EVOLUTION-MANAGER

Edit File: Lapack.h

/* * 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. Just those used (currently or previously) by C routines in R itself. 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> /* LAPACK function names are [dz]<name>(), where d denotes the real version of the function, z the complex version. (Only double-precision versions are used in R.) */ #ifdef __cplusplus extern "C" { #endif /* The LAPACK version: might change after installation with external 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 void F77_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); /* 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 void F77_NAME(ddisna)(const char* job, const int* m, const int* n, double* d, double* sep, int* info); //* 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 void F77_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); /* 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 void F77_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); /* DGBEQU - compute row and column scalings intended to equilibrate */ /* an M-by-N band matrix A and reduce its condition number */ La_extern void F77_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 void F77_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); /* 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 void F77_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 void F77_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); /* DGBTF2 - compute an LU factorization of a real m-by-n band */ /* matrix A using partial pivoting with row interchanges */ La_extern void F77_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 void F77_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 void F77_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); //* 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 void F77_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* info); /* DGEBAL - balance a general real matrix A */ La_extern void F77_NAME(dgebal)(const char* job, const int* n, double* a, const int* lda, int* ilo, int* ihi, double* scale, int* info); /* DGEBD2 - reduce a real general m by n matrix A to upper or */ /* lower bidiagonal form B by an orthogonal transformation */ La_extern void F77_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 void F77_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 void F77_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); /* DGEEQU - compute row and column scalings intended to equilibrate */ /* an M-by-N matrix A and reduce its condition number */ La_extern void F77_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 void F77_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* info); /* 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 void F77_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* info); /* DGEEV - compute for an N-by-N real nonsymmetric matrix A, the */ /* eigenvalues and, optionally, the left and/or right eigenvectors */ La_extern void F77_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); /* DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the */ /* eigenvalues and, optionally, the left and/or right eigenvectors */ La_extern void F77_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* info); /* DGEHD2 - reduce a real general matrix A to upper Hessenberg */ /* form H by an orthogonal similarity transformation */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* DGELSS - compute the minimum norm solution to a real linear */ /* least squares problem */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* DGERQ2 - compute an RQ factorization of a real m by n matrix A */ La_extern void F77_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 void F77_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 void F77_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 void F77_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); /* DGESVX - use the LU factorization to compute the solution to a */ /* real system of linear equations A * X = B, */ La_extern void F77_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); /* DGETF2 - compute an LU factorization of a general m-by-n */ /* matrix A using partial pivoting with row interchanges */ La_extern void F77_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 void F77_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 void F77_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 void F77_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); //* 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 void F77_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); /* DGGBAL - balance a pair of general real matrices (A,B); */ La_extern void F77_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* info); /* 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 void F77_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* info); /* DGGGLM - solve a general Gauss-Markov linear model (GLM) problem */ La_extern void F77_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 void F77_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); /* DGGLSE - solve the linear equality-constrained least squares */ /* (LSE) problem */ La_extern void F77_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 void F77_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 void F77_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 void F77_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* info); /* 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 void F77_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); /* DGTSV - solve the equation A*X = B, */ La_extern void F77_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 void F77_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); /* DGTTRF - compute an LU factorization of a real tridiagonal matrix */ /* A using elimination with partial pivoting and row interchanges */ La_extern void F77_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 void F77_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); //* 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 void F77_NAME(dopgtr)(const char* uplo, const int* n, const double* ap, const double* tau, double* q, const int* ldq, double* work, int* info); /* DOPMTR - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* DORG2L - generate an m by n real matrix Q with orthonormal */ /* columns, */ La_extern void F77_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 void F77_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 void F77_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); /* 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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_NAME(dorgtr)(const char* uplo, const int* n, double* a, const int* lda, const double* tau, double* work, const int* lwork, int* info); /* 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 void F77_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); /* 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 void F77_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* info); /* DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N */ /* matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* DORMHR - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* 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 void F77_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* info); /* DORMLQ - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* DORMQL - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* DORMQR - overwrite the general real M-by-N matrix C with SIDE = */ /* 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* 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 void F77_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); /* DORMRQ - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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); /* DORMTR - overwrite the general real M-by-N matrix C with */ /* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ La_extern void F77_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* info); //* 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 void F77_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); /* 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 void F77_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); /* 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 void F77_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); /* DPBSTF - compute a split Cholesky factorization of a real */ /* symmetric positive definite band matrix A */ La_extern void F77_NAME(dpbstf)(const char* uplo, const int* n, const int* kd, double* ab, const int* ldab, int* info); /* DPBSV - compute the solution to a real system of linear */ /* equations A * X = B, */ La_extern void F77_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); /* 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 void F77_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); /* DPBTF2 - compute the Cholesky factorization of a real */ /* symmetric positive definite band matrix A */ La_extern void F77_NAME(dpbtf2)(const char* uplo, const int* n, const int* kd, double* ab, const int* ldab, int* info); /* DPBTRF - compute the Cholesky factorization of a real */ /* symmetric positive definite band matrix A */ La_extern void F77_NAME(dpbtrf)(const char* uplo, const int* n, const int* kd, double* ab, const int* ldab, int* info); /* 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 void F77_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); //* 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 void F77_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); /* 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 void F77_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 void F77_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); /* DPOSV - compute the solution to a real system of linear */ /* equations A * X = B, */ La_extern void F77_NAME(dposv)(const char* uplo, const int* n, const int* nrhs, double* a, const int* lda, double* b, const int* ldb, int* info); /* 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 void F77_NAME(dposvx)(const int* fact, const char* uplo, const int* n, const int* nrhs, double* a, const int* lda, double* af, const int* ldaf, 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); /* DPOTF2 - compute the Cholesky factorization of a real */ /* symmetric positive definite matrix A */ La_extern void F77_NAME(dpotf2)(const char* uplo, const int* n, double* a, const int* lda, int* info); /* DPOTRF - compute the Cholesky factorization of a real */ /* symmetric positive definite matrix A */ La_extern void F77_NAME(dpotrf)(const char* uplo, const int* n, double* a, const int* lda, int* info); /* 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 void F77_NAME(dpotri)(const char* uplo, const int* n, double* a, const int* lda, int* info); /* 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 void F77_NAME(dpotrs)(const char* uplo, const int* n, const int* nrhs, const double* a, const int* lda, double* b, const int* ldb, int* info); /* 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 void F77_NAME(dppcon)(const char* uplo, const int* n, const double* ap, const double* anorm, double* rcond, double* work, int* iwork, int* info); /* 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 void F77_NAME(dppequ)(const char* uplo, const int* n, const double* ap, double* s, double* scond, double* amax, int* info); //* 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 void F77_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); /* DPPSV - compute the solution to a real system of linear */ /* equations A * X = B, */ La_extern void F77_NAME(dppsv)(const char* uplo, const int* n, const int* nrhs, const double* ap, double* b, const int* ldb, int* info); /* 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 void F77_NAME(dppsvx)(const char* fact, const char* uplo, const int* n, const int* nrhs, double* ap, double* afp, 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); /* DPPTRF - compute the Cholesky factorization of a real */ /* symmetric positive definite matrix A stored in packed format */ La_extern void F77_NAME(dpptrf)(const char* uplo, const int* n, double* ap, int* info); /* 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 void F77_NAME(dpptri)(const char* uplo, const int* n, double* ap, int* info); /* 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 void F77_NAME(dpptrs)(const char* uplo, const int* n, const int* nrhs, const double* ap, double* b, const int* ldb, int* info); //* 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 void F77_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 void F77_NAME(dpteqr)(const char* compz, const int* n, double* d, double* e, double* z, const int* ldz, double* work, int* info); /* 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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* DSBEVD - compute all the eigenvalues and, optionally, */ /* eigenvectors of a real symmetric band matrix A */ La_extern void F77_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); /* DSBEVX - compute selected eigenvalues and, optionally, */ /* eigenvectors of a real symmetric band matrix A */ La_extern void F77_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* info); /* DSBGST - reduce a real symmetric-definite banded generalized */ /* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */ La_extern void F77_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); /* 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 void F77_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); /* DSBTRD - reduce a real symmetric band matrix A to symmetric */ /* tridiagonal form T by an orthogonal similarity transformation */ La_extern void F77_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); //* 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 void F77_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); /* DSPEV - compute all the eigenvalues and, optionally, */ /* eigenvectors of a real symmetric matrix A in packed storage */ La_extern void F77_NAME(dspev)(const char* jobz, const char* uplo, const int* n, double* ap, double* w, double* z, const int* ldz, double* work, int* info); /* DSPEVD - compute all the eigenvalues and, optionally, */ /* eigenvectors of a real symmetric matrix A in packed storage */ La_extern void F77_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); /* DSPEVX - compute selected eigenvalues and, optionally, */ /* eigenvectors of a real symmetric matrix A in packed storage */ La_extern void F77_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); /* DSPGST - reduce a real symmetric-definite generalized */ /* eigenproblem to standard form, using packed storage */ La_extern void F77_NAME(dspgst)(const int* itype, const char* uplo, const int* n, double* ap, double* bp, int* info); /* 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 void F77_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); /* 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 void F77_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); /* DSPSV - compute the solution to a real system of linear */ /* equations A * X = B, */ La_extern void F77_NAME(dspsv)(const char* uplo, const int* n, const int* nrhs, double* ap, int* ipiv, double* b, const int* ldb, int* info); /* 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 void F77_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); /* DSPTRD - reduce a real symmetric matrix A stored in packed */ /* form to symmetric tridiagonal form T by an orthogonal */ /* similarity transformation */ La_extern void F77_NAME(dsptrd)(const char* uplo, const int* n, double* ap, double* d, double* e, double* tau, int* info); /* DSPTRF - compute the factorization of a real symmetric matrix */ /* A stored in packed format using the Bunch-Kaufman diagonal */ /* pivoting method */ La_extern void F77_NAME(dsptrf)(const char* uplo, const int* n, double* ap, int* ipiv, int* info); /* 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 void F77_NAME(dsptri)(const char* uplo, const int* n, double* ap, const int* ipiv, double* work, int* info); /* 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 void F77_NAME(dsptrs)(const char* uplo, const int* n, const int* nrhs, const double* ap, const int* ipiv, double* b, const int* ldb, int* info); //* Double precision Symmetric Tridiagonal matrices -> DST /* DSTEBZ - compute the eigenvalues of a symmetric tridiagonal */ /* matrix T */ La_extern void F77_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); /* DSTEDC - compute all eigenvalues and, optionally, eigenvectors */ /* of a symmetric tridiagonal matrix using the divide and conquer */ /* method */ La_extern void F77_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); /* DSTEIN - compute the eigenvectors of a real symmetric */ /* tridiagonal matrix T corresponding to specified eigenvalues, */ /* using inverse iteration */ La_extern void F77_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 void F77_NAME(dsteqr)(const char* compz, const int* n, double* d, double* e, double* z, const int* ldz, double* work, int* info); /* DSTERF - compute all eigenvalues of a symmetric tridiagonal */ /* matrix using the Pal-Walker-Kahan variant of the QL or QR */ /* algorithm */ La_extern void F77_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 void F77_NAME(dstev)(const char* jobz, const int* n, double* d, double* e, double* z, const int* ldz, double* work, int* info); /* DSTEVD - compute all eigenvalues and, optionally, eigenvectors */ /* of a real symmetric tridiagonal matrix */ La_extern void F77_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); /* DSTEVX - compute selected eigenvalues and, optionally, */ /* eigenvectors of a real symmetric tridiagonal matrix A */ La_extern void F77_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); //* 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 void F77_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); /* DSYEV - compute all eigenvalues and, optionally, eigenvectors */ /* of a real symmetric matrix A */ La_extern void F77_NAME(dsyev)(const char* jobz, const char* uplo, const int* n, double* a, const int* lda, double* w, double* work, const int* lwork, int* info); /* DSYEVD - compute all eigenvalues and, optionally, eigenvectors */ /* of a real symmetric matrix A */ La_extern void F77_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); /* DSYEVX - compute selected eigenvalues and, optionally, */ /* eigenvectors of a real symmetric matrix A */ La_extern void F77_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* info); /* DSYEVR - compute all eigenvalues and, optionally, eigenvectors */ /* of a real symmetric matrix A */ La_extern void F77_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); /* DSYGS2 - reduce a real symmetric-definite generalized */ /* eigenproblem to standard form */ La_extern void F77_NAME(dsygs2)(const int* itype, const char* uplo, const int* n, double* a, const int* lda, const double* b, const int* ldb, int* info); /* DSYGST - reduce a real symmetric-definite generalized */ /* eigenproblem to standard form */ La_extern void F77_NAME(dsygst)(const int* itype, const char* uplo, const int* n, double* a, const int* lda, const double* b, const int* ldb, int* info); /* 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 void F77_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); /* 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 void F77_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); /* DSYSV - compute the solution to a real system of linear */ /* equations A * X = B, */ La_extern void F77_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); /* DSYSVX - use the diagonal pivoting factorization to compute */ /* the solution to a real system of linear equations A * X = B, */ La_extern void F77_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); /* DSYTD2 - reduce a real symmetric matrix A to symmetric */ /* tridiagonal form T by an orthogonal similarity transformation */ La_extern void F77_NAME(dsytd2)(const char* uplo, const int* n, double* a, const int* lda, double* d, double* e, double* tau, int* info); /* DSYTF2 - compute the factorization of a real symmetric matrix */ /* A using the Bunch-Kaufman diagonal pivoting method */ La_extern void F77_NAME(dsytf2)(const char* uplo, const int* n, double* a, const int* lda, int* ipiv, int* info); /* DSYTRD - reduce a real symmetric matrix A to real symmetric */ /* tridiagonal form T by an orthogonal similarity transformation */ La_extern void F77_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); /* DSYTRF - compute the factorization of a real symmetric matrix */ /* A using the Bunch-Kaufman diagonal pivoting method */ La_extern void F77_NAME(dsytrf)(const char* uplo, const int* n, double* a, const int* lda, int* ipiv, double* work, const int* lwork, int* info); /* 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 void F77_NAME(dsytri)(const char* uplo, const int* n, double* a, const int* lda, const int* ipiv, double* work, int* info); /* 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 void F77_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); //* 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 void F77_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); /* 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 void F77_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); /* DTBTRS - solve a triangular system of the form A * X = B or */ /* A**T * X = B, */ La_extern void F77_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); //* 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 void F77_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); /* DTGSJA - compute the generalized singular value decomposition */ /* (GSVD); of two real upper triangular (or trapezoidal); matrices */ /* A and B */ La_extern void F77_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* info); //* 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 void F77_NAME(dtpcon)(const char* norm, const char* uplo, const char* diag, const int* n, const double* ap, double* rcond, double* work, int* iwork, int* info); /* 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 void F77_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* info); /* DTPTRI - compute the inverse of a real upper or lower */ /* triangular matrix A stored in packed format */ La_extern void F77_NAME(dtptri)(const char* uplo, const char* diag, const int* n, double* ap, int* info); /* DTPTRS - solve a triangular system of the form A * X = B or */ /* A**T * X = B, */ La_extern void F77_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* info); //* 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 void F77_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* info); /* DTREVC - compute some or all of the right and/or left */ /* eigenvectors of a real upper quasi-triangular matrix T */ La_extern void F77_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* info); /* 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 void F77_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); /* DTRRFS - provide error bounds and backward error estimates for */ /* the solution to a system of linear equations with a triangular */ /* coefficient matrix */ La_extern void F77_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* info); /* 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 void F77_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* info); /* 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 void F77_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); /* DTRSYL - solve the real Sylvester matrix equation */ La_extern void F77_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); /* DTRTI2 - compute the inverse of a real upper or lower */ /* triangular matrix */ La_extern void F77_NAME(dtrti2)(const char* uplo, const char* diag, const int* n, double* a, const int* lda, int* info); /* DTRTRI - compute the inverse of a real upper or lower */ /* triangular matrix A */ La_extern void F77_NAME(dtrtri)(const char* uplo, const char* diag, const int* n, double* a, const int* lda, int* info); /* DTRTRS - solve a triangular system of the form A * X = B or */ /* A**T * X = B */ La_extern void F77_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* info); //* 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 void F77_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* info); /* DHSEIN - use inverse iteration to find specified right and/or */ /* left eigenvectors of a real upper Hessenberg matrix H */ La_extern void F77_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* info); /* 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 void F77_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* info); /* 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 void F77_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 void F77_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 void F77_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 void F77_NAME(dlacpy)(const char* uplo, const int* m, const int* n, const double* a, const int* lda, double* b, const int* ldb); /* DLADIV - perform complex division in real arithmetic */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* 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 void F77_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 void F77_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 void F77_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 void F77_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 double F77_NAME(dlamch)(const char* cmach); /* 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 void F77_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 double F77_NAME(dlangb)(const char* norm, const int* n, const int* kl, const int* ku, const double* ab, const int* ldab, double* work); /* 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 double F77_NAME(dlange)(const char* norm, const int* m, const int* n, const double* a, const int* lda, double* work); /* 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 double F77_NAME(dlangt)(const char* norm, const int* n, const double* dl, const double* d, const double* du); /* 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 double F77_NAME(dlanhs)(const char* norm, const int* n, const double* a, const int* lda, double* work); /* 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 double F77_NAME(dlansb)(const char* norm, const char* uplo, const int* n, const int* k, const double* ab, const int* ldab, double* work); /* 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 double F77_NAME(dlansp)(const char* norm, const char* uplo, const int* n, const double* ap, double* work); /* 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 double F77_NAME(dlanst)(const char* norm, const int* n, const double* d, const double* e); /* 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 double F77_NAME(dlansy)(const char* norm, const char* uplo, const int* n, const double* a, const int* lda, double* work); /* 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 double F77_NAME(dlantb)(const char* norm, const char* uplo, const char* diag, const int* n, const int* k, const double* ab, const int* ldab, double* work); /* 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 double F77_NAME(dlantp)(const char* norm, const char* uplo, const char* diag, const int* n, const double* ap, double* work); /* 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 double F77_NAME(dlantr)(const char* norm, const char* uplo, const char* diag, const int* m, const int* n, const double* a, const int* lda, double* work); /* DLANV2 - compute the Schur factorization of a real 2-by-2 */ /* nonsymmetric matrix in standard form */ La_extern void F77_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 void F77_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 void F77_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 double F77_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 double F77_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 void F77_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, char* equed); /* DLAQGE - equilibrate a general M by N matrix A using the row */ /* and scaling factors in the vectors R and C */ La_extern void F77_NAME(dlaqge)(const int* m, const int* n, double* a, const int* lda, double* r, double* c, double* rowcnd, double* colcnd, const double* amax, char* equed); /* DLAQSB - equilibrate a symmetric band matrix A using the */ /* scaling factors in the vector S */ La_extern void F77_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, char* equed); /* DLAQSP - equilibrate a symmetric matrix A using the scaling */ /* factors in the vector S */ La_extern void F77_NAME(dlaqsp)(const char* uplo, const int* n, double* ap, const double* s, const double* scond, const double* amax, int* equed); /* DLAQSY - equilibrate a symmetric matrix A using the scaling */ /* factors in the vector S */ La_extern void F77_NAME(dlaqsy)(const char* uplo, const int* n, double* a, const int* lda, const double* s, const double* scond, const double* amax, int* equed); /* DLAQTR - solve the real quasi-triangular system */ /* op(T) * p = scale*c */ La_extern void F77_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 void F77_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 void F77_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); /* 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 void F77_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* lwork); /* DLARFG - generate a real elementary reflector H of order n, */ /* such that H * ( alpha ) = ( beta ), H' * H = I */ La_extern void F77_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 void F77_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); /* DLARFX - apply a real elementary reflector H to a real m by n */ /* matrix C, from either the left or the right */ La_extern void F77_NAME(dlarfx)(const char* side, const int* m, const int* n, const double* v, const double* tau, double* c, const int* ldc, double* work); /* DLARGV - generate a vector of real plane rotations, determined */ /* by elements of the real vectors x and y */ La_extern void F77_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 void F77_NAME(dlarnv)(const int* idist, int* iseed, const int* n, double* x); /* DLARTG - generate a plane rotation so that [ CS SN ] */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* DLASET - initialize an m-by-n matrix A to BETA on the diagonal */ /* and ALPHA on the offdiagonals */ La_extern void F77_NAME(dlaset)(const char* uplo, const int* m, const int* n, const double* alpha, const double* beta, double* a, const int* lda); /* DLASQ1 - DLASQ1 computes the singular values of a real N-by-N */ /* bidiagonal matrix with diagonal D and off-diagonal E */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* DLASRT - the numbers in D in increasing order (if ID = 'I'); */ /* or in decreasing order (if ID = 'D' ); */ La_extern void F77_NAME(dlasrt)(const char* id, const int* n, double* d, int* info); /* DLASSQ - return the values scl and smsq such that ( scl**2 */ /* );*smsq = x( 1 );**2 +...+ x( n );**2 + ( scale**2 );*sumsq, */ La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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); /* 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 void F77_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* info); /* 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 void F77_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* info); /* 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 void F77_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); /* DLATRS - solve one of the triangular systems A *x = s*b or */ /* A'*x = s*b with scaling to prevent overflow */ La_extern void F77_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* info); /* 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 void F77_NAME(dlauu2)(const char* uplo, const int* n, double* a, const int* lda, int* info); /* 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 void F77_NAME(dlauum)(const char* uplo, const int* n, double* a, const int* lda, int* info); /* ======================================================================== */ //* Selected Double Complex Lapack Routines /* ======== */ /* IZMAX1 finds the index of the element whose real part has maximum * absolute value. */ La_extern int F77_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 void F77_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); /* ZGESV computes the solution to a complex system of linear equations */ La_extern void F77_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 void F77_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 void F77_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); /* ZTRTRS solves triangular systems */ La_extern void F77_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 *info); /* 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 void F77_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); /* ZGHEEV - compute all eigenvalues and, optionally, eigenvectors */ /* of a Hermitian matrix A */ La_extern void F77_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); /* ZGGEEV - compute all eigenvalues and, optionally, eigenvectors */ /* of a complex non-symmetric matrix A */ La_extern void F77_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); /* NOTE: The following entry points were traditionally in this file, but are not provided by R's libRlapack */ /* DZSUM1 - take the sum of the absolute values of a complex */ /* vector and returns a double precision result */ La_extern double F77_NAME(dzsum1)(const int *n, Rcomplex *CX, const int *incx); /* ZLACN2 estimates the 1-norm of a square, complex matrix A. * Reverse communication is used for evaluating matrix-vector products. */ La_extern void F77_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 */ La_extern double F77_NAME(zlantr)(const char *norm, const char *uplo, const char *diag, const int *m, const int *n, Rcomplex *a, const int *lda, double *work); /* ======================================================================== */ //* Other double precision and double complex Lapack routines provided by libRlapack. /* These are extracted from the CLAPACK headers. */ La_extern void F77_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 *info); La_extern void F77_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 void F77_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 void F77_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); La_extern void F77_NAME(dgetc2)(int *n, double *a, int *lda, int *ipiv, int *jpiv, int *info); typedef int (*L_fp)(); La_extern void F77_NAME(dggesx)(char *jobvsl, char *jobvsr, char *sort, L_fp delctg, 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 *info); La_extern void F77_NAME(dggev)(char *jobvl, 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); La_extern void F77_NAME(dggevx)(char *balanc, char *jobvl, char *jobvr, 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); La_extern void F77_NAME(dgtts2)(int *itrans, int *n, int *nrhs, double *dl, double *d, double *du, double *du2, int *ipiv, double *b, int *ldb); La_extern void F77_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 void F77_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 void F77_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 void F77_NAME(dlalsd)(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); La_extern void F77_NAME(dlamc1)(int *beta, int *t, int *rnd, int *ieee1); La_extern void F77_NAME(dlamc2)(int *beta, int *t, int *rnd, double *eps, int *emin, double *rmin, int *emax, double *rmax); La_extern double F77_NAME(dlamc3)(double *a, double *b); La_extern void F77_NAME(dlamc4)(int *emin, double *start, int *base); La_extern void F77_NAME(dlamc5)(int *beta, int *p, int *emin, int *ieee, int *emax, double *rmax); La_extern void F77_NAME(dlaqp2)(int *m, int *n, int *offset, double *a, int *lda, int *jpvt, double *tau, double *vn1, double *vn2, double *work); La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_NAME(dlarz)(char *side, int *m, int *n, int *l, double *v, int *incv, double *tau, double *c, int *ldc, double *work); La_extern void F77_NAME(dlarzb)(char *side, char *trans, char *direct, 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 *ldwork); La_extern void F77_NAME(dlarzt)(char *direct, char *storev, int *n, int * k, double *v, int *ldv, double *tau, double *t, int *ldt); La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_NAME(dlasd4)(int *n, int *i, double *d, double *z, double *delta, double *rho, double * sigma, double *work, int *info); La_extern void F77_NAME(dlasd5)(int *i, double *d, double *z, double *delta, double *rho, double *dsigma, double * work); La_extern void F77_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 void F77_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 void F77_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 void F77_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 void F77_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 void F77_NAME(dlasdq)(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); La_extern void F77_NAME(dlasdt)(int *n, int *lvl, int *nd, int * inode, int *ndiml, int *ndimr, int *msub); La_extern void F77_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 void F77_NAME(dlasq6)(int *i0, int *n0, double *z, int *pp, double *dmin, double *dmin1, double *dmin2, double *dn, double *dnm1, double *dnm2); La_extern void F77_NAME(dlatdf)(int *ijob, int *n, double *z, int *ldz, double *rhs, double *rdsum, double *rdscal, int *ipiv, int *jpiv); La_extern void F77_NAME(dlatrz)(int *m, int *n, int *l, double * a, int *lda, double *tau, double *work); La_extern void F77_NAME(dormr3)(char *side, char *trans, int *m, int *n, int *k, int *l, double *a, int *lda, double *tau, double *c, int *ldc, double *work, int *info); La_extern void F77_NAME(dormrz)(char *side, 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); La_extern void F77_NAME(dptts2)(int *n, int *nrhs, double *d, double *e, double *b, int *ldb); La_extern void F77_NAME(dsbgvd)(char *jobz, 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); La_extern void F77_NAME(dsbgvx)(char *jobz, char *range, 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); La_extern void F77_NAME(dspgvd)(int *itype, char *jobz, char *uplo, int * n, double *ap, double *bp, double *w, double *z, int *ldz, double *work, int *lwork, int *iwork, int *liwork, int *info); La_extern void F77_NAME(dspgvx)(int *itype, char *jobz, char *range, 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); La_extern void F77_NAME(dstegr)(char *jobz, 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); La_extern void F77_NAME(dstevr)(char *jobz, 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); La_extern void F77_NAME(dsygvd)(int *itype, char *jobz, char *uplo, int * n, double *a, int *lda, double *b, int *ldb, double *w, double *work, int *lwork, int *iwork, int *liwork, int *info); La_extern void F77_NAME(dsygvx)(int *itype, char *jobz, char *range, 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); La_extern void F77_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 void F77_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 void F77_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 void F77_NAME(dtgsna)(char *job, 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); La_extern void F77_NAME(dtgsy2)(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); La_extern void F77_NAME(dtgsyl)(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); La_extern void F77_NAME(dtzrzf)(int *m, int *n, double *a, int * lda, double *tau, double *work, int *lwork, int *info); La_extern void F77_NAME(dpstrf)(const char* uplo, const int* n, double* a, const int* lda, int* piv, int* rank, double* tol, double *work, int* info); La_extern int F77_NAME(lsame)(const char *ca, const char *cb); La_extern void F77_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); La_extern void F77_NAME(zdrot)(const int *n, const Rcomplex *cx, const int *incx, Rcomplex *cy, const int *incy, const double *c, const double *s); La_extern void F77_NAME(zgebak)(const char *job, const char *side, int *n, int *ilo, int *ihi, double *scale, int *m, Rcomplex *v, int *ldv, int *info); La_extern void F77_NAME(zgebal)(const char *job, int *n, Rcomplex *a, int *lda, int *ilo, int *ihi, double *scale, int *info); La_extern void F77_NAME(zgebd2)(int *m, int *n, Rcomplex *a, int *lda, double *d, double *e, Rcomplex *tauq, Rcomplex *taup, Rcomplex *work, int *info); La_extern void F77_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 void F77_NAME(zgehd2)(int *n, int *ilo, int *ihi, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *info); La_extern void F77_NAME(zgehrd)(int *n, int *ilo, int *ihi, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zgelq2)(int *m, int *n, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info); La_extern void F77_NAME(zgelqf)(int *m, int *n, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info); La_extern void F77_NAME(zgeqr2)(int *m, int *n, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *info); La_extern void F77_NAME(zgeqrf)(int *m, int *n, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info); La_extern void F77_NAME(zgetf2)(int *m, int *n, Rcomplex *a, int *lda, int *ipiv, int *info); La_extern void F77_NAME(zgetrf)(int *m, int *n, Rcomplex *a, int *lda, int *ipiv, int *info); La_extern void F77_NAME(zgetrs)(const char *trans, int *n, int *nrhs, Rcomplex *a, int *lda, int *ipiv, Rcomplex *b, int *ldb, int *info); La_extern void F77_NAME(zhetd2)(const char *uplo, int *n, Rcomplex *a, int *lda, double *d, double *e, Rcomplex *tau, int *info); La_extern void F77_NAME(zhetrd)(const char *uplo, int *n, Rcomplex *a, int *lda, double *d, double *e, Rcomplex *tau, Rcomplex *work, int *lwork, int *info); La_extern void F77_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); La_extern void F77_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 void F77_NAME(zlacgv)(int *n, Rcomplex *x, int *incx); La_extern void F77_NAME(zlacpy)(const char *uplo, int *m, int *n, Rcomplex *a, int *lda, Rcomplex *b, int *ldb); La_extern void F77_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 double F77_NAME(zlange)(const char *norm, int *m, int *n, Rcomplex *a, int *lda, double *work); La_extern double F77_NAME(zlanhe)(const char *norm, const char *uplo, int *n, Rcomplex *a, int *lda, double *work); La_extern double F77_NAME(zlanhs)(const char *norm, int *n, Rcomplex *a, int *lda, double *work); La_extern void F77_NAME(zlaqp2)(int *m, int *n, int *offset, Rcomplex *a, int *lda, int *jpvt, Rcomplex *tau, double *vn1, double *vn2, Rcomplex *work); La_extern void F77_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 void F77_NAME(zlarf)(const char *side, int *m, int *n, Rcomplex *v, int *incv, Rcomplex *tau, Rcomplex *c, int * ldc, Rcomplex *work); La_extern void F77_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 *ldwork); La_extern void F77_NAME(zlarfg)(int *n, Rcomplex *alpha, Rcomplex * x, int *incx, Rcomplex *tau); La_extern void F77_NAME(zlarft)(const char *direct, const char *storev, int *n, int * k, Rcomplex *v, int *ldv, Rcomplex *tau, Rcomplex * t, int *ldt); La_extern void F77_NAME(zlarfx)(const char *side, int *m, int *n, Rcomplex *v, Rcomplex *tau, Rcomplex *c, int * ldc, Rcomplex *work); La_extern void F77_NAME(zlascl)(const char *type, int *kl, int *ku, double *cfrom, double *cto, int *m, int *n, Rcomplex *a, int *lda, int *info); La_extern void F77_NAME(zlaset)(const char *uplo, int *m, int *n, Rcomplex *alpha, Rcomplex *beta, Rcomplex *a, int * lda); La_extern void F77_NAME(zlasr)(const char *side, const char *pivot, const char *direct, int *m, int *n, double *c, double *s, Rcomplex *a, int *lda); La_extern void F77_NAME(zlassq)(int *n, Rcomplex *x, int *incx, double *scale, double *sumsq); La_extern void F77_NAME(zlaswp)(int *n, Rcomplex *a, int *lda, int *k1, int *k2, int *ipiv, int *incx); La_extern void F77_NAME(zlatrd)(const char *uplo, int *n, int *nb, Rcomplex *a, int *lda, double *e, Rcomplex *tau, Rcomplex *w, int *ldw); La_extern void F77_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 *info); La_extern void F77_NAME(zsteqr)(const char *compz, int *n, double *d, double *e, Rcomplex *z, int *ldz, double *work, int *info); /* ZTRCON estimates the reciprocal of the condition number of a * triangular matrix A, in either the 1-norm or the infinity-norm. */ La_extern void F77_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 *info); La_extern void F77_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 *info); La_extern void F77_NAME(zung2l)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *info); La_extern void F77_NAME(zung2r)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *info); La_extern void F77_NAME(zungbr)(const char *vect, int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zunghr)(int *n, int *ilo, int *ihi, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zungl2)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *info); La_extern void F77_NAME(zunglq)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zungql)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zungqr)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zungr2)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *info); La_extern void F77_NAME(zungrq)(int *m, int *n, int *k, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * work, int *lwork, int *info); La_extern void F77_NAME(zungtr)(const char *uplo, int *n, Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, int *info); La_extern void F77_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 *info); La_extern void F77_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); La_extern void F77_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 *info); La_extern void F77_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); /* 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 void F77_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); La_extern void F77_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 not included in a default build of LAPACK. Currently dgegv, dgeqpf, dggsvd and dggsvp are included in R, but that 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 void F77_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); /* DGEQPF - compute a QR factorization with column pivoting of a */ /* real M-by-N matrix A */ La_extern void F77_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 void F77_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* info); /* DTZRQF - reduce the M-by-N ( M<=N ); real upper trapezoidal */ /* matrix A to upper triangular form by means of orthogonal */ /* transformations */ La_extern void F77_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 void F77_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 void F77_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); La_extern void F77_NAME(dgegs)(char *jobvsl, 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); La_extern void F77_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 void F77_NAME(dggsvp)(char *jobu, char *jobv, 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); La_extern void F77_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: ***