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/** R : A Computer Language for Statistical Data Analysis* Copyright (C) 2003-2019 The R Core Team.* Copyright (C) 2008-2019 The R Foundation** This header file is free software; you can redistribute it and/or modify* it under the terms of the GNU Lesser General Public License as published by* the Free Software Foundation; either version 2.1 of the License, or* (at your option) any later version.** This file is part of R. R is distributed under the terms of the* GNU General Public License, either Version 2, June 1991 or Version 3,* June 2007. See doc/COPYRIGHTS for details of the copyright status of R.** This program is distributed in the hope that it will be useful,* but WITHOUT ANY WARRANTY; without even the implied warranty of* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the* GNU Lesser General Public License for more details.** You should have received a copy of the GNU Lesser General Public License* along with this program; if not, a copy is available at* https://www.R-project.org/Licenses/*//*C declarations of LAPACK Fortran subroutines included in R.Those used (currently or previously) by C routines in R itself,plus a few used in packages.Part of the API.R packages that use these should have PKG_LIBS in src/Makevars include$(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS)*/#ifndef R_LAPACK_H#define R_LAPACK_H#include <R_ext/RS.h> /* for F77_... */#include <R_ext/Complex.h> /* for Rcomplex */#include <R_ext/BLAS.h> /* defines FCLEN *//*LAPACK function names are [dz]<name>(), where d denotes the realversion of the function, z the complex version. (Onlydouble-precision versions are used in R.)*/#ifdef __cplusplusextern "C" {#endif/* The LAPACK version: might change after installation withexternal LAPACK*/extern void F77_NAME(ilaver)(int *major, int *minor, int *patch);// Never defined by R itself.#ifndef La_extern#define La_extern extern#endif// Utilities for Lapack-using packages :// ------------------------------------/* matrix norms: converting typstr[] to one of {'M', 'O', 'I', 'F'}* or signal error(): */// La_extern char La_norm_type(const char *typstr);/* matrix (reciprocal) condition numbers: convert typstr[] to 'O'(ne) or 'I'(nf)* or signal error(): */// La_extern char La_rcond_type(const char *typstr);/* Selected Double Precision Lapack Routines========*///* Double precision BiDiagonal and DIagonal matrices -> DBD & DDI/* DBDSQR - compute the singular value decomposition (SVD) of a real *//* N-by-N (upper or lower) bidiagonal matrix B */La_extern voidF77_NAME(dbdsqr)(const char* uplo, const int* n, const int* ncvt,const int* nru, const int* ncc, double* d, double* e,double* vt, const int* ldvt, double* u, const int* ldu,double* c, const int* ldc, double* work, int* info FCLEN);/* DDISNA - compute the reciprocal condition numbers for the *//* eigenvectors of a real symmetric or complex Hermitian matrix or *//* for the left or right singular vectors of a general m-by-n *//* matrix */La_extern voidF77_NAME(ddisna)(const char* job, const int* m, const int* n,double* d, double* sep, int* info FCLEN);//* Double precision General Banded matrices -> DGB/* DGBBRD - reduce a real general m-by-n band matrix A to upper *//* bidiagonal form B by an orthogonal transformation */La_extern voidF77_NAME(dgbbrd)(const char* vect, const int* m, const int* n,const int* ncc, const int* kl, const int* ku,double* ab, const int* ldab,double* d, double* e, double* q,const int* ldq, double* pt, const int* ldpt,double* c, const int* ldc,double* work, int* info FCLEN);/* DGBCON - estimate the reciprocal of the condition number of a *//* real general band matrix A, in either the 1-norm or the *//* infinity-norm */La_extern voidF77_NAME(dgbcon)(const char* norm, const int* n, const int* kl,const int* ku, double* ab, const int* ldab,int* ipiv, const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DGBEQU - compute row and column scalings intended to equilibrate *//* an M-by-N band matrix A and reduce its condition number */La_extern voidF77_NAME(dgbequ)(const int* m, const int* n, const int* kl, const int* ku,double* ab, const int* ldab, double* r, double* c,double* rowcnd, double* colcnd, double* amax, int* info);/* DGBRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is banded, and provides *//* error bounds and backward error estimates for the solution */La_extern voidF77_NAME(dgbrfs)(const char* trans, const int* n, const int* kl,const int* ku, const int* nrhs, double* ab,const int* ldab, double* afb, const int* ldafb,int* ipiv, double* b, const int* ldb,double* x, const int* ldx, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DGBSV - compute the solution to a real system of linear *//* equations A * X = B, where A is a band matrix of order N with *//* KL subdiagonals and KU superdiagonals, and X and B are *//* N-by-NRHS matrices */La_extern voidF77_NAME(dgbsv)(const int* n, const int* kl,const int* ku,const int* nrhs, double* ab, const int* ldab,int* ipiv, double* b, const int* ldb, int* info);/* DGBSVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B or A**T * X = B */La_extern voidF77_NAME(dgbsvx)(const int* fact, const char* trans,const int* n, const int* kl,const int* ku,const int* nrhs, double* ab, const int* ldab,double* afb, const int* ldafb, int* ipiv,const char* equed, double* r, double* c,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN FCLEN);/* DGBTF2 - compute an LU factorization of a real m-by-n band *//* matrix A using partial pivoting with row interchanges */La_extern voidF77_NAME(dgbtf2)(const int* m, const int* n, const int* kl,const int* ku,double* ab, const int* ldab, int* ipiv, int* info);/* DGBTRF - compute an LU factorization of a real m-by-n band *//* matrix A using partial pivoting with row interchanges */La_extern voidF77_NAME(dgbtrf)(const int* m, const int* n, const int* kl,const int* ku,double* ab, const int* ldab, int* ipiv, int* info);/* DGBTRS - solve a system of linear equations A * X = B or *//* A' * X = B with a general band matrix A using the LU *//* factorization computed by DGBTRF */La_extern voidF77_NAME(dgbtrs)(const char* trans, const int* n,const int* kl, const int* ku, const int* nrhs,const double* ab, const int* ldab, const int* ipiv,double* b, const int* ldb, int* info FCLEN);//* Double precision GEneral matrices -> DGE/* DGEBAK - form the right or left eigenvectors of a real general *//* matrix by backward transformation on the computed eigenvectors *//* of the balanced matrix output by DGEBAL */La_extern voidF77_NAME(dgebak)(const char* job, const char* side, const int* n,const int* ilo, const int* ihi, double* scale,const int* m, double* v, const int* ldv, int* infoFCLEN FCLEN);/* DGEBAL - balance a general real matrix A */La_extern voidF77_NAME(dgebal)(const char* job, const int* n, double* a, const int* lda,int* ilo, int* ihi, double* scale, int* info FCLEN);/* DGEBD2 - reduce a real general m by n matrix A to upper or *//* lower bidiagonal form B by an orthogonal transformation */La_extern voidF77_NAME(dgebd2)(const int* m, const int* n, double* a, const int* lda,double* d, double* e, double* tauq, double* taup,double* work, int* info);/* DGEBRD - reduce a general real M-by-N matrix A to upper or *//* lower bidiagonal form B by an orthogonal transformation */La_extern voidF77_NAME(dgebrd)(const int* m, const int* n, double* a, const int* lda,double* d, double* e, double* tauq, double* taup,double* work, const int* lwork, int* info);/* DGECON - estimate the reciprocal of the condition number of a *//* general real matrix A, in either the 1-norm or the *//* infinity-norm, using the LU factorization computed by DGETRF */La_extern voidF77_NAME(dgecon)(const char* norm, const int* n,const double* a, const int* lda,const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DGEEQU - compute row and column scalings intended to equilibrate *//* an M-by-N matrix A and reduce its condition number */La_extern voidF77_NAME(dgeequ)(const int* m, const int* n, double* a, const int* lda,double* r, double* c, double* rowcnd, double* colcnd,double* amax, int* info);/* DGEES - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues, the real Schur form T, and, optionally, the matrix *//* of Schur vectors Z */La_extern voidF77_NAME(dgees)(const char* jobvs, const char* sort,int (*select)(const double*, const double*),const int* n, double* a, const int* lda,int* sdim, double* wr, double* wi,double* vs, const int* ldvs,double* work, const int* lwork, int* bwork, int* infoFCLEN FCLEN);/* DGEESX - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues, the real Schur form T, and, optionally, the matrix *//* of Schur vectors Z */La_extern voidF77_NAME(dgeesx)(const char* jobvs, const char* sort,int (*select)(const double*, const double*),const char* sense, const int* n, double* a,const int* lda, int* sdim, double* wr, double* wi,double* vs, const int* ldvs, double* rconde,double* rcondv, double* work, const int* lwork,int* iwork, const int* liwork, int* bwork, int* infoFCLEN FCLEN FCLEN);/* DGEEV - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues and, optionally, the left and/or right eigenvectors */La_extern voidF77_NAME(dgeev)(const char* jobvl, const char* jobvr,const int* n, double* a, const int* lda,double* wr, double* wi, double* vl, const int* ldvl,double* vr, const int* ldvr,double* work, const int* lwork, int* info FCLEN FCLEN);/* DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues and, optionally, the left and/or right eigenvectors */La_extern voidF77_NAME(dgeevx)(const char* balanc, const char* jobvl, const char* jobvr,const char* sense, const int* n, double* a, const int* lda,double* wr, double* wi, double* vl, const int* ldvl,double* vr, const int* ldvr, int* ilo, int* ihi,double* scale, double* abnrm, double* rconde, double* rcondv,double* work, const int* lwork, int* iwork, int* infoFCLEN FCLEN FCLEN FCLEN);/* DGEHD2 - reduce a real general matrix A to upper Hessenberg *//* form H by an orthogonal similarity transformation */La_extern voidF77_NAME(dgehd2)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, double* tau,double* work, int* info);/* DGEHRD - reduce a real general matrix A to upper Hessenberg *//* form H by an orthogonal similarity transformation */La_extern voidF77_NAME(dgehrd)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGELQ2 - compute an LQ factorization of a real m by n matrix A */La_extern voidF77_NAME(dgelq2)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, int* info);/* DGELQF - compute an LQ factorization of a real M-by-N matrix A */La_extern voidF77_NAME(dgelqf)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGELS - solve overdetermined or underdetermined real linear *//* systems involving an M-by-N matrix A, or its transpose, using a *//* QR or LQ factorization of A */La_extern voidF77_NAME(dgels)(const char* trans, const int* m, const int* n,const int* nrhs, double* a, const int* lda,double* b, const int* ldb,double* work, const int* lwork, int* info FCLEN);/* DGELSS - compute the minimum norm solution to a real linear *//* least squares problem */La_extern voidF77_NAME(dgelss)(const int* m, const int* n, const int* nrhs,double* a, const int* lda, double* b, const int* ldb,double* s, double* rcond, int* rank,double* work, const int* lwork, int* info);/* DGELSY - compute the minimum-norm solution to a real linear *//* least squares problem */La_extern voidF77_NAME(dgelsy)(const int* m, const int* n, const int* nrhs,double* a, const int* lda, double* b, const int* ldb,int* jpvt, const double* rcond, int* rank,double* work, const int* lwork, int* info);/* DGEQL2 - compute a QL factorization of a real m by n matrix A */La_extern voidF77_NAME(dgeql2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGEQLF - compute a QL factorization of a real M-by-N matrix A */La_extern voidF77_NAME(dgeqlf)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGEQP3 - compute a QR factorization with column pivoting of a *//* real M-by-N matrix A using level 3 BLAS */La_extern voidF77_NAME(dgeqp3)(const int* m, const int* n, double* a, const int* lda,int* jpvt, double* tau, double* work, const int* lwork,int* info);/* DGEQR2 - compute a QR factorization of a real m by n matrix A */La_extern voidF77_NAME(dgeqr2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGEQRF - compute a QR factorization of a real M-by-N matrix A */La_extern voidF77_NAME(dgeqrf)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, const int* lwork, int* info);/* DGERFS - improve the computed solution to a system of linear *//* equations and provides error bounds and backward error *//* estimates for the solution */La_extern voidF77_NAME(dgerfs)(const char* trans, const int* n, const int* nrhs,double* a, const int* lda, double* af, const int* ldaf,int* ipiv, double* b, const int* ldb,double* x, const int* ldx, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DGERQ2 - compute an RQ factorization of a real m by n matrix A */La_extern voidF77_NAME(dgerq2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGERQF - compute an RQ factorization of a real M-by-N matrix A */La_extern voidF77_NAME(dgerqf)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, const int* lwork, int* info);/* DGESV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dgesv)(const int* n, const int* nrhs, double* a, const int* lda,int* ipiv, double* b, const int* ldb, int* info);/* DGESVD - compute the singular value decomposition (SVD); of a *//* real M-by-N matrix A, optionally computing the left and/or *//* right singular vectors */La_extern voidF77_NAME(dgesvd)(const char* jobu, const char* jobvt, const int* m,const int* n, double* a, const int* lda, double* s,double* u, const int* ldu, double* vt, const int* ldvt,double* work, const int* lwork, int* info FCLEN FCLEN);/* DGESVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B, */La_extern voidF77_NAME(dgesvx)(const char* fact, const char* trans, const int* n,const int* nrhs, double* a, const int* lda,double* af, const int* ldaf, int* ipiv,char* equed, double* r, double* c,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN FCLEN FCLEN);/* DGETF2 - compute an LU factorization of a general m-by-n *//* matrix A using partial pivoting with row interchanges */La_extern voidF77_NAME(dgetf2)(const int* m, const int* n, double* a, const int* lda,int* ipiv, int* info);/* DGETRF - compute an LU factorization of a general M-by-N *//* matrix A using partial pivoting with row interchanges */La_extern voidF77_NAME(dgetrf)(const int* m, const int* n, double* a, const int* lda,int* ipiv, int* info);/* DGETRI - compute the inverse of a matrix using the LU *//* factorization computed by DGETRF */La_extern voidF77_NAME(dgetri)(const int* n, double* a, const int* lda,int* ipiv, double* work, const int* lwork, int* info);/* DGETRS - solve a system of linear equations A * X = B or A' * *//* X = B with a general N-by-N matrix A using the LU factorization *//* computed by DGETRF */La_extern voidF77_NAME(dgetrs)(const char* trans, const int* n, const int* nrhs,const double* a, const int* lda, const int* ipiv,double* b, const int* ldb, int* info FCLEN);//* Double precision General matrices Generalized problems -> DGG/* DGGBAK - form the right or left eigenvectors of a real *//* generalized eigenvalue problem A*x = lambda*B*x, by backward *//* transformation on the computed eigenvectors of the balanced *//* pair of matrices output by DGGBAL */La_extern voidF77_NAME(dggbak)(const char* job, const char* side,const int* n, const int* ilo, const int* ihi,double* lscale, double* rscale, const int* m,double* v, const int* ldv, int* info FCLEN FCLEN);/* DGGBAL - balance a pair of general real matrices (A,B); */La_extern voidF77_NAME(dggbal)(const char* job, const int* n, double* a, const int* lda,double* b, const int* ldb, int* ilo, int* ihi,double* lscale, double* rscale, double* work, int* infoFCLEN);/* DGGES - compute for a pair of N-by-N real nonsymmetric *//* matrices A, B the generalized eigenvalues, the generalized *//* real Schur form (S,T), optionally, the left and/or right matrices *//* of Schur vectors (VSL and VSR)*/La_extern voidF77_NAME(dgges)(const char* jobvsl, const char* jobvsr, const char* sort,int (*delztg)(double*, double*, double*),const int* n, double* a, const int* lda,double* b, const int* ldb, double* alphar,double* alphai, const double* beta,double* vsl, const int* ldvsl,double* vsr, const int* ldvsr,double* work, const int* lwork, int* bwork, int* infoFCLEN FCLEN FCLEN);/* DGGGLM - solve a general Gauss-Markov linear model (GLM) problem */La_extern voidF77_NAME(dggglm)(const int* n, const int* m, const int* p,double* a, const int* lda, double* b, const int* ldb,double* d, double* x, double* y,double* work, const int* lwork, int* info);/* DGGHRD - reduce a pair of real matrices (A,B); to generalized *//* upper Hessenberg form using orthogonal transformations, where A *//* is a general matrix and B is upper triangular */La_extern voidF77_NAME(dgghrd)(const char* compq, const char* compz, const int* n,const int* ilo, const int* ihi, double* a, const int* lda,double* b, const int* ldb, double* q, const int* ldq,double* z, const int* ldz, int* info FCLEN FCLEN);/* DGGLSE - solve the linear equality-constrained least squares *//* (LSE) problem */La_extern voidF77_NAME(dgglse)(const int* m, const int* n, const int* p,double* a, const int* lda,double* b, const int* ldb,double* c, double* d, double* x,double* work, const int* lwork, int* info);/* DGGQRF - compute a generalized QR factorization of an N-by-M *//* matrix A and an N-by-P matrix B */La_extern voidF77_NAME(dggqrf)(const int* n, const int* m, const int* p,double* a, const int* lda, double* taua,double* b, const int* ldb, double* taub,double* work, const int* lwork, int* info);/* DGGRQF - compute a generalized RQ factorization of an M-by-N *//* matrix A and a P-by-N matrix B */La_extern voidF77_NAME(dggrqf)(const int* m, const int* p, const int* n,double* a, const int* lda, double* taua,double* b, const int* ldb, double* taub,double* work, const int* lwork, int* info);//* Double precision General Tridiagonal matrices -> DGT/* DGTCON - estimate the reciprocal of the condition number of a real *//* tridiagonal matrix A using the LU factorization as computed by DGTTRF */La_extern voidF77_NAME(dgtcon)(const char* norm, const int* n, double* dl, double* d,double* du, double* du2, int* ipiv, const double* anorm,double* rcond, double* work, int* iwork, int* infoFCLEN);/* DGTRFS - improve the computed solution to a system of linear equations *//* when the coefficient matrix is tridiagonal, and provides error bounds *//* and backward error estimates for the solution */La_extern voidF77_NAME(dgtrfs)(const char* trans, const int* n, const int* nrhs,double* dl, double* d, double* du, double* dlf,double* df, double* duf, double* du2,int* ipiv, double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DGTSV - solve the equation A*X = B, */La_extern voidF77_NAME(dgtsv)(const int* n, const int* nrhs,double* dl, double* d, double* du,double* b, const int* ldb, int* info);/* DGTSVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B or A**T * X = B, */La_extern voidF77_NAME(dgtsvx)(const int* fact, const char* trans,const int* n, const int* nrhs,double* dl, double* d, double* du,double* dlf, double* df, double* duf,double* du2, int* ipiv,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DGTTRF - compute an LU factorization of a real tridiagonal matrix *//* A using elimination with partial pivoting and row interchanges */La_extern voidF77_NAME(dgttrf)(const int* n, double* dl, double* d,double* du, double* du2, int* ipiv, int* info);/* DGTTRS - solve one of the systems of equations A*X = B or *//* A'*X = B, */La_extern voidF77_NAME(dgttrs)(const char* trans, const int* n, const int* nrhs,double* dl, double* d, double* du, double* du2,int* ipiv, double* b, const int* ldb, int* info FCLEN);//* Double precision Orthogonal matrices -> DOP & DOR/* DOPGTR - generate a real orthogonal matrix Q which is defined *//* as the product of n-1 elementary reflectors H(i); of order n, *//* as returned by DSPTRD using packed storage */La_extern voidF77_NAME(dopgtr)(const char* uplo, const int* n,const double* ap, const double* tau,double* q, const int* ldq,double* work, int* info FCLEN);/* DOPMTR - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dopmtr)(const char* side, const char* uplo,const char* trans, const int* m, const int* n,const double* ap, const double* tau,double* c, const int* ldc,double* work, int* info FCLEN FCLEN FCLEN);/* DORG2L - generate an m by n real matrix Q with orthonormal *//* columns, */La_extern voidF77_NAME(dorg2l)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work, int* info);/* DORG2R - generate an m by n real matrix Q with orthonormal *//* columns, */La_extern voidF77_NAME(dorg2r)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work, int* info);/* DORGBR - generate one of the real orthogonal matrices Q or *//* P**T determined by DGEBRD when reducing a real matrix A to *//* bidiagonal form */La_extern voidF77_NAME(dorgbr)(const char* vect, const int* m,const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info FCLEN);/* DORGHR - generate a real orthogonal matrix Q which is defined *//* as the product of IHI-ILO elementary reflectors of order N, as *//* returned by DGEHRD */La_extern voidF77_NAME(dorghr)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGL2 - generate an m by n real matrix Q with orthonormal *//* rows, */La_extern voidF77_NAME(dorgl2)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, int* info);/* DORGLQ - generate an M-by-N real matrix Q with orthonormal *//* rows, */La_extern voidF77_NAME(dorglq)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info);/* DORGQL - generate an M-by-N real matrix Q with orthonormal *//* columns, */La_extern voidF77_NAME(dorgql)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info);/* DORGQR - generate an M-by-N real matrix Q with orthonormal *//* columns, */La_extern voidF77_NAME(dorgqr)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGR2 - generate an m by n real matrix Q with orthonormal *//* rows, */La_extern voidF77_NAME(dorgr2)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, int* info);/* DORGRQ - generate an M-by-N real matrix Q with orthonormal rows */La_extern voidF77_NAME(dorgrq)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGTR - generate a real orthogonal matrix Q which is defined *//* as the product of n-1 elementary reflectors of order const int* n, as *//* returned by DSYTRD */La_extern voidF77_NAME(dorgtr)(const char* uplo, const int* n,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info FCLEN);/* DORM2L - overwrite the general real m by n matrix C with Q * *//* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and *//* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * *//* Q' if SIDE = 'R' and TRANS = 'T', */La_extern voidF77_NAME(dorm2l)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, int* info FCLEN FCLEN);/* DORM2R - overwrite the general real m by n matrix C with Q * C *//* if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and *//* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * *//* Q' if SIDE = 'R' and TRANS = 'T', */La_extern voidF77_NAME(dorm2r)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc, double* work, int* infoFCLEN FCLEN);/* DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N *//* matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormbr)(const char* vect, const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN FCLEN);/* DORMHR - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormhr)(const char* side, const char* trans, const int* m,const int* n, const int* ilo, const int* ihi,const double* a, const int* lda, const double* tau,double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN);/* DORML2 - overwrite the general real m by n matrix C with Q * *//* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and *//* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * *//* Q' if SIDE = 'R' and TRANS = 'T', */La_extern voidF77_NAME(dorml2)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc, double* work, int* infoFCLEN FCLEN);/* DORMLQ - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormlq)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN);/* DORMQL - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormql)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN);/* DORMQR - overwrite the general real M-by-N matrix C with SIDE = *//* 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormqr)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN);/* DORMR2 - overwrite the general real m by n matrix C with Q * *//* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and *//* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * *//* Q' if SIDE = 'R' and TRANS = 'T', */La_extern voidF77_NAME(dormr2)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, int* info FCLEN FCLEN);/* DORMRQ - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormrq)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info FCLEN FCLEN);/* DORMTR - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */La_extern voidF77_NAME(dormtr)(const char* side, const char* uplo,const char* trans, const int* m, const int* n,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* infoFCLEN FCLEN FCLEN);//* Double precision Positive definite Band matrices -> DPB/* DPBCON - estimate the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric positive definite band matrix *//* using the Cholesky factorization A = U**T*U or A = L*L**T *//* computed by DPBTRF */La_extern voidF77_NAME(dpbcon)(const char* uplo, const int* n, const int* kd,const double* ab, const int* ldab,const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DPBEQU - compute row and column scalings intended to *//* equilibrate a symmetric positive definite band matrix A and *//* reduce its condition number (with respect to the two-norm); */La_extern voidF77_NAME(dpbequ)(const char* uplo, const int* n, const int* kd,const double* ab, const int* ldab,double* s, double* scond, double* amax, int* info FCLEN);/* DPBRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric positive *//* definite and banded, and provides error bounds and backward *//* error estimates for the solution */La_extern voidF77_NAME(dpbrfs)(const char* uplo, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,const double* afb, const int* ldafb,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DPBSTF - compute a split Cholesky factorization of a real *//* symmetric positive definite band matrix A */La_extern voidF77_NAME(dpbstf)(const char* uplo, const int* n, const int* kd,double* ab, const int* ldab, int* info FCLEN);/* DPBSV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dpbsv)(const char* uplo, const int* n,const int* kd, const int* nrhs,double* ab, const int* ldab,double* b, const int* ldb, int* info FCLEN);/* DPBSVX - use the Cholesky factorization A = U**T*U or A = *//* L*L**T to compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dpbsvx)(const int* fact, const char* uplo, const int* n,const int* kd, const int* nrhs,double* ab, const int* ldab,double* afb, const int* ldafb,char* equed, double* s,double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN FCLEN);/* DPBTF2 - compute the Cholesky factorization of a real *//* symmetric positive definite band matrix A */La_extern voidF77_NAME(dpbtf2)(const char* uplo, const int* n, const int* kd,double* ab, const int* ldab, int* info FCLEN);/* DPBTRF - compute the Cholesky factorization of a real *//* symmetric positive definite band matrix A */La_extern voidF77_NAME(dpbtrf)(const char* uplo, const int* n, const int* kd,double* ab, const int* ldab, int* info FCLEN);/* DPBTRS - solve a system of linear equations A*X = B with a *//* symmetric positive definite band matrix A using the Cholesky *//* factorization A = U**T*U or A = L*L**T computed by DPBTRF */La_extern voidF77_NAME(dpbtrs)(const char* uplo, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,double* b, const int* ldb, int* info FCLEN);//* Double precision Positive definite matrices -> DPO/* DPOCON - estimate the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric positive definite matrix using *//* the Cholesky factorization A = U**T*U or A = L*L**T computed by *//* DPOTRF */La_extern voidF77_NAME(dpocon)(const char* uplo, const int* n,const double* a, const int* lda,const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DPOEQU - compute row and column scalings intended to *//* equilibrate a symmetric positive definite matrix A and reduce *//* its condition number (with respect to the two-norm); */La_extern voidF77_NAME(dpoequ)(const int* n, const double* a, const int* lda,double* s, double* scond, double* amax, int* info);/* DPORFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric positive *//* definite, */La_extern voidF77_NAME(dporfs)(const char* uplo, const int* n, const int* nrhs,const double* a, const int* lda,const double* af, const int* ldaf,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DPOSV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dposv)(const char* uplo, const int* n, const int* nrhs,double* a, const int* lda,double* b, const int* ldb, int* info FCLEN);/* DPOSVX - use the Cholesky factorization A = U**T*U or A = *//* L*L**T to compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dposvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,double* a, const int* lda,double* af, const int* ldaf, const char* equed,double* s, double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr, double* work,int* iwork, int* info FCLEN FCLEN);/* DPOTF2 - compute the Cholesky factorization of a real *//* symmetric positive definite matrix A */La_extern voidF77_NAME(dpotf2)(const char* uplo, const int* n,double* a, const int* lda, int* info FCLEN);/* DPOTRF - compute the Cholesky factorization of a real *//* symmetric positive definite matrix A */La_extern voidF77_NAME(dpotrf)(const char* uplo, const int* n,double* a, const int* lda, int* info FCLEN);/* DPOTRI - compute the inverse of a real symmetric positive *//* definite matrix A using the Cholesky factorization A = U**T*U *//* or A = L*L**T computed by DPOTRF */La_extern voidF77_NAME(dpotri)(const char* uplo, const int* n,double* a, const int* lda, int* info FCLEN);/* DPOTRS - solve a system of linear equations A*X = B with a *//* symmetric positive definite matrix A using the Cholesky *//* factorization A = U**T*U or A = L*L**T computed by DPOTRF */La_extern voidF77_NAME(dpotrs)(const char* uplo, const int* n,const int* nrhs, const double* a, const int* lda,double* b, const int* ldb, int* info FCLEN);/* DPPCON - estimate the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric positive definite packed *//* matrix using the Cholesky factorization A = U**T*U or A = *//* L*L**T computed by DPPTRF */La_extern voidF77_NAME(dppcon)(const char* uplo, const int* n,const double* ap, const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DPPEQU - compute row and column scalings intended to *//* equilibrate a symmetric positive definite matrix A in packed *//* storage and reduce its condition number (with respect to the *//* two-norm); */La_extern voidF77_NAME(dppequ)(const char* uplo, const int* n,const double* ap, double* s, double* scond,double* amax, int* info FCLEN);//* Double precision Positive definite matrices in Packed storage -> DPP/* DPPRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric positive *//* definite and packed, and provides error bounds and backward *//* error estimates for the solution */La_extern voidF77_NAME(dpprfs)(const char* uplo, const int* n, const int* nrhs,const double* ap, const double* afp,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DPPSV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dppsv)(const char* uplo, const int* n,const int* nrhs, const double* ap,double* b, const int* ldb, int* info FCLEN);/* DPPSVX - use the Cholesky factorization A = U**T*U or A = *//* L*L**T to compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dppsvx)(const char* fact, const char* uplo,const int* n, const int* nrhs, double* ap,double* afp, const char* equed, double* s,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* infoFCLEN FCLEN FCLEN);/* DPPTRF - compute the Cholesky factorization of a real *//* symmetric positive definite matrix A stored in packed format */La_extern voidF77_NAME(dpptrf)(const char* uplo, const int* n, double* ap, int* info FCLEN);/* DPPTRI - compute the inverse of a real symmetric positive *//* definite matrix A using the Cholesky factorization A = U**T*U *//* or A = L*L**T computed by DPPTRF */La_extern voidF77_NAME(dpptri)(const char* uplo, const int* n, double* ap, int* info FCLEN);/* DPPTRS - solve a system of linear equations A*X = B with a *//* symmetric positive definite matrix A in packed storage using *//* the Cholesky factorization A = U**T*U or A = L*L**T computed by *//* DPPTRF */La_extern voidF77_NAME(dpptrs)(const char* uplo, const int* n,const int* nrhs, const double* ap,double* b, const int* ldb, int* info FCLEN);//* Double precision symmetric Positive definite Tridiagonal matrices -> DPT/* DPTCON - compute the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric positive definite tridiagonal *//* matrix using the factorization A = L*D*L**T or A = U**T*D*U *//* computed by DPTTRF */La_extern voidF77_NAME(dptcon)(const int* n,const double* d, const double* e,const double* anorm, double* rcond,double* work, int* info);/* DPTEQR - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric positive definite tridiagonal matrix by first *//* factoring the matrix using DPTTRF, and then calling DBDSQR to *//* compute the singular values of the bidiagonal factor */La_extern voidF77_NAME(dpteqr)(const char* compz, const int* n, double* d,double* e, double* z, const int* ldz,double* work, int* info FCLEN);/* DPTRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric positive *//* definite and tridiagonal, and provides error bounds and *//* backward error estimates for the solution */La_extern voidF77_NAME(dptrfs)(const int* n, const int* nrhs,const double* d, const double* e,const double* df, const double* ef,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* info);/* DPTSV - compute the solution to a real system of linear *//* equations A*X = B, where A is an N-by-N symmetric positive *//* definite tridiagonal matrix, and X and B are N-by-NRHS matrices */La_extern voidF77_NAME(dptsv)(const int* n, const int* nrhs, double* d,double* e, double* b, const int* ldb, int* info);/* DPTSVX - use the factorization A = L*D*L**T to compute the *//* solution to a real system of linear equations A*X = B, where A *//* is an N-by-N symmetric positive definite tridiagonal matrix and *//* X and B are N-by-NRHS matrices */La_extern voidF77_NAME(dptsvx)(const int* fact, const int* n,const int* nrhs,const double* d, const double* e,double* df, double* ef,const double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, int* info);/* DPTTRF - compute the factorization of a real symmetric *//* positive definite tridiagonal matrix A */La_extern voidF77_NAME(dpttrf)(const int* n, double* d, double* e, int* info);/* DPTTRS - solve a system of linear equations A * X = B with a *//* symmetric positive definite tridiagonal matrix A using the *//* factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF */La_extern voidF77_NAME(dpttrs)(const int* n, const int* nrhs,const double* d, const double* e,double* b, const int* ldb, int* info);/* DRSCL - multiply an n-element real vector x by the real scalar *//* 1/a */La_extern voidF77_NAME(drscl)(const int* n, const double* da,double* x, const int* incx);//* Double precision Symmetric Band matrices -> DSB/* DSBEV - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric band matrix A */La_extern voidF77_NAME(dsbev)(const char* jobz, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* w, double* z, const int* ldz,double* work, int* info FCLEN FCLEN);/* DSBEVD - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric band matrix A */La_extern voidF77_NAME(dsbevd)(const char* jobz, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* w, double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info FCLEN FCLEN);/* DSBEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric band matrix A */La_extern voidF77_NAME(dsbevx)(const char* jobz, const char* range,const char* uplo, const int* n, const int* kd,double* ab, const int* ldab,double* q, const int* ldq,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* infoFCLEN FCLEN FCLEN);/* DSBGST - reduce a real symmetric-definite banded generalized *//* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */La_extern voidF77_NAME(dsbgst)(const char* vect, const char* uplo,const int* n, const int* ka, const int* kb,double* ab, const int* ldab,double* bb, const int* ldbb,double* x, const int* ldx,double* work, int* info FCLEN FCLEN);/* DSBGV - compute all the eigenvalues, and optionally, the *//* eigenvectors of a real generalized symmetric-definite banded *//* eigenproblem, of the form A*x=(lambda);*B*x */La_extern voidF77_NAME(dsbgv)(const char* jobz, const char* uplo,const int* n, const int* ka, const int* kb,double* ab, const int* ldab,double* bb, const int* ldbb,double* w, double* z, const int* ldz,double* work, int* info FCLEN FCLEN);/* DSBTRD - reduce a real symmetric band matrix A to symmetric *//* tridiagonal form T by an orthogonal similarity transformation */La_extern voidF77_NAME(dsbtrd)(const char* vect, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* d, double* e,double* q, const int* ldq,double* work, int* info FCLEN FCLEN);//* Double precision Symmetric Packed matrices -> DSP/* DSPCON - estimate the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric packed matrix A using the *//* factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF */La_extern voidF77_NAME(dspcon)(const char* uplo, const int* n,const double* ap, const int* ipiv,const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DSPEV - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */La_extern voidF77_NAME(dspev)(const char* jobz, const char* uplo, const int* n,double* ap, double* w, double* z, const int* ldz,double* work, int* info FCLEN FCLEN);/* DSPEVD - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */La_extern voidF77_NAME(dspevd)(const char* jobz, const char* uplo,const int* n, double* ap, double* w,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info FCLEN FCLEN);/* DSPEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */La_extern voidF77_NAME(dspevx)(const char* jobz, const char* range,const char* uplo, const int* n, double* ap,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info FCLEN FCLEN FCLEN);/* DSPGST - reduce a real symmetric-definite generalized *//* eigenproblem to standard form, using packed storage */La_extern voidF77_NAME(dspgst)(const int* itype, const char* uplo,const int* n, double* ap, double* bp, int* info FCLEN);/* DSPGV - compute all the eigenvalues and, optionally, the *//* eigenvectors of a real generalized symmetric-definite *//* eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, *//* or B*A*x=(lambda)*x */La_extern voidF77_NAME(dspgv)(const int* itype, const char* jobz,const char* uplo, const int* n,double* ap, double* bp, double* w,double* z, const int* ldz,double* work, int* info FCLEN FCLEN FCLEN);/* DSPRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric indefinite *//* and packed, and provides error bounds and backward error *//* estimates for the solution */La_extern voidF77_NAME(dsprfs)(const char* uplo, const int* n,const int* nrhs, const double* ap,const double* afp, const int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DSPSV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dspsv)(const char* uplo, const int* n,const int* nrhs, double* ap, int* ipiv,double* b, const int* ldb, int* info FCLEN);/* DSPSVX - use the diagonal pivoting factorization A = U*D*U**T *//* or A = L*D*L**T to compute the solution to a real system of *//* linear equations A * X = B, where A is an N-by-N symmetric *//* matrix stored in packed format and X and B are N-by-NRHS *//* matrices */La_extern voidF77_NAME(dspsvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,const double* ap, double* afp, int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DSPTRD - reduce a real symmetric matrix A stored in packed *//* form to symmetric tridiagonal form T by an orthogonal *//* similarity transformation */La_extern voidF77_NAME(dsptrd)(const char* uplo, const int* n,double* ap, double* d, double* e,double* tau, int* info FCLEN);/* DSPTRF - compute the factorization of a real symmetric matrix *//* A stored in packed format using the Bunch-Kaufman diagonal *//* pivoting method */La_extern voidF77_NAME(dsptrf)(const char* uplo, const int* n,double* ap, int* ipiv, int* info FCLEN);/* DSPTRI - compute the inverse of a real symmetric indefinite *//* matrix A in packed storage using the factorization A = U*D*U**T *//* or A = L*D*L**T computed by DSPTRF */La_extern voidF77_NAME(dsptri)(const char* uplo, const int* n,double* ap, const int* ipiv,double* work, int* info FCLEN);/* DSPTRS - solve a system of linear equations A*X = B with a *//* real symmetric matrix A stored in packed format using the *//* factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF */La_extern voidF77_NAME(dsptrs)(const char* uplo, const int* n,const int* nrhs, const double* ap,const int* ipiv, double* b, const int* ldb,int* info FCLEN);//* Double precision Symmetric Tridiagonal matrices -> DST/* DSTEBZ - compute the eigenvalues of a symmetric tridiagonal *//* matrix T */La_extern voidF77_NAME(dstebz)(const char* range, const char* order, const int* n,const double* vl, const double* vu,const int* il, const int* iu,const double *abstol,const double* d, const double* e,int* m, int* nsplit, double* w,int* iblock, int* isplit,double* work, int* iwork,int* info FCLEN FCLEN);/* DSTEDC - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric tridiagonal matrix using the divide and conquer *//* method */La_extern voidF77_NAME(dstedc)(const char* compz, const int* n,double* d, double* e,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info FCLEN);/* DSTEIN - compute the eigenvectors of a real symmetric *//* tridiagonal matrix T corresponding to specified eigenvalues, *//* using inverse iteration */La_extern voidF77_NAME(dstein)(const int* n, const double* d, const double* e,const int* m, const double* w,const int* iblock, const int* isplit,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info);/* DSTEQR - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric tridiagonal matrix using the implicit QL or QR *//* method */La_extern voidF77_NAME(dsteqr)(const char* compz, const int* n, double* d, double* e,double* z, const int* ldz, double* work, int* info FCLEN);/* DSTERF - compute all eigenvalues of a symmetric tridiagonal *//* matrix using the Pal-Walker-Kahan variant of the QL or QR *//* algorithm */La_extern voidF77_NAME(dsterf)(const int* n, double* d, double* e, int* info);/* DSTEV - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric tridiagonal matrix A */La_extern voidF77_NAME(dstev)(const char* jobz, const int* n,double* d, double* e,double* z, const int* ldz,double* work, int* info FCLEN);/* DSTEVD - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric tridiagonal matrix */La_extern voidF77_NAME(dstevd)(const char* jobz, const int* n,double* d, double* e,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info FCLEN);/* DSTEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric tridiagonal matrix A */La_extern voidF77_NAME(dstevx)(const char* jobz, const char* range,const int* n, double* d, double* e,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info FCLEN FCLEN);//* Double precision SYmmetric matrices -> DSY/* DSYCON - estimate the reciprocal of the condition number (in *//* the 1-norm); of a real symmetric matrix A using the *//* factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF */La_extern voidF77_NAME(dsycon)(const char* uplo, const int* n,const double* a, const int* lda,const int* ipiv,const double* anorm, double* rcond,double* work, int* iwork, int* info FCLEN);/* DSYEV - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric matrix A */La_extern voidF77_NAME(dsyev)(const char* jobz, const char* uplo,const int* n, double* a, const int* lda,double* w, double* work, const int* lwork, int* infoFCLEN FCLEN);/* DSYEVD - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric matrix A */La_extern voidF77_NAME(dsyevd)(const char* jobz, const char* uplo,const int* n, double* a, const int* lda,double* w, double* work, const int* lwork,int* iwork, const int* liwork, int* info FCLEN FCLEN);/* DSYEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A */La_extern voidF77_NAME(dsyevx)(const char* jobz, const char* range,const char* uplo, const int* n,double* a, const int* lda,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, const int* lwork, int* iwork,int* ifail, int* infoFCLEN FCLEN FCLEN);/* DSYEVR - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric matrix A */La_extern voidF77_NAME(dsyevr)(const char* jobz, const char* range, const char* uplo,const int *n, double *a, const int *lda,const double *vl, const double *vu,const int *il, const int *iu,const double *abstol, int *m, double *w,double *z, const int *ldz, int *isuppz,double *work, const int *lwork,int *iwork, const int *liwork,int *info FCLEN FCLEN FCLEN);/* DSYGS2 - reduce a real symmetric-definite generalized *//* eigenproblem to standard form */La_extern voidF77_NAME(dsygs2)(const int* itype, const char* uplo,const int* n, double* a, const int* lda,const double* b, const int* ldb, int* info FCLEN);/* DSYGST - reduce a real symmetric-definite generalized *//* eigenproblem to standard form */La_extern voidF77_NAME(dsygst)(const int* itype, const char* uplo,const int* n, double* a, const int* lda,const double* b, const int* ldb, int* info FCLEN);/* DSYGV - compute all the eigenvalues, and optionally, the *//* eigenvectors of a real generalized symmetric-definite *//* eigenproblem, of the form A*x=(lambda);*B*x, A*Bx=(lambda);*x, *//* or B*A*x=(lambda);*x */La_extern voidF77_NAME(dsygv)(const int* itype, const char* jobz,const char* uplo, const int* n,double* a, const int* lda,double* b, const int* ldb,double* w, double* work, const int* lwork,int* info FCLEN FCLEN);/* DSYRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric indefinite, *//* and provides error bounds and backward error estimates for the *//* solution */La_extern voidF77_NAME(dsyrfs)(const char* uplo, const int* n,const int* nrhs,const double* a, const int* lda,const double* af, const int* ldaf,const int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN);/* DSYSV - compute the solution to a real system of linear *//* equations A * X = B, */La_extern voidF77_NAME(dsysv)(const char* uplo, const int* n,const int* nrhs,double* a, const int* lda, int* ipiv,double* b, const int* ldb,double* work, const int* lwork, int* info FCLEN);/* DSYSVX - use the diagonal pivoting factorization to compute *//* the solution to a real system of linear equations A * X = B, */La_extern voidF77_NAME(dsysvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,const double* a, const int* lda,double* af, const int* ldaf, int* ipiv,const double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, const int* lwork,int* iwork, int* info FCLEN);/* DSYTD2 - reduce a real symmetric matrix A to symmetric *//* tridiagonal form T by an orthogonal similarity transformation */La_extern voidF77_NAME(dsytd2)(const char* uplo, const int* n,double* a, const int* lda,double* d, double* e, double* tau,int* info FCLEN);/* DSYTF2 - compute the factorization of a real symmetric matrix *//* A using the Bunch-Kaufman diagonal pivoting method */La_extern voidF77_NAME(dsytf2)(const char* uplo, const int* n,double* a, const int* lda,int* ipiv, int* info FCLEN);/* DSYTRD - reduce a real symmetric matrix A to real symmetric *//* tridiagonal form T by an orthogonal similarity transformation */La_extern voidF77_NAME(dsytrd)(const char* uplo, const int* n,double* a, const int* lda,double* d, double* e, double* tau,double* work, const int* lwork, int* info FCLEN);/* DSYTRF - compute the factorization of a real symmetric matrix *//* A using the Bunch-Kaufman diagonal pivoting method */La_extern voidF77_NAME(dsytrf)(const char* uplo, const int* n,double* a, const int* lda, int* ipiv,double* work, const int* lwork, int* info FCLEN);/* DSYTRI - compute the inverse of a real symmetric indefinite *//* matrix A using the factorization A = U*D*U**T or A = L*D*L**T *//* computed by DSYTRF */La_extern voidF77_NAME(dsytri)(const char* uplo, const int* n,double* a, const int* lda, const int* ipiv,double* work, int* info FCLEN);/* DSYTRS - solve a system of linear equations A*X = B with a *//* real symmetric matrix A using the factorization A = U*D*U**T or *//* A = L*D*L**T computed by DSYTRF */La_extern voidF77_NAME(dsytrs)(const char* uplo, const int* n,const int* nrhs,const double* a, const int* lda,const int* ipiv,double* b, const int* ldb, int* info FCLEN);//* Double precision Triangular Band matrices -> DTB/* DTBCON - estimate the reciprocal of the condition number of a *//* triangular band matrix A, in either the 1-norm or the *//* infinity-norm */La_extern voidF77_NAME(dtbcon)(const char* norm, const char* uplo,const char* diag, const int* n, const int* kd,const double* ab, const int* ldab,double* rcond, double* work,int* iwork, int* info FCLEN FCLEN FCLEN);/* DTBRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* band coefficient matrix */La_extern voidF77_NAME(dtbrfs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* kd,const int* nrhs,const double* ab, const int* ldab,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info FCLEN FCLEN FCLEN);/* DTBTRS - solve a triangular system of the form A * X = B or *//* A**T * X = B, */La_extern voidF77_NAME(dtbtrs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,double* b, const int* ldb, int* info FCLEN FCLEN FCLEN);//* Double precision Triangular matrices Generalized problems -> DTG/* DTGEVC - compute some or all of the right and/or left *//* generalized eigenvectors of a pair of real upper triangular *//* matrices (A,B); */La_extern voidF77_NAME(dtgevc)(const char* side, const char* howmny,const int* select, const int* n,const double* a, const int* lda,const double* b, const int* ldb,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work, int* info FCLEN FCLEN);/* DTGSJA - compute the generalized singular value decomposition *//* (GSVD); of two real upper triangular (or trapezoidal); matrices *//* A and B */La_extern voidF77_NAME(dtgsja)(const char* jobu, const char* jobv, const char* jobq,const int* m, const int* p, const int* n,const int* k, const int* l,double* a, const int* lda,double* b, const int* ldb,const double* tola, const double* tolb,double* alpha, double* beta,double* u, const int* ldu,double* v, const int* ldv,double* q, const int* ldq,double* work, int* ncycle, int* infoFCLEN FCLEN FCLEN);//* Double precision Triangular matrices Packed storage -> DTP/* DTPCON - estimate the reciprocal of the condition number of a *//* packed triangular matrix A, in either the 1-norm or the *//* infinity-norm */La_extern voidF77_NAME(dtpcon)(const char* norm, const char* uplo,const char* diag, const int* n,const double* ap, double* rcond,double* work, int* iwork, int* infoFCLEN FCLEN FCLEN);/* DTPRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* packed coefficient matrix */La_extern voidF77_NAME(dtprfs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* nrhs, const double* ap,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* infoFCLEN FCLEN FCLEN);/* DTPTRI - compute the inverse of a real upper or lower *//* triangular matrix A stored in packed format */La_extern voidF77_NAME(dtptri)(const char* uplo, const char* diag,const int* n, double* ap, int* info FCLEN FCLEN);/* DTPTRS - solve a triangular system of the form A * X = B or *//* A**T * X = B, */La_extern voidF77_NAME(dtptrs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* nrhs, const double* ap,double* b, const int* ldb, int* infoFCLEN FCLEN);//* Double precision TRiangular matrices -> DTR/* DTRCON - estimate the reciprocal of the condition number of a *//* triangular matrix A, in either the 1-norm or the infinity-norm */La_extern voidF77_NAME(dtrcon)(const char* norm, const char* uplo,const char* diag, const int* n,const double* a, const int* lda,double* rcond, double* work,int* iwork, int* infoFCLEN FCLEN FCLEN);/* DTREVC - compute some or all of the right and/or left *//* eigenvectors of a real upper quasi-triangular matrix T */La_extern voidF77_NAME(dtrevc)(const char* side, const char* howmny,const int* select, const int* n,const double* t, const int* ldt,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work, int* infoFCLEN FCLEN);/* DTREXC - reorder the real Schur factorization of a real matrix *//* A = Q*T*Q**T, so that the diagonal block of T with row index *//* IFST is moved to row ILST */La_extern voidF77_NAME(dtrexc)(const char* compq, const int* n,double* t, const int* ldt,double* q, const int* ldq,int* ifst, int* ILST,double* work, int* info FCLEN);/* DTRRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* coefficient matrix */La_extern voidF77_NAME(dtrrfs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* nrhs,const double* a, const int* lda,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* infoFCLEN FCLEN FCLEN);/* DTRSEN - reorder the real Schur factorization of a real matrix *//* A = Q*T*Q**T, so that a selected cluster of eigenvalues appears *//* in the leading diagonal blocks of the upper quasi-triangular *//* matrix T, */La_extern voidF77_NAME(dtrsen)(const char* job, const char* compq,const int* select, const int* n,double* t, const int* ldt,double* q, const int* ldq,double* wr, double* wi,int* m, double* s, double* sep,double* work, const int* lwork,int* iwork, const int* liwork, int* infoFCLEN FCLEN);/* DTRSNA - estimate reciprocal condition numbers for specified *//* eigenvalues and/or right eigenvectors of a real upper *//* quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q *//* orthogonal); */La_extern voidF77_NAME(dtrsna)(const char* job, const char* howmny,const int* select, const int* n,const double* t, const int* ldt,const double* vl, const int* ldvl,const double* vr, const int* ldvr,double* s, double* sep, const int* mm,int* m, double* work, const int* lwork,int* iwork, int* info FCLEN FCLEN);/* DTRSYL - solve the real Sylvester matrix equation */La_extern voidF77_NAME(dtrsyl)(const char* trana, const char* tranb,const int* isgn, const int* m, const int* n,const double* a, const int* lda,const double* b, const int* ldb,double* c, const int* ldc,double* scale, int* info FCLEN FCLEN);/* DTRTI2 - compute the inverse of a real upper or lower *//* triangular matrix */La_extern voidF77_NAME(dtrti2)(const char* uplo, const char* diag,const int* n, double* a, const int* lda,int* info FCLEN FCLEN);/* DTRTRI - compute the inverse of a real upper or lower *//* triangular matrix A */La_extern voidF77_NAME(dtrtri)(const char* uplo, const char* diag,const int* n, double* a, const int* lda,int* info FCLEN FCLEN);/* DTRTRS - solve a triangular system of the form A * X = B or *//* A**T * X = B */La_extern voidF77_NAME(dtrtrs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* nrhs,const double* a, const int* lda,double* b, const int* ldb, int* infoFCLEN FCLEN FCLEN);//* Double precision utilities in Lapack/* DHGEQZ - implement a single-/double-shift version of the QZ *//* method for finding the generalized eigenvalues *//* w(j);=(ALPHAR(j); + i*ALPHAI(j););/BETAR(j); of the equation *//* det( A - w(i); B ); = 0 In addition, the pair A,B may be *//* reduced to generalized Schur form */La_extern voidF77_NAME(dhgeqz)(const char* job, const char* compq, const char* compz,const int* n, const int *ILO, const int* IHI,double* a, const int* lda,double* b, const int* ldb,double* alphar, double* alphai, const double* beta,double* q, const int* ldq,double* z, const int* ldz,double* work, const int* lwork, int* infoFCLEN FCLEN FCLEN);/* DHSEIN - use inverse iteration to find specified right and/or *//* left eigenvectors of a real upper Hessenberg matrix H */La_extern voidF77_NAME(dhsein)(const char* side, const char* eigsrc,const char* initv, int* select,const int* n, double* h, const int* ldh,double* wr, double* wi,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work,int* ifaill, int* ifailr, int* infoFCLEN FCLEN FCLEN);/* DHSEQR - compute the eigenvalues of a real upper Hessenberg *//* matrix H and, optionally, the matrices T and Z from the Schur *//* decomposition H = Z T Z**T, where T is an upper *//* quasi-triangular matrix (the Schur form);, and Z is the *//* orthogonal matrix of Schur vectors */La_extern voidF77_NAME(dhseqr)(const char* job, const char* compz, const int* n,const int* ilo, const int* ihi,double* h, const int* ldh,double* wr, double* wi,double* z, const int* ldz,double* work, const int* lwork, int* infoFCLEN FCLEN);/* DLABAD - take as input the values computed by SLAMCH for *//* underflow and overflow, and returns the square root of each of *//* these values if the log of LARGE is sufficiently large */La_extern voidF77_NAME(dlabad)(double* small, double* large);/* DLABRD - reduce the first NB rows and columns of a real *//* general m by n matrix A to upper or lower bidiagonal form by an *//* orthogonal transformation Q' * A * P, and returns the matrices *//* X and Y which are needed to apply the transformation to the *//* unreduced part of A */La_extern voidF77_NAME(dlabrd)(const int* m, const int* n, const int* nb,double* a, const int* lda, double* d, double* e,double* tauq, double* taup,double* x, const int* ldx, double* y, const int* ldy);/* DLACON - estimate the 1-norm of a square, real matrix A */La_extern voidF77_NAME(dlacon)(const int* n, double* v, double* x,int* isgn, double* est, int* kase);/* DLACPY - copy all or part of a two-dimensional matrix A to *//* another matrix B */La_extern voidF77_NAME(dlacpy)(const char* uplo, const int* m, const int* n,const double* a, const int* lda,double* b, const int* ldb FCLEN);/* DLADIV - perform complex division in real arithmetic */La_extern voidF77_NAME(dladiv)(const double* a, const double* b,const double* c, const double* d,double* p, double* q);/* DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] *//* [ B C ] */La_extern voidF77_NAME(dlae2)(const double* a, const double* b, const double* c,double* rt1, double* rt2);/* DLAEBZ - contain the iteration loops which compute and use the *//* function N(w);, which is the count of eigenvalues of a *//* symmetric tridiagonal matrix T less than or equal to its *//* argument w */La_extern voidF77_NAME(dlaebz)(const int* ijob, const int* nitmax, const int* n,const int* mmax, const int* minp, const int* nbmin,const double* abstol, const double* reltol,const double* pivmin, double* d, double* e,double* e2, int* nval, double* ab, double* c,int* mout, int* nab, double* work, int* iwork,int* info);/* DLAED0 - compute all eigenvalues and corresponding *//* eigenvectors of a symmetric tridiagonal matrix using the divide *//* and conquer method */La_extern voidF77_NAME(dlaed0)(const int* icompq, const int* qsiz, const int* n,double* d, double* e, double* q, const int* ldq,double* qstore, const int* ldqs,double* work, int* iwork, int* info);/* DLAED1 - compute the updated eigensystem of a diagonal matrix *//* after modification by a rank-one symmetric matrix */La_extern voidF77_NAME(dlaed1)(const int* n, double* d, double* q, const int* ldq,int* indxq, const double* rho, const int* cutpnt,double* work, int* iwork, int* info);/* DLAED2 - merge the two sets of eigenvalues together into a *//* single sorted set */La_extern voidF77_NAME(dlaed2)(const int* k, const int* n, double* d,double* q, const int* ldq, int* indxq,double* rho, double* z,double* dlamda, double* w, double* q2,int* indx, int* indxc, int* indxp,int* coltyp, int* info);/* DLAED3 - find the roots of the secular equation, as defined by *//* the values in double* d, W, and RHO, between KSTART and KSTOP */La_extern voidF77_NAME(dlaed3)(const int* k, const int* n, const int* n1,double* d, double* q, const int* ldq,const double* rho, double* dlamda, double* q2,int* indx, int* ctot, double* w,double* s, int* info);/* DLAED4 - subroutine computes the I-th updated eigenvalue of a *//* symmetric rank-one modification to a diagonal matrix whose *//* elements are given in the array d, and that D(i); < D(j); for *//* i < j and that RHO > 0 */La_extern voidF77_NAME(dlaed4)(const int* n, const int* i, const double* d,const double* z, const double* delta,const double* rho, double* dlam, int* info);/* DLAED5 - subroutine computes the I-th eigenvalue of a *//* symmetric rank-one modification of a 2-by-2 diagonal matrix *//* diag( D ); + RHO The diagonal elements in the array D are *//* assumed to satisfy D(i); < D(j); for i < j */La_extern voidF77_NAME(dlaed5)(const int* i, const double* d, const double* z,double* delta, const double* rho, double* dlam);/* DLAED6 - compute the positive or negative root (closest to the *//* origin); of z(1); z(2); z(3); f(x); = rho + --------- + *//* ---------- + --------- d(1);-x d(2);-x d(3);-x It is assumed *//* that if ORGATI = .true */La_extern voidF77_NAME(dlaed6)(const int* kniter, const int* orgati,const double* rho, const double* d,const double* z, const double* finit,double* tau, int* info);/* DLAED7 - compute the updated eigensystem of a diagonal matrix *//* after modification by a rank-one symmetric matrix */La_extern voidF77_NAME(dlaed7)(const int* icompq, const int* n,const int* qsiz, const int* tlvls,const int* curlvl, const int* curpbm,double* d, double* q, const int* ldq,int* indxq, const double* rho, const int* cutpnt,double* qstore, double* qptr, const int* prmptr,const int* perm, const int* givptr,const int* givcol, const double* givnum,double* work, int* iwork, int* info);/* DLAED8 - merge the two sets of eigenvalues together into a *//* single sorted set */La_extern voidF77_NAME(dlaed8)(const int* icompq, const int* k,const int* n, const int* qsiz,double* d, double* q, const int* ldq,const int* indxq, double* rho,const int* cutpnt, const double* z,double* dlamda, double* q2, const int* ldq2,double* w, int* perm, int* givptr,int* givcol, double* givnum, int* indxp,int* indx, int* info);/* DLAED9 - find the roots of the secular equation, as defined by *//* the values in double* d, Z, and RHO, between KSTART and KSTOP */La_extern voidF77_NAME(dlaed9)(const int* k, const int* kstart, const int* kstop,const int* n, double* d, double* q, const int* ldq,const double* rho, const double* dlamda,const double* w, double* s, const int* lds, int* info);/* DLAEDA - compute the Z vector corresponding to the merge step *//* in the CURLVLth step of the merge process with TLVLS steps for *//* the CURPBMth problem */La_extern voidF77_NAME(dlaeda)(const int* n, const int* tlvls, const int* curlvl,const int* curpbm, const int* prmptr, const int* perm,const int* givptr, const int* givcol,const double* givnum, const double* q,const int* qptr, double* z, double* ztemp, int* info);/* DLAEIN - use inverse iteration to find a right or left *//* eigenvector corresponding to the eigenvalue (WR,WI); of a real *//* upper Hessenberg matrix H */La_extern voidF77_NAME(dlaein)(const int* rightv, const int* noinit, const int* n,const double* h, const int* ldh,const double* wr, const double* wi,double* vr, double* vi,double* b, const int* ldb, double* work,const double* eps3, const double* smlnum,const double* bignum, int* info);/* DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric *//* matrix [ A B ] [ B C ] */La_extern voidF77_NAME(dlaev2)(const double* a, const double* b, const double* c,double* rt1, double* rt2, double* cs1, double *sn1);/* DLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 *//* or 2 in an upper quasi-triangular matrix T by an orthogonal *//* similarity transformation */La_extern voidF77_NAME(dlaexc)(const int* wantq, const int* n, double* t, const int* ldt,double* q, const int* ldq, const int* j1,const int* n1, const int* n2, double* work, int* info);/* DLAG2 - compute the eigenvalues of a 2 x 2 generalized *//* eigenvalue problem A - w B, with scaling as necessary to aextern void *//* over-/underflow */La_extern voidF77_NAME(dlag2)(const double* a, const int* lda, const double* b,const int* ldb, const double* safmin,double* scale1, double* scale2,double* wr1, double* wr2, double* wi);/* DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such *//* that if ( UPPER ); then U'*A*Q = U'*( A1 A2 );*Q = ( x 0 ); *//* ( 0 A3 ); ( x x ); and V'*B*Q = V'*( B1 B2 );*Q = ( x 0 ); ( *//* 0 B3 ); ( x x ); or if ( .NOT.UPPER ); then U'*A*Q = U'*( A1 *//* 0 );*Q = ( x x ); ( A2 A3 ); ( 0 x ); and V'*B*Q = V'*( B1 0 *//* );*Q = ( x x ); ( B2 B3 ); ( 0 x ); The rows of the *//* transformed A and B are parallel, where U = ( CSU SNU );, V = *//* ( CSV SNV );, Q = ( CSQ SNQ ); ( -SNU CSU ); ( -SNV CSV ); ( *//* -SNQ CSQ ); Z' denotes the transpose of Z */La_extern voidF77_NAME(dlags2)(const int* upper,const double* a1, const double* a2, const double* a3,const double* b1, const double* b2, const double* b3,double* csu, double* snu,double* csv, double* snv, double *csq, double *snq);/* DLAGTF - factorize the matrix (T - lambda*I);, where T is an n *//* by n tridiagonal matrix and lambda is a scalar, as T - *//* lambda*I = PLU, */La_extern voidF77_NAME(dlagtf)(const int* n, double* a, const double* lambda,double* b, double* c, const double *tol,double* d, int* in, int* info);/* DLAGTM - perform a matrix-vector product of the form B := *//* alpha * A * X + beta * B where A is a tridiagonal matrix of *//* order N, B and X are N by NRHS matrices, and alpha and beta are *//* real scalars, each of which may be 0., 1., or -1 */La_extern voidF77_NAME(dlagtm)(const char* trans, const int* n, const int* nrhs,const double* alpha, const double* dl,const double* d, const double* du,const double* x, const int* ldx, const double* beta,double* b, const int* ldb FCLEN);/* DLAGTS - may be used to solve one of the systems of equations *//* (T - lambda*I);*x = y or (T - lambda*I);'*x = y, */La_extern voidF77_NAME(dlagts)(const int* job, const int* n,const double* a, const double* b,const double* c, const double* d,const int* in, double* y, double* tol, int* info);/* DLAHQR - an auxiliary routine called by DHSEQR to update the *//* eigenvalues and Schur decomposition already computed by DHSEQR, *//* by dealing with the Hessenberg submatrix in rows and columns *//* ILO to IHI */La_extern voidF77_NAME(dlahqr)(const int* wantt, const int* wantz, const int* n,const int* ilo, const int* ihi,double* H, const int* ldh, double* wr, double* wi,const int* iloz, const int* ihiz,double* z, const int* ldz, int* info);/* DLAIC1 - apply one step of incremental condition estimation in *//* its simplest version */La_extern voidF77_NAME(dlaic1)(const int* job, const int* j, const double* x,const double* sest, const double* w,const double* gamma, double* sestpr,double* s, double* c);/* DLALN2 - solve a system of the form (ca A - w D ); X = s B or *//* (ca A' - w D); X = s B with possible scaling ("s"); and *//* perturbation of A */La_extern voidF77_NAME(dlaln2)(const int* ltrans, const int* na, const int* nw,const double* smin, const double* ca,const double* a, const int* lda,const double* d1, const double* d2,const double* b, const int* ldb,const double* wr, const double* wi,double* x, const int* ldx, double* scale,double* xnorm, int* info);/* DLAMCH - determine double precision machine parameters */La_extern doubleF77_NAME(dlamch)(const char* cmach FCLEN);/* DLAMRG - will create a permutation list which will merge the *//* elements of A (which is composed of two independently sorted *//* sets); into a single set which is sorted in ascending order */La_extern voidF77_NAME(dlamrg)(const int* n1, const int* n2, const double* a,const int* dtrd1, const int* dtrd2, int* index);/* DLANGB - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of an n by n band matrix A, with kl sub-diagonals and ku *//* super-diagonals */La_extern doubleF77_NAME(dlangb)(const char* norm, const int* n,const int* kl, const int* ku, const double* ab,const int* ldab, double* work FCLEN);/* DLANGE - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a real matrix A */La_extern doubleF77_NAME(dlange)(const char* norm, const int* m, const int* n,const double* a, const int* lda, double* work FCLEN);/* DLANGT - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a real tridiagonal matrix A */La_extern doubleF77_NAME(dlangt)(const char* norm, const int* n,const double* dl, const double* d,const double* du FCLEN);/* DLANHS - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a Hessenberg matrix A */La_extern doubleF77_NAME(dlanhs)(const char* norm, const int* n,const double* a, const int* lda, double* work FCLEN);/* DLANSB - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of an n by n symmetric band matrix A, with k *//* super-diagonals */La_extern doubleF77_NAME(dlansb)(const char* norm, const char* uplo,const int* n, const int* k,const double* ab, const int* ldab, double* workFCLEN FCLEN);/* DLANSP - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a real symmetric matrix A, supplied in packed form */La_extern doubleF77_NAME(dlansp)(const char* norm, const char* uplo,const int* n, const double* ap, double* workFCLEN FCLEN);/* DLANST - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a real symmetric tridiagonal matrix A */La_extern doubleF77_NAME(dlanst)(const char* norm, const int* n,const double* d, const double* e FCLEN);/* DLANSY - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a real symmetric matrix A */La_extern doubleF77_NAME(dlansy)(const char* norm, const char* uplo, const int* n,const double* a, const int* lda, double* workFCLEN FCLEN);/* DLANTB - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of an n by n triangular band matrix A, with ( k + 1 ) diagonals */La_extern doubleF77_NAME(dlantb)(const char* norm, const char* uplo,const char* diag, const int* n, const int* k,const double* ab, const int* ldab, double* workFCLEN FCLEN FCLEN);/* DLANTP - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a triangular matrix A, supplied in packed form */La_extern doubleF77_NAME(dlantp)(const char* norm, const char* uplo, const char* diag,const int* n, const double* ap, double* workFCLEN FCLEN FCLEN);/* DLANTR - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of a trapezoidal or triangular matrix A */La_extern doubleF77_NAME(dlantr)(const char* norm, const char* uplo,const char* diag, const int* m, const int* n,const double* a, const int* lda, double* workFCLEN FCLEN FCLEN);/* DLANV2 - compute the Schur factorization of a real 2-by-2 *//* nonsymmetric matrix in standard form */La_extern voidF77_NAME(dlanv2)(double* a, double* b, double* c, double* d,double* rt1r, double* rt1i, double* rt2r, double* rt2i,double* cs, double *sn);/* DLAPLL - two column vectors X and Y, let A = ( X Y ); */La_extern voidF77_NAME(dlapll)(const int* n, double* x, const int* incx,double* y, const int* incy, double* ssmin);/* DLAPMT - rearrange the columns of the M by N matrix X as *//* specified by the permutation K(1);,K(2);,...,K(N); of the *//* integers 1,...,N */La_extern voidF77_NAME(dlapmt)(const int* forwrd, const int* m, const int* n,double* x, const int* ldx, const int* k);/* DLAPY2 - return sqrt(x**2+y**2);, taking care not to cause *//* unnecessary overflow */La_extern doubleF77_NAME(dlapy2)(const double* x, const double* y);/* DLAPY3 - return sqrt(x**2+y**2+z**2);, taking care not to *//* cause unnecessary overflow */La_extern doubleF77_NAME(dlapy3)(const double* x, const double* y, const double* z);/* DLAQGB - equilibrate a general M by N band matrix A with KL *//* subdiagonals and KU superdiagonals using the row and scaling *//* factors in the vectors R and C */La_extern voidF77_NAME(dlaqgb)(const int* m, const int* n,const int* kl, const int* ku,double* ab, const int* ldab,double* r, double* c,double* rowcnd, double* colcnd,const double* amax, const char* equed FCLEN);/* DLAQGE - equilibrate a general M by N matrix A using the row *//* and scaling factors in the vectors R and C */La_extern voidF77_NAME(dlaqge)(const int* m, const int* n,double* a, const int* lda,double* r, double* c,double* rowcnd, double* colcnd,const double* amax, const char* equed FCLEN);/* DLAQSB - equilibrate a symmetric band matrix A using the *//* scaling factors in the vector S */La_extern voidF77_NAME(dlaqsb)(const char* uplo, const int* n, const int* kd,double* ab, const int* ldab, const double* s,const double* scond, const double* amax,const char* equed FCLEN FCLEN);/* DLAQSP - equilibrate a symmetric matrix A using the scaling *//* factors in the vector S */La_extern voidF77_NAME(dlaqsp)(const char* uplo, const int* n,double* ap, const double* s, const double* scond,const double* amax, int* equed FCLEN);/* DLAQSY - equilibrate a symmetric matrix A using the scaling *//* factors in the vector S */La_extern voidF77_NAME(dlaqsy)(const char* uplo, const int* n,double* a, const int* lda,const double* s, const double* scond,const double* amax, int* equed FCLEN);/* DLAQTR - solve the real quasi-triangular system *//* op(T) * p = scale*c */La_extern voidF77_NAME(dlaqtr)(const int* ltran, const int* lreal, const int* n,const double* t, const int* ldt,const double* b, const double* w,double* scale, double* x, double* work, int* info);/* DLAR2V - apply a vector of real plane rotations from both *//* sides to a sequence of 2-by-2 real symmetric matrices, defined *//* by the elements of the vectors x, y and z */La_extern voidF77_NAME(dlar2v)(const int* n, double* x, double* y,double* z, const int* incx,const double* c, const double* s,const int* incc);/* DLARF - apply a real elementary reflector H to a real m by n *//* matrix C, from either the left or the right */La_extern voidF77_NAME(dlarf)(const char* side, const int* m, const int* n,const double* v, const int* incv, const double* tau,double* c, const int* ldc, double* work FCLEN);/* DLARFB - apply a real block reflector H or its transpose H' *//* to a real m by n matrix C, from either the left or the right */La_extern voidF77_NAME(dlarfb)(const char* side, const char* trans,const char* direct, const char* storev,const int* m, const int* n, const int* k,const double* v, const int* ldv,const double* t, const int* ldt,double* c, const int* ldc,double* work, const int* lworkFCLEN FCLEN FCLEN FCLEN);/* DLARFG - generate a real elementary reflector H of order n, *//* such that H * ( alpha ) = ( beta ), H' * H = I */La_extern voidF77_NAME(dlarfg)(const int* n, const double* alpha,double* x, const int* incx, double* tau);/* DLARFT - form the triangular factor T of a real block *//* reflector H of order n, which is defined as a product of k *//* elementary reflectors */La_extern voidF77_NAME(dlarft)(const char* direct, const char* storev,const int* n, const int* k, double* v, const int* ldv,const double* tau, double* t, const int* ldt FCLEN FCLEN);/* DLARFX - apply a real elementary reflector H to a real m by n *//* matrix C, from either the left or the right */La_extern voidF77_NAME(dlarfx)(const char* side, const int* m, const int* n,const double* v, const double* tau,double* c, const int* ldc, double* work FCLEN);/* DLARGV - generate a vector of real plane rotations, determined *//* by elements of the real vectors x and y */La_extern voidF77_NAME(dlargv)(const int* n, double* x, const int* incx,double* y, const int* incy, double* c, const int* incc);/* DLARNV - return a vector of n random real numbers from a *//* uniform or normal distribution */La_extern voidF77_NAME(dlarnv)(const int* idist, int* iseed, const int* n, double* x);/* DLARTG - generate a plane rotation so that [ CS SN ] */La_extern voidF77_NAME(dlartg)(const double* f, const double* g, double* cs,double* sn, double *r);/* DLARTV - apply a vector of real plane rotations to elements of *//* the real vectors x and y */La_extern voidF77_NAME(dlartv)(const int* n, double* x, const int* incx,double* y, const int* incy,const double* c, const double* s,const int* incc);/* DLARUV - return a vector of n random real numbers from a *//* uniform (0,1); */La_extern voidF77_NAME(dlaruv)(int* iseed, const int* n, double* x);/* DLAS2 - compute the singular values of the 2-by-2 matrix *//* [ F G ] [ 0 H ] */La_extern voidF77_NAME(dlas2)(const double* f, const double* g, const double* h,double* ssmin, double* ssmax);/* DLASCL - multiply the M by N real matrix A by the real scalar *//* CTO/CFROM */La_extern voidF77_NAME(dlascl)(const char* type,const int* kl,const int* ku,double* cfrom, double* cto,const int* m, const int* n,double* a, const int* lda, int* info FCLEN);/* DLASET - initialize an m-by-n matrix A to BETA on the diagonal *//* and ALPHA on the offdiagonals */La_extern voidF77_NAME(dlaset)(const char* uplo, const int* m, const int* n,const double* alpha, const double* beta,double* a, const int* lda FCLEN);/* DLASQ1 - DLASQ1 computes the singular values of a real N-by-N *//* bidiagonal matrix with diagonal D and off-diagonal E */La_extern voidF77_NAME(dlasq1)(const int* n, double* d, double* e,double* work, int* info);/* DLASQ2 - DLASQ2 computes the singular values of a real N-by-N *//* unreduced bidiagonal matrix with squared diagonal elements in *//* Q and squared off-diagonal elements in E */La_extern voidF77_NAME(dlasq2)(const int* m, double* q, double* e,double* qq, double* ee, const double* eps,const double* tol2, const double* small2,double* sup, int* kend, int* info);/* DLASQ3 - DLASQ3 is the workhorse of the whole bidiagonal SVD *//* algorithm */La_extern voidF77_NAME(dlasq3)(int* n, double* q, double* e, double* qq,double* ee, double* sup, double *sigma,int* kend, int* off, int* iphase,const int* iconv, const double* eps,const double* tol2, const double* small2);/* DLASQ4 - DLASQ4 estimates TAU, the smallest eigenvalue of a *//* matrix */La_extern voidF77_NAME(dlasq4)(const int* n, const double* q, const double* e,double* tau, double* sup);/* DLASR - perform the transformation A := P*A, when SIDE = 'L' *//* or 'l' ( Left-hand side ); A := A*P', when SIDE = 'R' or 'r' *//* ( Right-hand side ); where A is an m by n real matrix and P is *//* an orthogonal matrix, */La_extern voidF77_NAME(dlasr)(const char* side, const char* pivot,const char* direct, const int* m, const int* n,const double* c, const double* s,double* a, const int* lda FCLEN FCLEN FCLEN);/* DLASRT - the numbers in D in increasing order (if ID = 'I'); *//* or in decreasing order (if ID = 'D' ); */La_extern voidF77_NAME(dlasrt)(const char* id, const int* n, double* d, int* info FCLEN);/* DLASSQ - return the values scl and smsq such that ( scl**2 *//* );*smsq = x( 1 );**2 +...+ x( n );**2 + ( scale**2 );*sumsq, */La_extern voidF77_NAME(dlassq)(const int* n, const double* x, const int* incx,double* scale, double* sumsq);/* DLASV2 - compute the singular value decomposition of a 2-by-2 *//* triangular matrix [ F G ] [ 0 H ] */La_extern voidF77_NAME(dlasv2)(const double* f, const double* g, const double* h,double* ssmin, double* ssmax, double* snr, double* csr,double* snl, double* csl);/* DLASWP - perform a series of row interchanges on the matrix A */La_extern voidF77_NAME(dlaswp)(const int* n, double* a, const int* lda,const int* k1, const int* k2,const int* ipiv, const int* incx);/* DLASY2 - solve for the N1 by N2 matrix double* x, 1 <= N1,N2 <= 2, in *//* op(TL);*X + ISGN*X*op(TR); = SCALE*B, */La_extern voidF77_NAME(dlasy2)(const int* ltranl, const int* ltranr,const int* isgn, const int* n1, const int* n2,const double* tl, const int* ldtl,const double* tr, const int* ldtr,const double* b, const int* ldb,double* scale, double* x, const int* ldx,double* xnorm, int* info);/* DLASYF - compute a partial factorization of a real symmetric *//* matrix A using the Bunch-Kaufman diagonal pivoting method */La_extern voidF77_NAME(dlasyf)(const char* uplo, const int* n,const int* nb, const int* kb,double* a, const int* lda, int* ipiv,double* w, const int* ldw, int* info FCLEN);/* DLATBS - solve one of the triangular systems A *x = s*b or *//* A'*x = s*b with scaling to prevent overflow, where A is an *//* upper or lower triangular band matrix */La_extern voidF77_NAME(dlatbs)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const int* kd,const double* ab, const int* ldab,double* x, double* scale, double* cnorm, int* infoFCLEN FCLEN FCLEN FCLEN);/* DLATPS - solve one of the triangular systems A *x = s*b or *//* A'*x = s*b with scaling to prevent overflow, where A is an *//* upper or lower triangular matrix stored in packed form */La_extern voidF77_NAME(dlatps)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const double* ap,double* x, double* scale, double* cnorm, int* infoFCLEN FCLEN FCLEN FCLEN);/* DLATRD - reduce NB rows and columns of a real symmetric matrix *//* A to symmetric tridiagonal form by an orthogonal similarity *//* transformation Q' * A * Q, and returns the matrices V and W *//* which are needed to apply the transformation to the unreduced *//* part of A */La_extern voidF77_NAME(dlatrd)(const char* uplo, const int* n, const int* nb,double* a, const int* lda, double* e, double* tau,double* w, const int* ldw FCLEN);/* DLATRS - solve one of the triangular systems A *x = s*b or *//* A'*x = s*b with scaling to prevent overflow */La_extern voidF77_NAME(dlatrs)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const double* a, const int* lda,double* x, double* scale, double* cnorm, int* infoFCLEN FCLEN FCLEN FCLEN );/* DLAUU2 - compute the product U * U' or L' * const int* l, where the *//* triangular factor U or L is stored in the upper or lower *//* triangular part of the array A */La_extern voidF77_NAME(dlauu2)(const char* uplo, const int* n,double* a, const int* lda, int* info FCLEN);/* DLAUUM - compute the product U * U' or L' * L, where the *//* triangular factor U or L is stored in the upper or lower *//* triangular part of the array A */La_extern voidF77_NAME(dlauum)(const char* uplo, const int* n,double* a, const int* lda, int* info FCLEN);/* ======================================================================== *///* Selected Double Complex Lapack Routines/* ========*//* IZMAX1 finds the index of the element whose real part has maximum* absolute value. Returns Fortran INTEGER. */La_extern intF77_NAME(izmax1)(const int *n, Rcomplex *cx, const int *incx);/* ZGECON estimates the reciprocal of the condition number of a general* complex matrix A, in either the 1-norm or the infinity-norm, using* the LU factorization computed by ZGETRF.*/La_extern voidF77_NAME(zgecon)(const char* norm, const int *n,const Rcomplex *a, const int *lda,const double *anorm, double *rcond,Rcomplex *work, double *rwork, int *info FCLEN);/* ZGESV computes the solution to a complex system of linear equations */La_extern voidF77_NAME(zgesv)(const int *n, const int *nrhs, Rcomplex *a,const int *lda, int *ipiv, Rcomplex *b,const int *ldb, int *info);/* ZGEQP3 computes a QR factorization with column pivoting */La_extern voidF77_NAME(zgeqp3)(const int *m, const int *n,Rcomplex *a, const int *lda,int *jpvt, Rcomplex *tau,Rcomplex *work, const int *lwork,double *rwork, int *info);/* ZUNMQR applies Q or Q**H from the Left or Right */La_extern voidF77_NAME(zunmqr)(const char* side, const char* trans,const int *m, const int *n, const int *k,Rcomplex *a, const int *lda,Rcomplex *tau,Rcomplex *c, const int *ldc,Rcomplex *work, const int *lwork, int *info FCLEN FCLEN);/* ZTRTRS solves triangular systems */La_extern voidF77_NAME(ztrtrs)(const char* uplo, const char* trans, const char* diag,const int *n, const int *nrhs,Rcomplex *a, const int *lda,Rcomplex *b, const int *ldb, int *infoFCLEN FCLEN FCLEN);/* ZGESVD - compute the singular value decomposition (SVD); of a *//* real M-by-N matrix A, optionally computing the left and/or *//* right singular vectors */La_extern voidF77_NAME(zgesvd)(const char* jobu, const char* jobvt,const int *m, const int *n,Rcomplex *a, const int *lda, double *s,Rcomplex *u, const int *ldu,Rcomplex *vt, const int *ldvt,Rcomplex *work, const int *lwork, double *rwork,int *info FCLEN FCLEN);/* ZGHEEV - compute all eigenvalues and, optionally, eigenvectors *//* of a Hermitian matrix A */La_extern voidF77_NAME(zheev)(const char* jobz, const char* uplo,const int *n, Rcomplex *a, const int *lda,double *w, Rcomplex *work, const int *lwork,double *rwork, int *info FCLEN FCLEN);/* ZGGEEV - compute all eigenvalues and, optionally, eigenvectors *//* of a complex non-symmetric matrix A */La_extern voidF77_NAME(zgeev)(const char* jobvl, const char* jobvr,const int *n, Rcomplex *a, const int *lda,Rcomplex *wr, Rcomplex *vl, const int *ldvl,Rcomplex *vr, const int *ldvr,Rcomplex *work, const int *lwork,double *rwork, int *info FCLEN FCLEN);/* ZLACN2 estimates the 1-norm of a square, complex matrix A.* Reverse communication is used for evaluating matrix-vector products.* Added in R 2.7.0*/La_extern voidF77_NAME(zlacn2)(const int *n, Rcomplex *v, Rcomplex *x,double *est, int *kase, int *isave);/* ZLANTR - return the value of the one norm, or the Frobenius norm,* or the infinity norm, or the element of largest absolute value of* a trapezoidal or triangular matrix A.* Added in R 2.7.0*/La_extern doubleF77_NAME(zlantr)(const char* norm, const char* uplo, const char* diag,const int *m, const int *n, Rcomplex *a,const int *lda, double *work FCLEN FCLEN FCLEN);/* DZSUM1 - take the sum of the absolute values of a complex* vector and returns a double precision result* Added in R 2.15.2*/La_extern doubleF77_NAME(dzsum1)(const int *n, Rcomplex *CX, const int *incx);/* Added in R 3.6.2 */La_extern voidF77_NAME(zpotrf)(const char* uplo, const int* n,Rcomplex* a, const int* lda, int* info FCLEN);La_extern voidF77_NAME(zpotri)(const char* uplo, const int* n,Rcomplex* a, const int* lda, int* info FCLEN);La_extern voidF77_NAME(zpotrs)(const char* uplo, const int* n,const int* nrhs, const Rcomplex* a, const int* lda,Rcomplex* b, const int* ldb, int* info FCLEN);/* ======================================================================== *///* Other double precision and double complex Lapack routines provided by libRlapack./*These are extracted from the CLAPACK headers.*/La_extern voidF77_NAME(dbdsdc)(const char* uplo, const char* compq, int *n,double * d, double *e, double *u, int *ldu, double *vt,int *ldvt, double *q, int *iq, double *work, int * iwork, int *infoFCLEN FCLEN);La_extern voidF77_NAME(dgelsd)(int *m, int *n, int *nrhs,double *a, int *lda, double *b, int *ldb, double *s, double *rcond, int *rank, double *work, int *lwork,int *iwork, int *info);La_extern voidF77_NAME(dgesc2)(int *n, double *a, int *lda,double *rhs, int *ipiv, int *jpiv, double *scale);/* DGESDD - compute the singular value decomposition (SVD); of a *//* real M-by-N matrix A, optionally computing the left and/or *//* right singular vectors. If singular vectors are desired, it uses a *//* divide-and-conquer algorithm. */La_extern voidF77_NAME(dgesdd)(const char* jobz,const int *m, const int *n,double *a, const int *lda, double *s,double *u, const int *ldu,double *vt, const int *ldvt,double *work, const int *lwork, int *iwork, int *info FCLEN );La_extern voidF77_NAME(dgetc2)(int *n, double *a, int *lda, int*ipiv, int *jpiv, int *info);typedef int (*L_fp)();La_extern voidF77_NAME(dggesx)(const char* jobvsl, const char* jobvsr, const char* sort, L_fpdelctg, const char* sense, int *n, double *a, int *lda,double *b, int *ldb, int *sdim, double *alphar,double *alphai, double *beta, double *vsl, int *ldvsl,double *vsr, int *ldvsr, double *rconde, double *rcondv, double *work, int *lwork, int *iwork, int *liwork, int *bwork, int *infoFCLEN FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dggev)(const char* jobvl, const char* jobvr, int *n, double *a, int *lda, double *b, int *ldb, double *alphar,double *alphai, double *beta, double *vl, int *ldvl,double *vr, int *ldvr, double *work, int *lwork,int *info FCLEN FCLEN);La_extern voidF77_NAME(dggevx)(const char* balanc, const char* jobvl, const char* jobvr, const char*sense, int *n, double *a, int *lda, double *b,int *ldb, double *alphar, double *alphai, double *beta, double *vl, int *ldvl, double *vr, int *ldvr,int *ilo, int *ihi, double *lscale, double *rscale,double *abnrm, double *bbnrm, double *rconde, double *rcondv, double *work, int *lwork, int *iwork, int *bwork, int *info FCLEN FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dgtts2)(int *itrans, int *n, int *nrhs,double *dl, double *d, double *du, double *du2,int *ipiv, double *b, int *ldb);La_extern voidF77_NAME(dlagv2)(double *a, int *lda, double *b, int *ldb, double *alphar,double *alphai, double * beta, double *csl, double *snl,double *csr, double * snr);La_extern voidF77_NAME(dlals0)(int *icompq, int *nl, int *nr,int *sqre, int *nrhs, double *b, int *ldb, double*bx, int *ldbx, int *perm, int *givptr, int *givcol,int *ldgcol, double *givnum, int *ldgnum, double *poles, double *difl, double *difr, double *z, int *k, double *c, double *s, double *work, int *info);La_extern voidF77_NAME(dlalsa)(int *icompq, int *smlsiz, int *n,int *nrhs, double *b, int *ldb, double *bx, int *ldbx, double *u, int *ldu, double *vt, int *k,double *difl, double *difr, double *z, double *poles, int *givptr, int *givcol, int *ldgcol, int *perm, double *givnum, double *c, double *s, double *work, int *iwork, int *info);La_extern voidF77_NAME(dlalsd)(const char* uplo, int *smlsiz, int *n, int*nrhs, double *d, double *e, double *b, int *ldb,double *rcond, int *rank, double *work, int *iwork,int *info FCLEN);La_extern voidF77_NAME(dlamc1)(int *beta, int *t, int *rnd, int*ieee1);La_extern voidF77_NAME(dlamc2)(int *beta, int *t, int *rnd,double *eps, int *emin, double *rmin, int *emax,double *rmax);La_extern doubleF77_NAME(dlamc3)(double *a, double *b);La_extern voidF77_NAME(dlamc4)(int *emin, double *start, int *base);La_extern voidF77_NAME(dlamc5)(int *beta, int *p, int *emin,int *ieee, int *emax, double *rmax);La_extern voidF77_NAME(dlaqp2)(int *m, int *n, int *offset,double *a, int *lda, int *jpvt, double *tau,double *vn1, double *vn2, double *work);La_extern voidF77_NAME(dlaqps)(int *m, int *n, int *offset, int*nb, int *kb, double *a, int *lda, int *jpvt,double *tau, double *vn1, double *vn2, double *auxv,double *f, int *ldf);La_extern voidF77_NAME(dlar1v)(int *n, int *b1, int *bn, double*sigma, double *d, double *l, double *ld, double *lld, double *gersch, double *z, double *ztz, double*mingma, int *r, int *isuppz, double *work);La_extern voidF77_NAME(dlarrb)(int *n, double *d, double *l,double *ld, double *lld, int *ifirst, int *ilast,double *sigma, double *reltol, double *w, double *wgap, double *werr, double *work, int *iwork, int *info);La_extern voidF77_NAME(dlarre)(int *n, double *d, double *e,double *tol, int *nsplit, int *isplit, int *m,double *w, double *woff, double *gersch, double *work,int *info);La_extern voidF77_NAME(dlarrf)(int *n, double *d, double *l,double *ld, double *lld, int *ifirst, int *ilast,double *w, double *dplus, double *lplus, double *work,int *iwork, int *info);La_extern voidF77_NAME(dlarrv)(int *n, double *d, double *l,int *isplit, int *m, double *w, int *iblock,double *gersch, double *tol, double *z, int *ldz,int *isuppz, double *work, int *iwork, int *info);La_extern voidF77_NAME(dlarz)(const char* side, int *m, int *n, int *l,double *v, int *incv, double *tau, double *c,int *ldc, double *work FCLEN);La_extern voidF77_NAME(dlarzb)(const char* side, const char* trans, const char* direct, const char*storev, int *m, int *n, int *k, int *l, double *v,int *ldv, double *t, int *ldt, double *c, int *ldc, double *work, int *ldworkFCLEN FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dlarzt)(const char* direct, const char* storev, int *n, int *k, double *v, int *ldv, double *tau, double *t,int *ldt FCLEN FCLEN);La_extern voidF77_NAME(dlasd0)(int *n, int *sqre, double *d,double *e, double *u, int *ldu, double *vt, int *ldvt, int *smlsiz, int *iwork, double *work, int *info);La_extern voidF77_NAME(dlasd1)(int *nl, int *nr, int *sqre,double *d, double *alpha, double *beta, double *u,int *ldu, double *vt, int *ldvt, int *idxq, int *iwork, double *work, int *info);La_extern voidF77_NAME(dlasd2)(int *nl, int *nr, int *sqre, int*k, double *d, double *z, double *alpha, double *beta, double *u, int *ldu, double *vt, int *ldvt,double *dsigma, double *u2, int *ldu2, double *vt2,int *ldvt2, int *idxp, int *idx, int *idxc, int *idxq, int *coltyp, int *info);La_extern voidF77_NAME(dlasd3)(int *nl, int *nr, int *sqre, int*k, double *d, double *q, int *ldq, double *dsigma,double *u, int *ldu, double *u2, int *ldu2,double *vt, int *ldvt, double *vt2, int *ldvt2,int *idxc, int *ctot, double *z, int *info);La_extern voidF77_NAME(dlasd4)(int *n, int *i, double *d,double *z, double *delta, double *rho, double *sigma, double *work, int *info);La_extern voidF77_NAME(dlasd5)(int *i, double *d, double *z,double *delta, double *rho, double *dsigma, double *work);La_extern voidF77_NAME(dlasd6)(int *icompq, int *nl, int *nr,int *sqre, double *d, double *vf, double *vl,double *alpha, double *beta, int *idxq, int *perm,int *givptr, int *givcol, int *ldgcol, double *givnum,int *ldgnum, double *poles, double *difl, double *difr, double *z, int *k, double *c, double *s,double *work, int *iwork, int *info);La_extern voidF77_NAME(dlasd7)(int *icompq, int *nl, int *nr,int *sqre, int *k, double *d, double *z,double *zw, double *vf, double *vfw, double *vl,double *vlw, double *alpha, double *beta, double *dsigma, int *idx, int *idxp, int *idxq, int *perm,int *givptr, int *givcol, int *ldgcol, double *givnum,int *ldgnum, double *c, double *s, int *info);La_extern voidF77_NAME(dlasd8)(int *icompq, int *k, double *d,double *z, double *vf, double *vl, double *difl,double *difr, int *lddifr, double *dsigma, double *work, int *info);La_extern voidF77_NAME(dlasd9)(int *icompq, int *ldu, int *k,double *d, double *z, double *vf, double *vl,double *difl, double *difr, double *dsigma, double *work, int *info);La_extern voidF77_NAME(dlasda)(int *icompq, int *smlsiz, int *n,int *sqre, double *d, double *e, double *u, int*ldu, double *vt, int *k, double *difl, double *difr,double *z, double *poles, int *givptr, int *givcol,int *ldgcol, int *perm, double *givnum, double *c,double *s, double *work, int *iwork, int *info);La_extern voidF77_NAME(dlasdq)(const char* uplo, int *sqre, int *n, int *ncvt, int *nru, int *ncc, double *d, double *e,double *vt, int *ldvt, double *u, int *ldu,double *c, int *ldc, double *work, int *info FCLEN);La_extern voidF77_NAME(dlasdt)(int *n, int *lvl, int *nd, int *inode, int *ndiml, int *ndimr, int *msub);La_extern voidF77_NAME(dlasq5)(int *i0, int *n0, double *z,int *pp, double *tau, double *dmin, double *dmin1,double *dmin2, double *dn, double *dnm1, double *dnm2,int *ieee);La_extern voidF77_NAME(dlasq6)(int *i0, int *n0, double *z,int *pp, double *dmin, double *dmin1, double *dmin2,double *dn, double *dnm1, double *dnm2);La_extern voidF77_NAME(dlatdf)(int *ijob, int *n, double *z,int *ldz, double *rhs, double *rdsum, double *rdscal,int *ipiv, int *jpiv);La_extern voidF77_NAME(dlatrz)(int *m, int *n, int *l, double *a, int *lda, double *tau, double *work);La_extern voidF77_NAME(dormr3)(const char* side, const char* trans, int *m, int *n,int *k, int *l, double *a, int *lda, double *tau,double *c, int *ldc, double *work, int *info FCLEN FCLEN);La_extern voidF77_NAME(dormrz)(const char* side, const char* trans, int *m, int *n,int *k, int *l, double *a, int *lda, double *tau,double *c, int *ldc, double *work, int *lwork,int *info FCLEN FCLEN);La_extern voidF77_NAME(dptts2)(int *n, int *nrhs, double *d,double *e, double *b, int *ldb);La_extern voidF77_NAME(dsbgvd)(const char* jobz, const char* uplo, int *n, int *ka,int *kb, double *ab, int *ldab, double *bb, int *ldbb, double *w, double *z, int *ldz, double *work,int *lwork, int *iwork, int *liwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dsbgvx)(const char* jobz, const char* range, const char* uplo, int *n,int *ka, int *kb, double *ab, int *ldab, double *bb, int *ldbb, double *q, int *ldq, double *vl,double *vu, int *il, int *iu, double *abstol, int*m, double *w, double *z, int *ldz, double *work,int *iwork, int *ifail, int *info FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dspgvd)(int *itype, const char* jobz, const char* uplo, int *n, double *ap, double *bp, double *w, double *z,int *ldz, double *work, int *lwork, int *iwork,int *liwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dspgvx)(int *itype, const char* jobz, const char* range, const char*uplo, int *n, double *ap, double *bp, double *vl,double *vu, int *il, int *iu, double *abstol, int*m, double *w, double *z, int *ldz, double *work,int *iwork, int *ifail, int *info FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dstegr)(const char* jobz, const char* range, int *n, double *d, double *e, double *vl, double *vu, int *il,int *iu, double *abstol, int *m, double *w,double *z, int *ldz, int *isuppz, double *work,int *lwork, int *iwork, int *liwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dstevr)(const char* jobz, const char* range, int *n,double *d, double *e, double *vl, double *vu, int *il,int *iu, double *abstol, int *m, double *w,double *z, int *ldz, int *isuppz, double *work,int *lwork, int *iwork, int *liwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dsygvd)(int *itype, const char* jobz, const char* uplo, int *n, double *a, int *lda, double *b, int *ldb,double *w, double *work, int *lwork, int *iwork,int *liwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dsygvx)(int *itype, const char* jobz, const char* range,const char* uplo, int *n, double *a, int *lda, double *b,int *ldb, double *vl, double *vu, int *il, int *iu,double *abstol, int *m, double *w, double *z,int *ldz, double *work, int *lwork, int *iwork,int *ifail, int *info FCLEN FCLEN FCLEN);La_extern voidF77_NAME(dtgex2)(int *wantq, int *wantz, int *n,double *a, int *lda, double *b, int *ldb, double *q, int *ldq, double *z, int *ldz, int *j1, int *n1, int *n2, double *work, int *lwork, int *info);La_extern voidF77_NAME(dtgexc)(int *wantq, int *wantz, int *n,double *a, int *lda, double *b, int *ldb, double *q, int *ldq, double *z, int *ldz, int *ifst,int *ilst, double *work, int *lwork, int *info);La_extern voidF77_NAME(dtgsen)(int *ijob, int *wantq, int *wantz,int *select, int *n, double *a, int *lda, double *b, int *ldb, double *alphar, double *alphai, double *beta, double *q, int *ldq, double *z, int *ldz,int *m, double *pl, double *pr, double *dif,double *work, int *lwork, int *iwork, int *liwork,int *info);La_extern voidF77_NAME(dtgsna)(const char* job, const char* howmny, int *select,int *n, double *a, int *lda, double *b, int *ldb,double *vl, int *ldvl, double *vr, int *ldvr,double *s, double *dif, int *mm, int *m, double *work, int *lwork, int *iwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dtgsy2)(const char* trans, int *ijob, int *m, int *n, double *a, int *lda, double *b, int *ldb,double *c, int *ldc, double *d, int *ldd,double *e, int *lde, double *f, int *ldf, double *scale, double *rdsum, double *rdscal, int *iwork, int*pq, int *info FCLEN);La_extern voidF77_NAME(dtgsyl)(const char* trans, int *ijob, int *m, int *n, double *a, int *lda, double *b, int *ldb,double *c, int *ldc, double *d, int *ldd,double *e, int *lde, double *f, int *ldf, double *scale, double *dif, double *work, int *lwork, int *iwork, int *info FCLEN);La_extern voidF77_NAME(dtzrzf)(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork, int *info);La_extern voidF77_NAME(dpstrf)(const char* uplo, const int* n,double* a, const int* lda, int* piv, int* rank,double* tol, double *work, int* info FCLEN);/* This returns Fortran LOGICAL. Compiler-specific, butint_least32_t in gfortran */La_extern intF77_NAME(lsame)(const char* ca, const char* cb FCLEN FCLEN);La_extern voidF77_NAME(zbdsqr)(const char* uplo, int *n, int *ncvt, int *nru, int *ncc, double *d, double *e, Rcomplex *vt,int *ldvt, Rcomplex *u, int *ldu, Rcomplex *c,int *ldc, double *rwork, int *info FCLEN);La_extern voidF77_NAME(zdrot)(const int *n, const Rcomplex *cx, const int *incx,Rcomplex *cy, const int *incy, const double *c, const double *s);La_extern voidF77_NAME(zgebak)(const char* job, const char* side, int *n, int *ilo,int *ihi, double *scale, int *m, Rcomplex *v,int *ldv, int *info FCLEN FCLEN);La_extern voidF77_NAME(zgebal)(const char* job, int *n, Rcomplex *a, int*lda, int *ilo, int *ihi, double *scale, int *info FCLEN);La_extern voidF77_NAME(zgebd2)(int *m, int *n, Rcomplex *a,int *lda, double *d, double *e, Rcomplex *tauq,Rcomplex *taup, Rcomplex *work, int *info);La_extern voidF77_NAME(zgebrd)(int *m, int *n, Rcomplex *a,int *lda, double *d, double *e, Rcomplex *tauq,Rcomplex *taup, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zgehd2)(int *n, int *ilo, int *ihi,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zgehrd)(int *n, int *ilo, int *ihi,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zgelq2)(int *m, int *n, Rcomplex *a,int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zgelqf)(int *m, int *n, Rcomplex *a,int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,int *info);La_extern voidF77_NAME(zgeqr2)(int *m, int *n, Rcomplex *a,int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zgeqrf)(int *m, int *n, Rcomplex *a,int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,int *info);La_extern voidF77_NAME(zgetf2)(int *m, int *n, Rcomplex *a,int *lda, int *ipiv, int *info);La_extern voidF77_NAME(zgetrf)(int *m, int *n, Rcomplex *a,int *lda, int *ipiv, int *info);La_extern voidF77_NAME(zgetrs)(const char* trans, int *n, int *nrhs,Rcomplex *a, int *lda, int *ipiv, Rcomplex *b,int *ldb, int *info FCLEN);La_extern voidF77_NAME(zhetd2)(const char* uplo, int *n, Rcomplex *a, int *lda, double *d,double *e, Rcomplex *tau, int *info FCLEN);La_extern voidF77_NAME(zhetrd)(const char* uplo, int *n, Rcomplex *a,int *lda, double *d, double *e, Rcomplex *tau,Rcomplex *work, int *lwork, int *info FCLEN);La_extern voidF77_NAME(zhseqr)(const char* job, const char* compz, int *n, int *ilo,int *ihi, Rcomplex *h, int *ldh, Rcomplex *w,Rcomplex *z, int *ldz, Rcomplex *work, int *lwork,int *info FCLEN FCLEN);La_extern voidF77_NAME(zlabrd)(int *m, int *n, int *nb,Rcomplex *a, int *lda, double *d, double *e,Rcomplex *tauq, Rcomplex *taup, Rcomplex *x, int *ldx, Rcomplex *y, int *ldy);La_extern voidF77_NAME(zlacgv)(int *n, Rcomplex *x, int *incx);La_extern voidF77_NAME(zlacpy)(const char* uplo, int *m, int *n,Rcomplex *a, int *lda, Rcomplex *b, int *ldb FCLEN);La_extern voidF77_NAME(zlahqr)(int *wantt, int *wantz, int *n,int *ilo, int *ihi, Rcomplex *h, int *ldh,Rcomplex *w, int *iloz, int *ihiz, Rcomplex *z,int *ldz, int *info);La_extern doubleF77_NAME(zlange)(const char* norm, int *m, int *n, Rcomplex *a, int *lda,double *work FCLEN);La_extern doubleF77_NAME(zlanhe)(const char* norm, const char* uplo, int *n, Rcomplex *a,int *lda, double *work FCLEN FCLEN);La_extern doubleF77_NAME(zlanhs)(const char* norm, int *n, Rcomplex *a, int *lda,double *work FCLEN);La_extern voidF77_NAME(zlaqp2)(int *m, int *n, int *offset,Rcomplex *a, int *lda, int *jpvt, Rcomplex *tau,double *vn1, double *vn2, Rcomplex *work);La_extern voidF77_NAME(zlaqps)(int *m, int *n, int *offset, int*nb, int *kb, Rcomplex *a, int *lda, int *jpvt,Rcomplex *tau, double *vn1, double *vn2, Rcomplex *auxv, Rcomplex *f, int *ldf);La_extern voidF77_NAME(zlarf)(const char* side, int *m, int *n, Rcomplex*v, int *incv, Rcomplex *tau, Rcomplex *c, int *ldc, Rcomplex *work FCLEN);La_extern voidF77_NAME(zlarfb)(const char* side, const char* trans,const char* direct, const char* storev,int *m, int *n, int *k, Rcomplex *v, int *ldv,Rcomplex *t, int *ldt, Rcomplex *c, int *ldc, Rcomplex *work, int *ldworkFCLEN FCLEN FCLEN FCLEN);La_extern voidF77_NAME(zlarfg)(int *n, Rcomplex *alpha, Rcomplex *x, int *incx, Rcomplex *tau);La_extern voidF77_NAME(zlarft)(const char* direct, const char* storev, int *n, int *k, Rcomplex *v, int *ldv, Rcomplex *tau, Rcomplex *t, int *ldt FCLEN FCLEN);La_extern voidF77_NAME(zlarfx)(const char* side, int *m, int *n,Rcomplex *v, Rcomplex *tau, Rcomplex *c, int *ldc, Rcomplex *work FCLEN);La_extern voidF77_NAME(zlascl)(const char* type, int *kl, int *ku,double *cfrom, double *cto, int *m, int *n,Rcomplex *a, int *lda, int *info FCLEN);La_extern voidF77_NAME(zlaset)(const char* uplo, int *m, int *n,Rcomplex *alpha, Rcomplex *beta, Rcomplex *a, int *lda FCLEN);La_extern voidF77_NAME(zlasr)(const char* side, const char* pivot, const char* direct,int *m, int *n, double *c, double *s, Rcomplex *a, int *ldaFCLEN FCLEN FCLEN);La_extern voidF77_NAME(zlassq)(int *n, Rcomplex *x, int *incx,double *scale, double *sumsq);La_extern voidF77_NAME(zlaswp)(int *n, Rcomplex *a, int *lda,int *k1, int *k2, int *ipiv, int *incx);La_extern voidF77_NAME(zlatrd)(const char* uplo, int *n, int *nb,Rcomplex *a, int *lda, double *e, Rcomplex *tau,Rcomplex *w, int *ldw FCLEN);La_extern voidF77_NAME(zlatrs)(const char* uplo, const char* trans,const char* diag, const char* normin,int *n, Rcomplex *a, int *lda, Rcomplex *x,double *scale, double *cnorm, int *infoFCLEN FCLEN FCLEN FCLEN);La_extern voidF77_NAME(zsteqr)(const char* compz, int *n, double *d,double *e, Rcomplex *z, int *ldz, double *work,int *info FCLEN);/* ZTRCON estimates the reciprocal of the condition number of a* triangular matrix A, in either the 1-norm or the infinity-norm.*/La_extern voidF77_NAME(ztrcon)(const char* norm, const char* uplo, const char* diag,const int *n, const Rcomplex *a, const int *lda,double *rcond, Rcomplex *work, double *rwork, int *infoFCLEN FCLEN FCLEN);La_extern voidF77_NAME(ztrevc)(const char* side, const char* howmny, int *select,int *n, Rcomplex *t, int *ldt, Rcomplex *vl,int *ldvl, Rcomplex *vr, int *ldvr, int *mm, int*m, Rcomplex *work, double *rwork, int *infoFCLEN FCLEN);La_extern voidF77_NAME(zung2l)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zung2r)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zungbr)(const char* vect, int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info FCLEN);La_extern voidF77_NAME(zunghr)(int *n, int *ilo, int *ihi,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zungl2)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zunglq)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zungql)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zungqr)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zungr2)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info);La_extern voidF77_NAME(zungrq)(int *m, int *n, int *k,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info);La_extern voidF77_NAME(zungtr)(const char* uplo, int *n, Rcomplex *a,int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,int *info FCLEN);La_extern voidF77_NAME(zunm2r)(const char* side, const char* trans, int *m, int *n,int *k, Rcomplex *a, int *lda, Rcomplex *tau,Rcomplex *c, int *ldc, Rcomplex *work, int *infoFCLEN FCLEN);La_extern voidF77_NAME(zunmbr)(const char* vect, const char* side, const char* trans, int *m,int *n, int *k, Rcomplex *a, int *lda, Rcomplex*tau, Rcomplex *c, int *ldc, Rcomplex *work, int *lwork, int *info FCLEN FCLEN FCLEN);La_extern voidF77_NAME(zunml2)(const char* side, const char* trans, int *m, int *n,int *k, Rcomplex *a, int *lda, Rcomplex *tau,Rcomplex *c, int *ldc, Rcomplex *work, int *infoFCLEN FCLEN);La_extern voidF77_NAME(zunmlq)(const char* side, const char* trans, int *m, int *n,int *k, Rcomplex *a, int *lda, Rcomplex *tau,Rcomplex *c, int *ldc, Rcomplex *work, int *lwork,int *info FCLEN FCLEN);/* Added in R 3.1.0 *//* ZGESVD - compute the singular value decomposition (SVD); of a *//* real M-by-N matrix A, optionally computing the left and/or *//* right singular vectors */La_extern voidF77_NAME(zgesdd)(const char* jobz,const int *m, const int *n,Rcomplex *a, const int *lda, double *s,Rcomplex *u, const int *ldu,Rcomplex *vt, const int *ldvt,Rcomplex *work, const int *lwork, double *rwork,int *iwork, int *info FCLEN);La_extern voidF77_NAME(zgelsd)(int *m, int *n, int *nrhs,Rcomplex *a, int *lda, Rcomplex *b, int *ldb, double *s,double *rcond, int *rank,Rcomplex *work, int *lwork, double *rwork, int *iwork, int *info);/* =========================== DEPRECATED ==============================Routines below were deprecated in LAPACK 3.6.0, and are notincluded in a default build of LAPACK.Currently dgegv, dgeqpf, dggsvd and dggsvp are included in R, butthat may change in future.*//* DGEGV - compute for a pair of n-by-n real nonsymmetric *//* matrices A and B, the generalized eigenvalues (alphar +/- *//* alphai*i, beta);, and optionally, the left and/or right *//* generalized eigenvectors (VL and VR); */La_extern voidF77_NAME(dgegv)(const char* jobvl, const char* jobvr,const int* n, double* a, const int* lda,double* b, const int* ldb,double* alphar, double* alphai,const double* beta, double* vl, const int* ldvl,double* vr, const int* ldvr,double* work, const int* lwork, int* info FCLEN FCLEN);/* DGEQPF - compute a QR factorization with column pivoting of a *//* real M-by-N matrix A */La_extern voidF77_NAME(dgeqpf)(const int* m, const int* n, double* a, const int* lda,int* jpvt, double* tau, double* work, int* info);/* DGGSVD - compute the generalized singular value decomposition *//* (GSVD) of an M-by-N real matrix A and P-by-N real matrix B */La_extern voidF77_NAME(dggsvd)(const char* jobu, const char* jobv, const char* jobq,const int* m, const int* n, const int* p,const int* k, const int* l,double* a, const int* lda,double* b, const int* ldb,const double* alpha, const double* beta,double* u, const int* ldu,double* v, const int* ldv,double* q, const int* ldq,double* work, int* iwork, int* infoFCLEN FCLEN FCLEN);/* DTZRQF - reduce the M-by-N ( M<=N ); real upper trapezoidal *//* matrix A to upper triangular form by means of orthogonal *//* transformations */La_extern voidF77_NAME(dtzrqf)(const int* m, const int* n,double* a, const int* lda,double* tau, int* info);/* DLAHRD - reduce the first NB columns of a real general *//* n-by-(n-k+1); matrix A so that elements below the k-th *//* subdiagonal are zero */La_extern voidF77_NAME(dlahrd)(const int* n, const int* k, const int* nb,double* a, const int* lda,double* tau, double* t, const int* ldt,double* y, const int* ldy);/* DLATZM - apply a Householder matrix generated by DTZRQF to a *//* matrix */La_extern voidF77_NAME(dlatzm)(const char* side, const int* m, const int* n,const double* v, const int* incv,const double* tau, double* c1, double* c2,const int* ldc, double* work FCLEN);La_extern voidF77_NAME(dgegs)(const char* jobvsl, const char* jobvsr, int *n,double *a, int *lda, double *b, int *ldb, double *alphar, double *alphai, double *beta, double *vsl,int *ldvsl, double *vsr, int *ldvsr, double *work,int *lwork, int *info FCLEN FCLEN);La_extern voidF77_NAME(dgelsx)(int *m, int *n, int *nrhs,double *a, int *lda, double *b, int *ldb, int *jpvt, double *rcond, int *rank, double *work, int *info);La_extern voidF77_NAME(dggsvp)(const char* jobu, const char* jobv, const char* jobq, int *m,int *p, int *n, double *a, int *lda, double *b,int *ldb, double *tola, double *tolb, int *k, int*l, double *u, int *ldu, double *v, int *ldv,double *q, int *ldq, int *iwork, double *tau,double *work, int *info FCLEN FCLEN FCLEN);La_extern voidF77_NAME(zlahrd)(int *n, int *k, int *nb,Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *t,int *ldt, Rcomplex *y, int *ldy);#ifdef __cplusplus}#endif#endif /* R_LAPACK_H */// Local variables: ***// mode: outline-minor ***// outline-regexp: "^\^L\\|^//[*]+" ***// End: ***