def_lapack.hpp

// 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