #define arma_ssyevd SSYEVD + #define arma_dsyevd DSYEVD + + #define arma_cheevd CHEEVD + #define arma_zheevd ZHEEVD + + #define arma_sggev SGGEV + #define arma_dggev DGGEV + + #define arma_cggev CGGEV + #define arma_zggev ZGGEV + + #define arma_spotrf SPOTRF + #define arma_dpotrf DPOTRF + #define arma_cpotrf CPOTRF + #define arma_zpotrf ZPOTRF + + #define arma_spotrs SPOTRS + #define arma_dpotrs DPOTRS + #define arma_cpotrs CPOTRS + #define arma_zpotrs ZPOTRS + + #define arma_spbtrf SPBTRF + #define arma_dpbtrf DPBTRF + #define arma_cpbtrf CPBTRF + #define arma_zpbtrf ZPBTRF + + #define arma_spotri SPOTRI + #define arma_dpotri DPOTRI + #define arma_cpotri CPOTRI + #define arma_zpotri ZPOTRI + + #define arma_sgeqrf SGEQRF + #define arma_dgeqrf DGEQRF + #define arma_cgeqrf CGEQRF + #define arma_zgeqrf ZGEQRF + + #define arma_sgeqp3 SGEQP3 + #define arma_dgeqp3 DGEQP3 + #define arma_cgeqp3 CGEQP3 + #define arma_zgeqp3 ZGEQP3 + + #define arma_sorgqr SORGQR + #define arma_dorgqr DORGQR + + #define arma_cungqr CUNGQR + #define arma_zungqr ZUNGQR + + #define arma_sgesvd SGESVD + #define arma_dgesvd DGESVD + + #define arma_cgesvd CGESVD + #define arma_zgesvd ZGESVD + + #define arma_sgesdd SGESDD + #define arma_dgesdd DGESDD + #define arma_cgesdd CGESDD + #define arma_zgesdd ZGESDD + + #define arma_sgesv SGESV + #define arma_dgesv DGESV + #define arma_cgesv CGESV + #define arma_zgesv ZGESV + + #define arma_sgesvx SGESVX + #define arma_dgesvx DGESVX + #define arma_cgesvx CGESVX + #define arma_zgesvx ZGESVX + + #define arma_sposv SPOSV + #define arma_dposv DPOSV + #define arma_cposv CPOSV + #define arma_zposv ZPOSV + + #define arma_sposvx SPOSVX + #define arma_dposvx DPOSVX + #define arma_cposvx CPOSVX + #define arma_zposvx ZPOSVX + + #define arma_sgels SGELS + #define arma_dgels DGELS + #define arma_cgels CGELS + #define arma_zgels ZGELS + + #define arma_sgelsd SGELSD + #define arma_dgelsd DGELSD + #define arma_cgelsd CGELSD + #define arma_zgelsd ZGELSD + + #define arma_strtrs STRTRS + #define arma_dtrtrs DTRTRS + #define arma_ctrtrs CTRTRS + #define arma_ztrtrs ZTRTRS + + #define arma_sgbtrf SGBTRF + #define arma_dgbtrf DGBTRF + #define arma_cgbtrf CGBTRF + #define arma_zgbtrf ZGBTRF + + #define arma_sgbtrs SGBTRS + #define arma_dgbtrs DGBTRS + #define arma_cgbtrs CGBTRS + #define arma_zgbtrs ZGBTRS + + #define arma_sgbsv SGBSV + #define arma_dgbsv DGBSV + #define arma_cgbsv CGBSV + #define arma_zgbsv ZGBSV + + #define arma_sgbsvx SGBSVX + #define arma_dgbsvx DGBSVX + #define arma_cgbsvx CGBSVX + #define arma_zgbsvx ZGBSVX + + #define arma_sgtsv SGTSV + #define arma_dgtsv DGTSV + #define arma_cgtsv CGTSV + #define arma_zgtsv ZGTSV + + #define arma_sgtsvx SGTSVX + #define arma_dgtsvx DGTSVX + #define arma_cgtsvx CGTSVX + #define arma_zgtsvx ZGTSVX + + #define arma_sgees SGEES + #define arma_dgees DGEES + #define arma_cgees CGEES + #define arma_zgees ZGEES + + #define arma_strsyl STRSYL + #define arma_dtrsyl DTRSYL + #define arma_ctrsyl CTRSYL + #define arma_ztrsyl ZTRSYL + + #define arma_sgges SGGES + #define arma_dgges DGGES + #define arma_cgges CGGES + #define arma_zgges ZGGES + + #define arma_slange SLANGE + #define arma_dlange DLANGE + #define arma_clange CLANGE + #define arma_zlange ZLANGE + + #define arma_slansy SLANSY + #define arma_dlansy DLANSY + #define arma_clansy CLANSY + #define arma_zlansy ZLANSY + + #define arma_clanhe CLANHE + #define arma_zlanhe ZLANHE + + #define arma_slangb SLANGB + #define arma_dlangb DLANGB + #define arma_clangb CLANGB + #define arma_zlangb ZLANGB + + #define arma_sgecon SGECON + #define arma_dgecon DGECON + #define arma_cgecon CGECON + #define arma_zgecon ZGECON + + #define arma_spocon SPOCON + #define arma_dpocon DPOCON + #define arma_cpocon CPOCON + #define arma_zpocon ZPOCON + + #define arma_strcon STRCON + #define arma_dtrcon DTRCON + #define arma_ctrcon CTRCON + #define arma_ztrcon ZTRCON + + #define arma_sgbcon SGBCON + #define arma_dgbcon DGBCON + #define arma_cgbcon CGBCON + #define arma_zgbcon ZGBCON + + #define arma_ilaenv ILAENV + + #define arma_slahqr SLAHQR + #define arma_dlahqr DLAHQR + + #define arma_sstedc SSTEDC + #define arma_dstedc DSTEDC + + #define arma_strevc STREVC + #define arma_dtrevc DTREVC + + #define arma_sgehrd SGEHRD + #define arma_dgehrd DGEHRD + #define arma_cgehrd CGEHRD + #define arma_zgehrd ZGEHRD + + #define arma_spstrf SPSTRF + #define arma_dpstrf DPSTRF + #define arma_cpstrf CPSTRF + #define arma_zpstrf ZPSTRF + +#endif + + +typedef blas_int (*fn_select_s2) (const float*, const float* ); +typedef blas_int (*fn_select_s3) (const float*, const float*, const float*); + +typedef blas_int (*fn_select_d2) (const double*, const double* ); +typedef blas_int (*fn_select_d3) (const double*, const double*, const double*); + +typedef blas_int (*fn_select_c1) (const blas_cxf* ); +typedef blas_int (*fn_select_c2) (const blas_cxf*, const blas_cxf*); + +typedef blas_int (*fn_select_z1) (const blas_cxd* ); +typedef blas_int (*fn_select_z2) (const blas_cxd*, const blas_cxd*); + + +// NOTE: "For arguments of CHARACTER type, the character length is passed as a hidden argument at the end of the argument list." +// NOTE: https://gcc.gnu.org/onlinedocs/gfortran/Argument-passing-conventions.html + + +extern "C" +{ +#if defined(ARMA_USE_FORTRAN_HIDDEN_ARGS) + + // LU decomposition + void arma_fortran(arma_sgetrf)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetrf)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetrf)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetrf)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations using pre-computed LU decomposition + void arma_fortran(arma_sgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, const blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info, const blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, const blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info, const blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, const blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info, const blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, const blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info, const blas_len trans_len) ARMA_NOEXCEPT; + + // matrix inversion (using pre-computed LU decomposition) + void arma_fortran(arma_sgetri)(const blas_int* n, float* a, const blas_int* lda, const blas_int* ipiv, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetri)(const blas_int* n, double* a, const blas_int* lda, const blas_int* ipiv, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetri)(const blas_int* n, blas_cxf* a, const blas_int* lda, const blas_int* ipiv, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetri)(const blas_int* n, blas_cxd* a, const blas_int* lda, const blas_int* ipiv, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // matrix inversion (triangular matrices) + void arma_fortran(arma_strtri)(const char* uplo, const char* diag, const blas_int* n, float* a, const blas_int* lda, blas_int* info, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrtri)(const char* uplo, const char* diag, const blas_int* n, double* a, const blas_int* lda, blas_int* info, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrtri)(const char* uplo, const char* diag, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrtri)(const char* uplo, const char* diag, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (real) + void arma_fortran(arma_sgeev)(const char* jobvl, const char* jobvr, const blas_int* n, float* a, const blas_int* lda, float* wr, float* wi, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, float* work, const blas_int* lwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeev)(const char* jobvl, const char* jobvr, const blas_int* n, double* a, const blas_int* lda, double* wr, double* wi, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, double* work, const blas_int* lwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (complex) + void arma_fortran(arma_cgeev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* w, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* w, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (real; advanced form) + void arma_fortran(arma_sgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, float* a, const blas_int* lda, float* wr, float* wi, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, float* scale, float* abnrm, float* rconde, float* rcondv, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info, blas_len balanc_len, blas_len jobvl_len, blas_len jobvr_len, blas_len sense_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, double* a, const blas_int* lda, double* wr, double* wi, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, double* scale, double* abnrm, double* rconde, double* rcondv, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info, blas_len balanc_len, blas_len jobvl_len, blas_len jobvr_len, blas_len sense_len) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (complex; advanced form) + void arma_fortran(arma_cgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* w, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, float* scale, float* abnrm, float* rconde, float* rcondv, blas_cxf* work, const blas_int* lwork, float* rwork, const blas_int* info, blas_len balanc_len, blas_len jobvl_len, blas_len jobvr_len, blas_len sense_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* w, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, double* scale, double* abnrm, double* rconde, double* rcondv, blas_cxd* work, const blas_int* lwork, double* rwork, const blas_int* info, blas_len balanc_len, blas_len jobvl_len, blas_len jobvr_len, blas_len sense_len) ARMA_NOEXCEPT; + + // eigen decomposition of symmetric real matrices + void arma_fortran(arma_ssyev)(const char* jobz, const char* uplo, const blas_int* n, float* a, const blas_int* lda, float* w, float* work, const blas_int* lwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dsyev)(const char* jobz, const char* uplo, const blas_int* n, double* a, const blas_int* lda, double* w, double* work, const blas_int* lwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // eigen decomposition of hermitian matrices (complex) + void arma_fortran(arma_cheev)(const char* jobz, const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, float* w, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zheev)(const char* jobz, const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, double* w, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // eigen decomposition of symmetric real matrices by divide and conquer + void arma_fortran(arma_ssyevd)(const char* jobz, const char* uplo, const blas_int* n, float* a, const blas_int* lda, float* w, float* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dsyevd)(const char* jobz, const char* uplo, const blas_int* n, double* a, const blas_int* lda, double* w, double* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // eigen decomposition of hermitian matrices (complex) by divide and conquer + void arma_fortran(arma_cheevd)(const char* jobz, const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, float* w, blas_cxf* work, const blas_int* lwork, float* rwork, const blas_int* lrwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zheevd)(const char* jobz, const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, double* w, blas_cxd* work, const blas_int* lwork, double* rwork, const blas_int* lrwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len jobz_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // eigen decomposition of general real matrix pair + void arma_fortran(arma_sggev)(const char* jobvl, const char* jobvr, const blas_int* n, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* alphar, float* alphai, float* beta, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, float* work, const blas_int* lwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dggev)(const char* jobvl, const char* jobvr, const blas_int* n, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* alphar, double* alphai, double* beta, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, double* work, const blas_int* lwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + + // eigen decomposition of general complex matrix pair + void arma_fortran(arma_cggev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_cxf* alpha, blas_cxf* beta, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zggev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_cxd* alpha, blas_cxd* beta, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info, blas_len jobvl_len, blas_len jobvr_len) ARMA_NOEXCEPT; + + // Cholesky decomposition + void arma_fortran(arma_spotrf)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotrf)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotrf)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotrf)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // solve system of linear equations using pre-computed Cholesky decomposition + void arma_fortran(arma_spotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // Cholesky decomposition (band matrices) + void arma_fortran(arma_spbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, float* ab, const blas_int* ldab, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, double* ab, const blas_int* ldab, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, blas_cxf* ab, const blas_int* ldab, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, blas_cxd* ab, const blas_int* ldab, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // matrix inversion (using pre-computed Cholesky decomposition) + void arma_fortran(arma_spotri)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotri)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotri)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotri)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // QR decomposition + void arma_fortran(arma_sgeqrf)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeqrf)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgeqrf)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* tau, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeqrf)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* tau, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // QR decomposition with pivoting (real matrices) + void arma_fortran(arma_sgeqp3)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, blas_int* jpvt, float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeqp3)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, blas_int* jpvt, double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // QR decomposition with pivoting (complex matrices) + void arma_fortran(arma_cgeqp3)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* jpvt, blas_cxf* tau, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeqp3)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* jpvt, blas_cxd* tau, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // Q matrix calculation from QR decomposition (real matrices) + void arma_fortran(arma_sorgqr)(const blas_int* m, const blas_int* n, const blas_int* k, float* a, const blas_int* lda, const float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dorgqr)(const blas_int* m, const blas_int* n, const blas_int* k, double* a, const blas_int* lda, const double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // Q matrix calculation from QR decomposition (complex matrices) + void arma_fortran(arma_cungqr)(const blas_int* m, const blas_int* n, const blas_int* k, blas_cxf* a, const blas_int* lda, const blas_cxf* tau, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zungqr)(const blas_int* m, const blas_int* n, const blas_int* k, blas_cxd* a, const blas_int* lda, const blas_cxd* tau, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // SVD (real matrices) + void arma_fortran(arma_sgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* s, float* u, const blas_int* ldu, float* vt, const blas_int* ldvt, float* work, const blas_int* lwork, blas_int* info, blas_len jobu_len, blas_len jobvt_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* s, double* u, const blas_int* ldu, double* vt, const blas_int* ldvt, double* work, const blas_int* lwork, blas_int* info, blas_len jobu_len, blas_len jobvt_len) ARMA_NOEXCEPT; + + // SVD (complex matrices) + void arma_fortran(arma_cgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, float* s, blas_cxf* u, const blas_int* ldu, blas_cxf* vt, const blas_int* ldvt, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info, blas_len jobu_len, blas_len jobvt_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, double* s, blas_cxd* u, const blas_int* ldu, blas_cxd* vt, const blas_int* ldvt, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info, blas_len jobu_len, blas_len jobvt_len) ARMA_NOEXCEPT; + + // SVD (real matrices) by divide and conquer + void arma_fortran(arma_sgesdd)(const char* jobz, const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* s, float* u, const blas_int* ldu, float* vt, const blas_int* ldvt, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info, blas_len jobz_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesdd)(const char* jobz, const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* s, double* u, const blas_int* ldu, double* vt, const blas_int* ldvt, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info, blas_len jobz_len) ARMA_NOEXCEPT; + + // SVD (complex matrices) by divide and conquer + void arma_fortran(arma_cgesdd)(const char* jobz, const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, float* s, blas_cxf* u, const blas_int* ldu, blas_cxf* vt, const blas_int* ldvt, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* iwork, blas_int* info, blas_len jobz_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesdd)(const char* jobz, const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, double* s, blas_cxd* u, const blas_int* ldu, blas_cxd* vt, const blas_int* ldvt, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* iwork, blas_int* info, blas_len jobz_len) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix) + void arma_fortran(arma_sgesv)(const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesv)(const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgesv)(const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesv)(const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix, advanced form, real matrices) + void arma_fortran(arma_sgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* af, const blas_int* ldaf, blas_int* ipiv, char* equed, float* r, float* c, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* af, const blas_int* ldaf, blas_int* ipiv, char* equed, double* r, double* c, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix, advanced form, complex matrices) + void arma_fortran(arma_cgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* af, const blas_int* ldaf, blas_int* ipiv, char* equed, float* r, float* c, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* af, const blas_int* ldaf, blas_int* ipiv, char* equed, double* r, double* c, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve system of linear equations (symmetric positive definite matrix) + void arma_fortran(arma_sposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // solve system of linear equations (symmetric positive definite matrix, advanced form, real matrices) + void arma_fortran(arma_sposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* af, const blas_int* ldaf, char* equed, float* s, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len uplo_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* af, const blas_int* ldaf, char* equed, double* s, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len uplo_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve system of linear equations (hermitian positive definite matrix, advanced form, complex matrices) + void arma_fortran(arma_cposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* af, const blas_int* ldaf, char* equed, float* s, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info, blas_len fact_len, blas_len uplo_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* af, const blas_int* ldaf, char* equed, double* s, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info, blas_len fact_len, blas_len uplo_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve over/under-determined system of linear equations + void arma_fortran(arma_sgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* work, const blas_int* lwork, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* work, const blas_int* lwork, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_cxf* work, const blas_int* lwork, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_cxd* work, const blas_int* lwork, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + + // approximately solve system of linear equations using svd (real) + void arma_fortran(arma_sgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* S, const float* rcond, blas_int* rank, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* S, const double* rcond, blas_int* rank, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // approximately solve system of linear equations using svd (complex) + void arma_fortran(arma_cgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, float* S, const float* rcond, blas_int* rank, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, double* S, const double* rcond, blas_int* rank, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (triangular matrix) + void arma_fortran(arma_strtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info, blas_len uplo_len, blas_len trans_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info, blas_len uplo_len, blas_len trans_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info, blas_len uplo_len, blas_len trans_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info, blas_len uplo_len, blas_len trans_len, blas_len diag_len) ARMA_NOEXCEPT; + + // LU factorisation (general band matrix) + void arma_fortran(arma_sgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, float* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, double* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, blas_cxf* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, blas_cxd* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations using pre-computed LU decomposition (general band matrix) + void arma_fortran(arma_sgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const float* ab, const blas_int* ldab, const blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const double* ab, const blas_int* ldab, const blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const blas_cxf* ab, const blas_int* ldab, const blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const blas_cxd* ab, const blas_int* ldab, const blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info, blas_len trans_len) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix) + void arma_fortran(arma_sgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, float* ab, const blas_int* ldab, blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, double* ab, const blas_int* ldab, blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxf* ab, const blas_int* ldab, blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxd* ab, const blas_int* ldab, blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix, advanced form, real matrices) + void arma_fortran(arma_sgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, float* ab, const blas_int* ldab, float* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, float* r, float* c, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, double* ab, const blas_int* ldab, double* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, double* r, double* c, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix, advanced form, complex matrices) + void arma_fortran(arma_cgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxf* ab, const blas_int* ldab, blas_cxf* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, float* r, float* c, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxd* ab, const blas_int* ldab, blas_cxd* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, double* r, double* c, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info, blas_len fact_len, blas_len trans_len, blas_len equed_len) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix) + void arma_fortran(arma_sgtsv)(const blas_int* n, const blas_int* nrhs, float* dl, float* d, float* du, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgtsv)(const blas_int* n, const blas_int* nrhs, double* dl, double* d, double* du, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgtsv)(const blas_int* n, const blas_int* nrhs, blas_cxf* dl, blas_cxf* d, blas_cxf* du, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgtsv)(const blas_int* n, const blas_int* nrhs, blas_cxd* dl, blas_cxd* d, blas_cxd* du, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix, advanced form, real matrices) + void arma_fortran(arma_sgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const float* dl, const float* d, const float* du, float* dlf, float* df, float* duf, float* du2, blas_int* ipiv, const float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const double* dl, const double* d, const double* du, double* dlf, double* df, double* duf, double* du2, blas_int* ipiv, const double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info, blas_len fact_len, blas_len trans_len) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix, advanced form, complex matrices) + void arma_fortran(arma_cgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxf* dl, const blas_cxf* d, const blas_cxf* du, blas_cxf* dlf, blas_cxf* df, blas_cxf* duf, blas_cxf* du2, blas_int* ipiv, const blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info, blas_len fact_len, blas_len trans_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxd* dl, const blas_cxd* d, const blas_cxd* du, blas_cxd* dlf, blas_cxd* df, blas_cxd* duf, blas_cxd* du2, blas_int* ipiv, const blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info, blas_len fact_len, blas_len trans_len) ARMA_NOEXCEPT; + + // Schur decomposition (real matrices) + void arma_fortran(arma_sgees)(const char* jobvs, const char* sort, fn_select_s2 select, const blas_int* n, float* a, const blas_int* lda, blas_int* sdim, float* wr, float* wi, float* vs, const blas_int* ldvs, float* work, const blas_int* lwork, blas_int* bwork, blas_int* info, blas_len jobvs_len, blas_len sort_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgees)(const char* jobvs, const char* sort, fn_select_d2 select, const blas_int* n, double* a, const blas_int* lda, blas_int* sdim, double* wr, double* wi, double* vs, const blas_int* ldvs, double* work, const blas_int* lwork, blas_int* bwork, blas_int* info, blas_len jobvs_len, blas_len sort_len) ARMA_NOEXCEPT; + + // Schur decomposition (complex matrices) + void arma_fortran(arma_cgees)(const char* jobvs, const char* sort, fn_select_c1 select, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* sdim, blas_cxf* w, blas_cxf* vs, const blas_int* ldvs, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* bwork, blas_int* info, blas_len jobvs_len, blas_len sort_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgees)(const char* jobvs, const char* sort, fn_select_z1 select, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* sdim, blas_cxd* w, blas_cxd* vs, const blas_int* ldvs, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* bwork, blas_int* info, blas_len jobvs_len, blas_len sort_len) ARMA_NOEXCEPT; + + // solve a Sylvester equation ax + xb = c, with a and b assumed to be in Schur form + void arma_fortran(arma_strsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const float* a, const blas_int* lda, const float* b, const blas_int* ldb, float* c, const blas_int* ldc, float* scale, blas_int* info, blas_len transa_len, blas_len transb_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const double* a, const blas_int* lda, const double* b, const blas_int* ldb, double* c, const blas_int* ldc, double* scale, blas_int* info, blas_len transa_len, blas_len transb_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const blas_cxf* a, const blas_int* lda, const blas_cxf* b, const blas_int* ldb, blas_cxf* c, const blas_int* ldc, float* scale, blas_int* info, blas_len transa_len, blas_len transb_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const blas_cxd* a, const blas_int* lda, const blas_cxd* b, const blas_int* ldb, blas_cxd* c, const blas_int* ldc, double* scale, blas_int* info, blas_len transa_len, blas_len transb_len) ARMA_NOEXCEPT; + + // QZ decomposition (real matrices) + void arma_fortran(arma_sgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_s3 selctg, const blas_int* n, float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* sdim, float* alphar, float* alphai, float* beta, float* vsl, const blas_int* ldvsl, float* vsr, const blas_int* ldvsr, float* work, const blas_int* lwork, blas_int* bwork, blas_int* info, blas_len jobvsl_len, blas_len jobvsr_len, blas_len sort_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_d3 selctg, const blas_int* n, double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* sdim, double* alphar, double* alphai, double* beta, double* vsl, const blas_int* ldvsl, double* vsr, const blas_int* ldvsr, double* work, const blas_int* lwork, blas_int* bwork, blas_int* info, blas_len jobvsl_len, blas_len jobvsr_len, blas_len sort_len) ARMA_NOEXCEPT; + + // QZ decomposition (complex matrices) + void arma_fortran(arma_cgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_c2 selctg, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* sdim, blas_cxf* alpha, blas_cxf* beta, blas_cxf* vsl, const blas_int* ldvsl, blas_cxf* vsr, const blas_int* ldvsr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* bwork, blas_int* info, blas_len jobvsl_len, blas_len jobvsr_len, blas_len sort_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_z2 selctg, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* sdim, blas_cxd* alpha, blas_cxd* beta, blas_cxd* vsl, const blas_int* ldvsl, blas_cxd* vsr, const blas_int* ldvsr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* bwork, blas_int* info, blas_len jobvsl_len, blas_len jobvsr_len, blas_len sort_len) ARMA_NOEXCEPT; + + // 1-norm (general matrix) + float arma_fortran(arma_slange)(const char* norm, const blas_int* m, const blas_int* n, const float* a, const blas_int* lda, float* work, blas_len norm_len) ARMA_NOEXCEPT; + double arma_fortran(arma_dlange)(const char* norm, const blas_int* m, const blas_int* n, const double* a, const blas_int* lda, double* work, blas_len norm_len) ARMA_NOEXCEPT; + float arma_fortran(arma_clange)(const char* norm, const blas_int* m, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work, blas_len norm_len) ARMA_NOEXCEPT; + double arma_fortran(arma_zlange)(const char* norm, const blas_int* m, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work, blas_len norm_len) ARMA_NOEXCEPT; + + // 1-norm (real symmetric matrix) + float arma_fortran(arma_slansy)(const char* norm, const char* uplo, const blas_int* n, const float* a, const blas_int* lda, float* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + double arma_fortran(arma_dlansy)(const char* norm, const char* uplo, const blas_int* n, const double* a, const blas_int* lda, double* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + float arma_fortran(arma_clansy)(const char* norm, const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + double arma_fortran(arma_zlansy)(const char* norm, const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // 1-norm (complex hermitian matrix) + float arma_fortran(arma_clanhe)(const char* norm, const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + double arma_fortran(arma_zlanhe)(const char* norm, const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work, blas_len norm_len, blas_len uplo_len) ARMA_NOEXCEPT; + + // 1-norm (band matrix) + float arma_fortran(arma_slangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const float* ab, const blas_int* ldab, float* work, blas_len norm_len) ARMA_NOEXCEPT; + double arma_fortran(arma_dlangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const double* ab, const blas_int* ldab, double* work, blas_len norm_len) ARMA_NOEXCEPT; + float arma_fortran(arma_clangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxf* ab, const blas_int* ldab, float* work, blas_len norm_len) ARMA_NOEXCEPT; + double arma_fortran(arma_zlangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxd* ab, const blas_int* ldab, double* work, blas_len norm_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, generic matrix) + void arma_fortran(arma_sgecon)(const char* norm, const blas_int* n, const float* a, const blas_int* lda, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgecon)(const char* norm, const blas_int* n, const double* a, const blas_int* lda, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, generic matrix) + void arma_fortran(arma_cgecon)(const char* norm, const blas_int* n, const blas_cxf* a, const blas_int* lda, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgecon)(const char* norm, const blas_int* n, const blas_cxd* a, const blas_int* lda, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, symmetric positive definite matrix) + void arma_fortran(arma_spocon)(const char* uplo, const blas_int* n, const float* a, const blas_int* lda, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpocon)(const char* uplo, const blas_int* n, const double* a, const blas_int* lda, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, hermitian positive definite matrix) + void arma_fortran(arma_cpocon)(const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpocon)(const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, triangular matrix) + void arma_fortran(arma_strcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const float* a, const blas_int* lda, float* rcond, float* work, blas_int* iwork, blas_int* info, blas_len norm_len, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const double* a, const blas_int* lda, double* rcond, double* work, blas_int* iwork, blas_int* info, blas_len norm_len, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, triangular matrix) + void arma_fortran(arma_ctrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* rcond, blas_cxf* work, float* rwork, blas_int* info, blas_len norm_len, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* rcond, blas_cxd* work, double* rwork, blas_int* info, blas_len norm_len, blas_len uplo_len, blas_len diag_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, band matrix) + void arma_fortran(arma_sgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const float* ab, const blas_int* ldab, const blas_int* ipiv, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const double* ab, const blas_int* ldab, const blas_int* ipiv, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, band matrix) + void arma_fortran(arma_cgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxf* ab, const blas_int* ldab, const blas_int* ipiv, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxd* ab, const blas_int* ldab, const blas_int* ipiv, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info, blas_len norm_len) ARMA_NOEXCEPT; + + // obtain parameters according to the local configuration of lapack + blas_int arma_fortran(arma_ilaenv)(const blas_int* ispec, const char* name, const char* opts, const blas_int* n1, const blas_int* n2, const blas_int* n3, const blas_int* n4, blas_len name_len, blas_len opts_len) ARMA_NOEXCEPT; + + // calculate eigenvalues of an upper Hessenberg matrix + void arma_fortran(arma_slahqr)(const blas_int* wantt, const blas_int* wantz, const blas_int* n, const blas_int* ilo, const blas_int* ihi, float* h, const blas_int* ldh, float* wr, float* wi, const blas_int* iloz, const blas_int* ihiz, float* z, const blas_int* ldz, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dlahqr)(const blas_int* wantt, const blas_int* wantz, const blas_int* n, const blas_int* ilo, const blas_int* ihi, double* h, const blas_int* ldh, double* wr, double* wi, const blas_int* iloz, const blas_int* ihiz, double* z, const blas_int* ldz, blas_int* info) ARMA_NOEXCEPT; + + // calculate eigenvalues of a symmetric tridiagonal matrix + void arma_fortran(arma_sstedc)(const char* compz, const blas_int* n, float* d, float* e, float* z, const blas_int* ldz, float* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len compz_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dstedc)(const char* compz, const blas_int* n, double* d, double* e, double* z, const blas_int* ldz, double* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info, blas_len compz_len) ARMA_NOEXCEPT; + + // calculate eigenvectors of a Schur form matrix + void arma_fortran(arma_strevc)(const char* side, const char* howmny, blas_int* select, const blas_int* n, const float* t, const blas_int* ldt, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, const blas_int* mm, blas_int* m, float* work, blas_int* info, blas_len side_len, blas_len howmny_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrevc)(const char* side, const char* howmny, blas_int* select, const blas_int* n, const double* t, const blas_int* ldt, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, const blas_int* mm, blas_int* m, double* work, blas_int* info, blas_len side_len, blas_len howmny_len) ARMA_NOEXCEPT; + + // hessenberg decomposition + void arma_fortran(arma_sgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, float* a, const blas_int* lda, float* tao, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, double* a, const blas_int* lda, double* tao, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, blas_cxf* a, const blas_int* lda, blas_cxf* tao, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, blas_cxd* a, const blas_int* lda, blas_cxd* tao, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // pivoted cholesky + void arma_fortran(arma_spstrf)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* piv, blas_int* rank, const float* tol, float* work, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_dpstrf)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* piv, blas_int* rank, const double* tol, double* work, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_cpstrf)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* piv, blas_int* rank, const float* tol, float* work, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + void arma_fortran(arma_zpstrf)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* piv, blas_int* rank, const double* tol, double* work, blas_int* info, blas_len uplo_len) ARMA_NOEXCEPT; + +#else + + // prototypes without hidden arguments + + // LU decomposition + void arma_fortran(arma_sgetrf)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetrf)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetrf)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetrf)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations using pre-computed LU decomposition + void arma_fortran(arma_sgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, const blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, const blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, const blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetrs)(const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, const blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // matrix inversion (using pre-computed LU decomposition) + void arma_fortran(arma_sgetri)(const blas_int* n, float* a, const blas_int* lda, const blas_int* ipiv, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgetri)(const blas_int* n, double* a, const blas_int* lda, const blas_int* ipiv, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgetri)(const blas_int* n, blas_cxf* a, const blas_int* lda, const blas_int* ipiv, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgetri)(const blas_int* n, blas_cxd* a, const blas_int* lda, const blas_int* ipiv, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // matrix inversion (triangular matrices) + void arma_fortran(arma_strtri)(const char* uplo, const char* diag, const blas_int* n, float* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrtri)(const char* uplo, const char* diag, const blas_int* n, double* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrtri)(const char* uplo, const char* diag, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrtri)(const char* uplo, const char* diag, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (real) + void arma_fortran(arma_sgeev)(const char* jobvl, const char* jobvr, const blas_int* n, float* a, const blas_int* lda, float* wr, float* wi, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeev)(const char* jobvl, const char* jobvr, const blas_int* n, double* a, const blas_int* lda, double* wr, double* wi, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (complex) + void arma_fortran(arma_cgeev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* w, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* w, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (real; advanced form) + void arma_fortran(arma_sgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, float* a, const blas_int* lda, float* wr, float* wi, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, float* scale, float* abnrm, float* rconde, float* rcondv, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, double* a, const blas_int* lda, double* wr, double* wi, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, double* scale, double* abnrm, double* rconde, double* rcondv, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general matrix (complex; advanced form) + void arma_fortran(arma_cgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* w, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, float* scale, float* abnrm, float* rconde, float* rcondv, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeevx)(const char* balanc, const char* jobvl, const char* jobvr, const char* sense, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* w, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_int* ilo, blas_int* ihi, double* scale, double* abnrm, double* rconde, double* rcondv, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of symmetric real matrices + void arma_fortran(arma_ssyev)(const char* jobz, const char* uplo, const blas_int* n, float* a, const blas_int* lda, float* w, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dsyev)(const char* jobz, const char* uplo, const blas_int* n, double* a, const blas_int* lda, double* w, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of hermitian matrices (complex) + void arma_fortran(arma_cheev)(const char* jobz, const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, float* w, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zheev)(const char* jobz, const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, double* w, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of symmetric real matrices by divide and conquer + void arma_fortran(arma_ssyevd)(const char* jobz, const char* uplo, const blas_int* n, float* a, const blas_int* lda, float* w, float* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dsyevd)(const char* jobz, const char* uplo, const blas_int* n, double* a, const blas_int* lda, double* w, double* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of hermitian matrices (complex) by divide and conquer + void arma_fortran(arma_cheevd)(const char* jobz, const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, float* w, blas_cxf* work, const blas_int* lwork, float* rwork, const blas_int* lrwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zheevd)(const char* jobz, const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, double* w, blas_cxd* work, const blas_int* lwork, double* rwork, const blas_int* lrwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general real matrix pair + void arma_fortran(arma_sggev)(const char* jobvl, const char* jobvr, const blas_int* n, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* alphar, float* alphai, float* beta, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dggev)(const char* jobvl, const char* jobvr, const blas_int* n, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* alphar, double* alphai, double* beta, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // eigen decomposition of general complex matrix pair + void arma_fortran(arma_cggev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_cxf* alpha, blas_cxf* beta, blas_cxf* vl, const blas_int* ldvl, blas_cxf* vr, const blas_int* ldvr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zggev)(const char* jobvl, const char* jobvr, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_cxd* alpha, blas_cxd* beta, blas_cxd* vl, const blas_int* ldvl, blas_cxd* vr, const blas_int* ldvr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // Cholesky decomposition + void arma_fortran(arma_spotrf)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotrf)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotrf)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotrf)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations with pre-computed Cholesky decomposition + void arma_fortran(arma_spotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotrs)(const char* uplo, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // Cholesky decomposition (band matrices) + void arma_fortran(arma_spbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, float* ab, const blas_int* ldab, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, double* ab, const blas_int* ldab, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, blas_cxf* ab, const blas_int* ldab, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpbtrf)(const char* uplo, const blas_int* n, const blas_int* kd, blas_cxd* ab, const blas_int* ldab, blas_int* info) ARMA_NOEXCEPT; + + // matrix inversion (using pre-computed Cholesky decomposition) + void arma_fortran(arma_spotri)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpotri)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cpotri)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpotri)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* info) ARMA_NOEXCEPT; + + // QR decomposition + void arma_fortran(arma_sgeqrf)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeqrf)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgeqrf)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* tau, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeqrf)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* tau, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // QR decomposition with pivoting (real matrices) + void arma_fortran(arma_sgeqp3)(const blas_int* m, const blas_int* n, float* a, const blas_int* lda, blas_int* jpvt, float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgeqp3)(const blas_int* m, const blas_int* n, double* a, const blas_int* lda, blas_int* jpvt, double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // QR decomposition with pivoting (complex matrices) + void arma_fortran(arma_cgeqp3)(const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* jpvt, blas_cxf* tau, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgeqp3)(const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* jpvt, blas_cxd* tau, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // Q matrix calculation from QR decomposition (real matrices) + void arma_fortran(arma_sorgqr)(const blas_int* m, const blas_int* n, const blas_int* k, float* a, const blas_int* lda, const float* tau, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dorgqr)(const blas_int* m, const blas_int* n, const blas_int* k, double* a, const blas_int* lda, const double* tau, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // Q matrix calculation from QR decomposition (complex matrices) + void arma_fortran(arma_cungqr)(const blas_int* m, const blas_int* n, const blas_int* k, blas_cxf* a, const blas_int* lda, const blas_cxf* tau, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zungqr)(const blas_int* m, const blas_int* n, const blas_int* k, blas_cxd* a, const blas_int* lda, const blas_cxd* tau, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // SVD (real matrices) + void arma_fortran(arma_sgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* s, float* u, const blas_int* ldu, float* vt, const blas_int* ldvt, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* s, double* u, const blas_int* ldu, double* vt, const blas_int* ldvt, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // SVD (complex matrices) + void arma_fortran(arma_cgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, float* s, blas_cxf* u, const blas_int* ldu, blas_cxf* vt, const blas_int* ldvt, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesvd)(const char* jobu, const char* jobvt, const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, double* s, blas_cxd* u, const blas_int* ldu, blas_cxd* vt, const blas_int* ldvt, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // SVD (real matrices) by divide and conquer + void arma_fortran(arma_sgesdd)(const char* jobz, const blas_int* m, const blas_int* n, float* a, const blas_int* lda, float* s, float* u, const blas_int* ldu, float* vt, const blas_int* ldvt, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesdd)(const char* jobz, const blas_int* m, const blas_int* n, double* a, const blas_int* lda, double* s, double* u, const blas_int* ldu, double* vt, const blas_int* ldvt, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // SVD (complex matrices) by divide and conquer + void arma_fortran(arma_cgesdd)(const char* jobz, const blas_int* m, const blas_int* n, blas_cxf* a, const blas_int* lda, float* s, blas_cxf* u, const blas_int* ldu, blas_cxf* vt, const blas_int* ldvt, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesdd)(const char* jobz, const blas_int* m, const blas_int* n, blas_cxd* a, const blas_int* lda, double* s, blas_cxd* u, const blas_int* ldu, blas_cxd* vt, const blas_int* ldvt, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix) + void arma_fortran(arma_sgesv)(const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesv)(const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgesv)(const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesv)(const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix, advanced form, real matrices) + void arma_fortran(arma_sgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* af, const blas_int* ldaf, blas_int* ipiv, char* equed, float* r, float* c, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* af, const blas_int* ldaf, blas_int* ipiv, char* equed, double* r, double* c, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general square matrix, advanced form, complex matrices) + void arma_fortran(arma_cgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* af, const blas_int* ldaf, blas_int* ipiv, char* equed, float* r, float* c, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgesvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* af, const blas_int* ldaf, blas_int* ipiv, char* equed, double* r, double* c, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (symmetric positive definite matrix) + void arma_fortran(arma_sposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zposv)(const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (symmetric positive definite matrix, advanced form, real matrices) + void arma_fortran(arma_sposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* af, const blas_int* ldaf, char* equed, float* s, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* af, const blas_int* ldaf, char* equed, double* s, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (hermitian positive definite matrix, advanced form, complex matrices) + void arma_fortran(arma_cposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* af, const blas_int* ldaf, char* equed, float* s, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zposvx)(const char* fact, const char* uplo, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* af, const blas_int* ldaf, char* equed, double* s, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // solve over/under-determined system of linear equations + void arma_fortran(arma_sgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgels)(const char* trans, const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // approximately solve system of linear equations using svd (real) + void arma_fortran(arma_sgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, float* a, const blas_int* lda, float* b, const blas_int* ldb, float* S, const float* rcond, blas_int* rank, float* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, double* a, const blas_int* lda, double* b, const blas_int* ldb, double* S, const double* rcond, blas_int* rank, double* work, const blas_int* lwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + + // approximately solve system of linear equations using svd (complex) + void arma_fortran(arma_cgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, float* S, const float* rcond, blas_int* rank, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgelsd)(const blas_int* m, const blas_int* n, const blas_int* nrhs, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, double* S, const double* rcond, blas_int* rank, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (triangular matrix) + void arma_fortran(arma_strtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrtrs)(const char* uplo, const char* trans, const char* diag, const blas_int* n, const blas_int* nrhs, const blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // LU factorisation (general band matrix) + void arma_fortran(arma_sgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, float* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, double* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, blas_cxf* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbtrf)(const blas_int* m, const blas_int* n, const blas_int* kl, const blas_int* ku, blas_cxd* ab, const blas_int* ldab, blas_int* ipiv, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations using pre-computed LU decomposition (general band matrix) + void arma_fortran(arma_sgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const float* ab, const blas_int* ldab, const blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const double* ab, const blas_int* ldab, const blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const blas_cxf* ab, const blas_int* ldab, const blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbtrs)(const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, const blas_cxd* ab, const blas_int* ldab, const blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix) + void arma_fortran(arma_sgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, float* ab, const blas_int* ldab, blas_int* ipiv, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, double* ab, const blas_int* ldab, blas_int* ipiv, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxf* ab, const blas_int* ldab, blas_int* ipiv, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbsv)(const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxd* ab, const blas_int* ldab, blas_int* ipiv, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix, advanced form, real matrices) + void arma_fortran(arma_sgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, float* ab, const blas_int* ldab, float* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, float* r, float* c, float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, double* ab, const blas_int* ldab, double* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, double* r, double* c, double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (general band matrix, advanced form, complex matrices) + void arma_fortran(arma_cgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxf* ab, const blas_int* ldab, blas_cxf* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, float* r, float* c, blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_int* nrhs, blas_cxd* ab, const blas_int* ldab, blas_cxd* afb, const blas_int* ldafb, blas_int* ipiv, char* equed, double* r, double* c, blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix) + void arma_fortran(arma_sgtsv)(const blas_int* n, const blas_int* nrhs, float* dl, float* d, float* du, float* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgtsv)(const blas_int* n, const blas_int* nrhs, double* dl, double* d, double* du, double* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgtsv)(const blas_int* n, const blas_int* nrhs, blas_cxf* dl, blas_cxf* d, blas_cxf* du, blas_cxf* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgtsv)(const blas_int* n, const blas_int* nrhs, blas_cxd* dl, blas_cxd* d, blas_cxd* du, blas_cxd* b, const blas_int* ldb, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix, advanced form, real matrices) + void arma_fortran(arma_sgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const float* dl, const float* d, const float* du, float* dlf, float* df, float* duf, float* du2, blas_int* ipiv, const float* b, const blas_int* ldb, float* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const double* dl, const double* d, const double* du, double* dlf, double* df, double* duf, double* du2, blas_int* ipiv, const double* b, const blas_int* ldb, double* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // solve system of linear equations (tridiagonal band matrix, advanced form, complex matrices) + void arma_fortran(arma_cgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxf* dl, const blas_cxf* d, const blas_cxf* du, blas_cxf* dlf, blas_cxf* df, blas_cxf* duf, blas_cxf* du2, blas_int* ipiv, const blas_cxf* b, const blas_int* ldb, blas_cxf* x, const blas_int* ldx, float* rcond, float* ferr, float* berr, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgtsvx)(const char* fact, const char* trans, const blas_int* n, const blas_int* nrhs, const blas_cxd* dl, const blas_cxd* d, const blas_cxd* du, blas_cxd* dlf, blas_cxd* df, blas_cxd* duf, blas_cxd* du2, blas_int* ipiv, const blas_cxd* b, const blas_int* ldb, blas_cxd* x, const blas_int* ldx, double* rcond, double* ferr, double* berr, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // Schur decomposition (real matrices) + void arma_fortran(arma_sgees)(const char* jobvs, const char* sort, fn_select_s2 select, const blas_int* n, float* a, const blas_int* lda, blas_int* sdim, float* wr, float* wi, float* vs, const blas_int* ldvs, float* work, const blas_int* lwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgees)(const char* jobvs, const char* sort, fn_select_d2 select, const blas_int* n, double* a, const blas_int* lda, blas_int* sdim, double* wr, double* wi, double* vs, const blas_int* ldvs, double* work, const blas_int* lwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + + // Schur decomposition (complex matrices) + void arma_fortran(arma_cgees)(const char* jobvs, const char* sort, fn_select_c1 select, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* sdim, blas_cxf* w, blas_cxf* vs, const blas_int* ldvs, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgees)(const char* jobvs, const char* sort, fn_select_z1 select, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* sdim, blas_cxd* w, blas_cxd* vs, const blas_int* ldvs, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + + // solve a Sylvester equation ax + xb = c, with a and b assumed to be in Schur form + void arma_fortran(arma_strsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const float* a, const blas_int* lda, const float* b, const blas_int* ldb, float* c, const blas_int* ldc, float* scale, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const double* a, const blas_int* lda, const double* b, const blas_int* ldb, double* c, const blas_int* ldc, double* scale, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ctrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const blas_cxf* a, const blas_int* lda, const blas_cxf* b, const blas_int* ldb, blas_cxf* c, const blas_int* ldc, float* scale, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrsyl)(const char* transa, const char* transb, const blas_int* isgn, const blas_int* m, const blas_int* n, const blas_cxd* a, const blas_int* lda, const blas_cxd* b, const blas_int* ldb, blas_cxd* c, const blas_int* ldc, double* scale, blas_int* info) ARMA_NOEXCEPT; + + // QZ decomposition (real matrices) + void arma_fortran(arma_sgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_s3 selctg, const blas_int* n, float* a, const blas_int* lda, float* b, const blas_int* ldb, blas_int* sdim, float* alphar, float* alphai, float* beta, float* vsl, const blas_int* ldvsl, float* vsr, const blas_int* ldvsr, float* work, const blas_int* lwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_d3 selctg, const blas_int* n, double* a, const blas_int* lda, double* b, const blas_int* ldb, blas_int* sdim, double* alphar, double* alphai, double* beta, double* vsl, const blas_int* ldvsl, double* vsr, const blas_int* ldvsr, double* work, const blas_int* lwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + + // QZ decomposition (complex matrices) + void arma_fortran(arma_cgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_c2 selctg, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_cxf* b, const blas_int* ldb, blas_int* sdim, blas_cxf* alpha, blas_cxf* beta, blas_cxf* vsl, const blas_int* ldvsl, blas_cxf* vsr, const blas_int* ldvsr, blas_cxf* work, const blas_int* lwork, float* rwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgges)(const char* jobvsl, const char* jobvsr, const char* sort, fn_select_z2 selctg, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_cxd* b, const blas_int* ldb, blas_int* sdim, blas_cxd* alpha, blas_cxd* beta, blas_cxd* vsl, const blas_int* ldvsl, blas_cxd* vsr, const blas_int* ldvsr, blas_cxd* work, const blas_int* lwork, double* rwork, blas_int* bwork, blas_int* info) ARMA_NOEXCEPT; + + // 1-norm (general matrix) + float arma_fortran(arma_slange)(const char* norm, const blas_int* m, const blas_int* n, const float* a, const blas_int* lda, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_dlange)(const char* norm, const blas_int* m, const blas_int* n, const double* a, const blas_int* lda, double* work) ARMA_NOEXCEPT; + float arma_fortran(arma_clange)(const char* norm, const blas_int* m, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_zlange)(const char* norm, const blas_int* m, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work) ARMA_NOEXCEPT; + + // 1-norm (real symmetric matrix) + float arma_fortran(arma_slansy)(const char* norm, const char* uplo, const blas_int* n, const float* a, const blas_int* lda, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_dlansy)(const char* norm, const char* uplo, const blas_int* n, const double* a, const blas_int* lda, double* work) ARMA_NOEXCEPT; + float arma_fortran(arma_clansy)(const char* norm, const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_zlansy)(const char* norm, const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work) ARMA_NOEXCEPT; + + // 1-norm (complex hermitian matrix) + float arma_fortran(arma_clanhe)(const char* norm, const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_zlanhe)(const char* norm, const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* work) ARMA_NOEXCEPT; + + // 1-norm (band matrix) + float arma_fortran(arma_slangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const float* ab, const blas_int* ldab, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_dlangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const double* ab, const blas_int* ldab, double* work) ARMA_NOEXCEPT; + float arma_fortran(arma_clangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxf* ab, const blas_int* ldab, float* work) ARMA_NOEXCEPT; + double arma_fortran(arma_zlangb)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxd* ab, const blas_int* ldab, double* work) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, generic matrix) + void arma_fortran(arma_sgecon)(const char* norm, const blas_int* n, const float* a, const blas_int* lda, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgecon)(const char* norm, const blas_int* n, const double* a, const blas_int* lda, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, generic matrix) + void arma_fortran(arma_cgecon)(const char* norm, const blas_int* n, const blas_cxf* a, const blas_int* lda, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgecon)(const char* norm, const blas_int* n, const blas_cxd* a, const blas_int* lda, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, symmetric positive definite matrix) + void arma_fortran(arma_spocon)(const char* uplo, const blas_int* n, const float* a, const blas_int* lda, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpocon)(const char* uplo, const blas_int* n, const double* a, const blas_int* lda, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, hermitian positive definite matrix) + void arma_fortran(arma_cpocon)(const char* uplo, const blas_int* n, const blas_cxf* a, const blas_int* lda, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpocon)(const char* uplo, const blas_int* n, const blas_cxd* a, const blas_int* lda, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, triangular matrix) + void arma_fortran(arma_strcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const float* a, const blas_int* lda, float* rcond, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const double* a, const blas_int* lda, double* rcond, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, triangular matrix) + void arma_fortran(arma_ctrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const blas_cxf* a, const blas_int* lda, float* rcond, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_ztrcon)(const char* norm, const char* uplo, const char* diag, const blas_int* n, const blas_cxd* a, const blas_int* lda, double* rcond, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (real, band matrix) + void arma_fortran(arma_sgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const float* ab, const blas_int* ldab, const blas_int* ipiv, const float* anorm, float* rcond, float* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const double* ab, const blas_int* ldab, const blas_int* ipiv, const double* anorm, double* rcond, double* work, blas_int* iwork, blas_int* info) ARMA_NOEXCEPT; + + // reciprocal of condition number (complex, band matrix) + void arma_fortran(arma_cgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxf* ab, const blas_int* ldab, const blas_int* ipiv, const float* anorm, float* rcond, blas_cxf* work, float* rwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgbcon)(const char* norm, const blas_int* n, const blas_int* kl, const blas_int* ku, const blas_cxd* ab, const blas_int* ldab, const blas_int* ipiv, const double* anorm, double* rcond, blas_cxd* work, double* rwork, blas_int* info) ARMA_NOEXCEPT; + + // obtain parameters according to the local configuration of lapack + // NOTE: DO NOT USE THIS FORM; kept only for compatibility + // NOTE: this function takes 'name' and 'opts' argumments, which are strings with length != 1; their length needs to be given via "hidden" parameters, which this form lacks + blas_int arma_fortran(arma_ilaenv)(const blas_int* ispec, const char* name, const char* opts, const blas_int* n1, const blas_int* n2, const blas_int* n3, const blas_int* n4) ARMA_NOEXCEPT; + + // calculate eigenvalues of an upper Hessenberg matrix + void arma_fortran(arma_slahqr)(const blas_int* wantt, const blas_int* wantz, const blas_int* n, const blas_int* ilo, const blas_int* ihi, float* h, const blas_int* ldh, float* wr, float* wi, const blas_int* iloz, const blas_int* ihiz, float* z, const blas_int* ldz, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dlahqr)(const blas_int* wantt, const blas_int* wantz, const blas_int* n, const blas_int* ilo, const blas_int* ihi, double* h, const blas_int* ldh, double* wr, double* wi, const blas_int* iloz, const blas_int* ihiz, double* z, const blas_int* ldz, blas_int* info) ARMA_NOEXCEPT; + + // calculate eigenvalues of a symmetric tridiagonal matrix + void arma_fortran(arma_sstedc)(const char* compz, const blas_int* n, float* d, float* e, float* z, const blas_int* ldz, float* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dstedc)(const char* compz, const blas_int* n, double* d, double* e, double* z, const blas_int* ldz, double* work, const blas_int* lwork, blas_int* iwork, const blas_int* liwork, blas_int* info) ARMA_NOEXCEPT; + + // calculate eigenvectors of a Schur form matrix + void arma_fortran(arma_strevc)(const char* side, const char* howmny, blas_int* select, const blas_int* n, const float* t, const blas_int* ldt, float* vl, const blas_int* ldvl, float* vr, const blas_int* ldvr, const blas_int* mm, blas_int* m, float* work, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dtrevc)(const char* side, const char* howmny, blas_int* select, const blas_int* n, const double* t, const blas_int* ldt, double* vl, const blas_int* ldvl, double* vr, const blas_int* ldvr, const blas_int* mm, blas_int* m, double* work, blas_int* info) ARMA_NOEXCEPT; + + // hessenberg decomposition + void arma_fortran(arma_sgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, float* a, const blas_int* lda, float* tao, float* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, double* a, const blas_int* lda, double* tao, double* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, blas_cxf* a, const blas_int* lda, blas_cxf* tao, blas_cxf* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zgehrd)(const blas_int* n, const blas_int* ilo, const blas_int* ihi, blas_cxd* a, const blas_int* lda, blas_cxd* tao, blas_cxd* work, const blas_int* lwork, blas_int* info) ARMA_NOEXCEPT; + + // pivoted cholesky + void arma_fortran(arma_spstrf)(const char* uplo, const blas_int* n, float* a, const blas_int* lda, blas_int* piv, blas_int* rank, const float* tol, float* work, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_dpstrf)(const char* uplo, const blas_int* n, double* a, const blas_int* lda, blas_int* piv, blas_int* rank, const double* tol, double* work, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_cpstrf)(const char* uplo, const blas_int* n, blas_cxf* a, const blas_int* lda, blas_int* piv, blas_int* rank, const float* tol, float* work, blas_int* info) ARMA_NOEXCEPT; + void arma_fortran(arma_zpstrf)(const char* uplo, const blas_int* n, blas_cxd* a, const blas_int* lda, blas_int* piv, blas_int* rank, const double* tol, double* work, blas_int* info) ARMA_NOEXCEPT; + +#endif +} + +#undef ARMA_NOEXCEPT + +#endif -- cgit v1.2.1