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Lapack.h

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 2003-4 The R Development Core Team.
 *
 *  This program 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 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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#ifndef R_LAPACK_H
#define R_LAPACK_H
/* C declarations of BLAS routines.  R packages that use these should have */
/* src/Makevars declare PKG_LIBS = $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) */

#include <R_ext/RS.h>         /* for F77_... */
#include <R_ext/Complex.h>    /* for Rcomplex */
#include <R_ext/BLAS.h>

#ifdef  __cplusplus
extern "C" {
#endif

/* Selected Double Precision Lapack Routines 
   ========
 */

/* Double precision BiDiagonal matrices */

/* DBDSQR - compute the singular value decomposition (SVD) of a real */
/* N-by-N (upper or lower) bidiagonal matrix B */
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 */
void
F77_NAME(ddisna)(const char* job, const int* m, const int* n,
             double* d, double* sep, int* info);

/* Double precision General Banded matrices */

/* DGBBRD - reduce a real general m-by-n band matrix A to upper */
/* bidiagonal form B by an orthogonal transformation  */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */

/* 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  */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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);
/* 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); */
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);
/* DGEHD2 - reduce a real general matrix A to upper Hessenberg */
/* form H by an orthogonal similarity transformation */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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);
/* DGEQPF - compute a QR factorization with column pivoting of a */
/* real M-by-N matrix A */
void
F77_NAME(dgeqpf)(const int* m, const int* n, double* a, const int* lda,
             int* jpvt, double* tau, double* work, int* info);
/* DGEQR2 - compute a QR factorization of a real m by n matrix A */
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 */
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 */
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 */
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 */
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, */
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 */
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, */
void
F77_NAME(dgesvx)(const int* 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 */
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 */
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 */
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 */
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 */

/* 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 */
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); */
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)*/
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 */
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 */
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 */
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 */
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 */
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);
/* DGGSVD - compute the generalized singular value decomposition */
/* (GSVD) of an M-by-N real matrix A and P-by-N real matrix B */
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);

/* Double precision General Tridiagonal matrices */

/* DGTCON - estimate the reciprocal of the condition number of a real */
/* tridiagonal matrix A using the LU factorization as computed by DGTTRF */
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 */
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, */
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, */
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 */
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, */
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 */

/* 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 */
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' */
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, */
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, */
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 */
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 */
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, */
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, */
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, */
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, */
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, */
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 */
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 */
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', */
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', */
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' */
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' */
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', */
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'  */
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' */
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' */
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', */
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' */
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' */
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 */ 

/* 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 */
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); */
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 */
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 */
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, */
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, */
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 */
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 */
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 */
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 */

/* 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 */
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); */
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, */
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, */
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, */
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 */
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 */
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 */
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 */
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 */
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); */
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 */

/* 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 */
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, */
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, */
void
F77_NAME(dppsvx)(const int* 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 */
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  */
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 */
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 */

/* 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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
void
F77_NAME(drscl)(const int* n, const double* da,
            double* x, const int* incx);

/* Double precision Symmetric Band matrices */

/* DSBEV - compute all the eigenvalues and, optionally, */
/* eigenvectors of a real symmetric band matrix A */
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 */
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 */
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, */
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 */
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 */
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 */

/* 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 */
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 */
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 */
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 */
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 */
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 */
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 */
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, */
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 */
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 */
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 */
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 */
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 */
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 */

/* DSTEBZ - compute the eigenvalues of a symmetric tridiagonal */
/* matrix T */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */

/* 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 */
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 */
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 */
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 */
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                                    */
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 */
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 */
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 */
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 */
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, */
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, */
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 */
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 */
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 */
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 */
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 */
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 */
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 */

/* DTBCON - estimate the reciprocal of the condition number of a */
/* triangular band matrix A, in either the 1-norm or the */
/* infinity-norm */
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 */
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,  */
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 */

/* DTGEVC - compute some or all of the right and/or left */
/* generalized eigenvectors of a pair of real upper triangular */
/* matrices (A,B); */
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 */
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 */

/* DTPCON - estimate the reciprocal of the condition number of a */
/* packed triangular matrix A, in either the 1-norm or the */
/* infinity-norm */
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 */
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);

/* Double precision TRiangular matrices */

/* DTPTRI - compute the inverse of a real upper or lower */
/* triangular matrix A stored in packed format */
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, */
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); 

/* DTRCON - estimate the reciprocal of the condition number of a */
/* triangular matrix A, in either the 1-norm or the infinity-norm */
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 */
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 */
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 */
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, */
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); */
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 */
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 */
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 */
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  */
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); 

/* DTZRQF - reduce the M-by-N ( M<=N ); real upper trapezoidal */
/* matrix A to upper triangular form by means of orthogonal */
/* transformations  */
void
F77_NAME(dtzrqf)(const int* m, const int* n,
             double* a, const int* lda,
             double* tau, int* info);



/* Double precision utilties 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 */
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 */
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 */
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 */
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 */
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 */
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 */
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  */
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 ] */
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  */
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 */
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 */
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 */
void
F77_NAME(dlaed2)(const int* k, const int* n, double* d,
             double* q, const int* ldq, int* indxq,
             double* rho, const int* cutpnt, double* z,
             double* dlamda, double* q2, const int *ldq2,
             int* indxc, int* w, int* indxp, int* indx,
             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 */
void
F77_NAME(dlaed3)(const int* k, const int* kstart,
             const int *kstop, const int* n,
             double* d, double* q, const int* ldq,
             const double* rho, const int* cutpnt,
             double* dlamda, int* q2, const int* ldq2,
             int* indxc, int* ctot, double* w,
             double* s, const int* lds, 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 */
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  */
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  */
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 */
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 */
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 */
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 */
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 */
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 ] */
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 */
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 avoid */
/* over-/underflow */
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 */
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, */
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 */
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, */
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 */
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);
/* 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 */
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);
/* DLAIC1 - apply one step of incremental condition estimation in */
/* its simplest version */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 ); */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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  */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
void
F77_NAME(dlarnv)(const int* idist, int* iseed, const int* n, double* x);
/* DLARTG - generate a plane rotation so that   [ CS SN ]  */
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 */
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); */
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 ] */
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 */
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 */
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 */
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 */
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 */
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 */
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, */
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' ); */
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, */
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 ] */
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 */
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, */
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 */
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 */
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 */
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 */
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 */
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);
/* DLATZM - apply a Householder matrix generated by DTZRQF to a */
/* matrix */
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);
/* 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 */
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 */
void
F77_NAME(dlauum)(const char* uplo, const int* n,
             double* a, const int* lda, int* info);


/* ======================================================================== */

/* Selected Double Complex Lapack Routines 
   ========
 */

/* ZGESV computes the solution to a complex system of linear equations */
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 */
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 */
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 */
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                                          */
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 */
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 */
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  */
double
F77_NAME(dzsum1)(const int* n, Rcomplex *CX, const int* incx);

/* 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 */
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.
*/

void
F77_NAME(dbdsdc)(char *uplo, 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);

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);
 
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);
 
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);

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.                                   */
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);
 
void
F77_NAME(dgetc2)(int *n, double *a, int *lda, int 
      *ipiv, int *jpiv, int *info);

typedef int (*L_fp)();
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);
 
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);
 
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);
 
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);
 
void
F77_NAME(dgtts2)(int *itrans, int *n, int *nrhs, 
      double *dl, double *d, double *du, double *du2, 
      int *ipiv, double *b, int *ldb);
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);

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);
 
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);
 
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);
 
void
F77_NAME(dlamc1)(int *beta, int *t, int *rnd, int 
      *ieee1);
 
void
F77_NAME(dlamc2)(int *beta, int *t, int *rnd, 
      double *eps, int *emin, double *rmin, int *emax, 
      double *rmax);
 
void
F77_NAME(dlamc3)(double *a, double *b);
 
void
F77_NAME(dlamc4)(int *emin, double *start, int *base);
 
void
F77_NAME(dlamc5)(int *beta, int *p, int *emin, 
      int *ieee, int *emax, double *rmax);

void
F77_NAME(dlaqp2)(int *m, int *n, int *offset, 
      double *a, int *lda, int *jpvt, double *tau, 
      double *vn1, double *vn2, double *work);
 
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);

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);
 
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);
 
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);
 
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);
 
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);

void
F77_NAME(dlarz)(char *side, int *m, int *n, int *l, 
      double *v, int *incv, double *tau, double *c, 
      int *ldc, double *work);
 
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);
 
void
F77_NAME(dlarzt)(char *direct, char *storev, int *n, int *
      k, double *v, int *ldv, double *tau, double *t, 
      int *ldt);
 
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);
 
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);
 
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);
 
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);
 
void
F77_NAME(dlasd4)(int *n, int *i, double *d, 
      double *z, double *delta, double *rho, double *
      sigma, double *work, int *info);
 
void
F77_NAME(dlasd5)(int *i, double *d, double *z, 
      double *delta, double *rho, double *dsigma, double *
      work);
 
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);
 
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);
 
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);
 
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);

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);
 
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);
 
void
F77_NAME(dlasdt)(int *n, int *lvl, int *nd, int *
      inode, int *ndiml, int *ndimr, int *msub);
 
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);
 
void
F77_NAME(dlasq6)(int *i0, int *n0, double *z, 
      int *pp, double *dmin, double *dmin1, double *dmin2,
       double *dn, double *dnm1, double *dnm2);
 
void
F77_NAME(dlatdf)(int *ijob, int *n, double *z, 
      int *ldz, double *rhs, double *rdsum, double *rdscal, 
      int *ipiv, int *jpiv);
 
void
F77_NAME(dlatrz)(int *m, int *n, int *l, double *
      a, int *lda, double *tau, double *work);
 
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);

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);

void
F77_NAME(dptts2)(int *n, int *nrhs, double *d, 
      double *e, double *b, int *ldb);
 
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);
 
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);

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);

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);

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);
 
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);
 
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);
 
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);
 
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);
 
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);
 
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);
 
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);
 
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);
 
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);
 
void
F77_NAME(dtzrzf)(int *m, int *n, double *a, int *
      lda, double *tau, double *work, int *lwork, int *info);
 

void
F77_NAME(zbdsqr)(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);
 
void
F77_NAME(zdrot)(int *n, Rcomplex *cx, int *incx, 
      Rcomplex *cy, int *incy, double *c, double *s);
 
void
F77_NAME(zgebak)(char *job, char *side, int *n, int *ilo,
      int *ihi, double *scale, int *m, Rcomplex *v,
      int *ldv, int *info);

void
F77_NAME(zgebal)(char *job, int *n, Rcomplex *a, int
      *lda, int *ilo, int *ihi, double *scale, int *info);

void
F77_NAME(zgebd2)(int *m, int *n, Rcomplex *a,
      int *lda, double *d, double *e, Rcomplex *tauq,
      Rcomplex *taup, Rcomplex *work, int *info);

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);
void
F77_NAME(zgehd2)(int *n, int *ilo, int *ihi,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *info);

void
F77_NAME(zgehrd)(int *n, int *ilo, int *ihi,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zgelq2)(int *m, int *n, Rcomplex *a,
      int *lda, Rcomplex *tau, Rcomplex *work, int *info);

void
F77_NAME(zgelqf)(int *m, int *n, Rcomplex *a,
      int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,
       int *info);

void
F77_NAME(zgeqr2)(int *m, int *n, Rcomplex *a,
      int *lda, Rcomplex *tau, Rcomplex *work, int *info);

void
F77_NAME(zgeqrf)(int *m, int *n, Rcomplex *a,
             int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,
             int *info);

void
F77_NAME(zgetf2)(int *m, int *n, Rcomplex *a,
      int *lda, int *ipiv, int *info);

void
F77_NAME(zgetrf)(int *m, int *n, Rcomplex *a,
      int *lda, int *ipiv, int *info);

void
F77_NAME(zgetrs)(char *trans, int *n, int *nrhs,
      Rcomplex *a, int *lda, int *ipiv, Rcomplex *b,
      int *ldb, int *info);


void
F77_NAME(zhetd2)(char *uplo, int *n, Rcomplex *a, int *lda, double *d,
             double *e, Rcomplex *tau, int *info);

void
F77_NAME(zhetrd)(char *uplo, int *n, Rcomplex *a,
      int *lda, double *d, double *e, Rcomplex *tau,
      Rcomplex *work, int *lwork, int *info);

void
F77_NAME(zhseqr)(char *job, char *compz, int *n, int *ilo,
       int *ihi, Rcomplex *h, int *ldh, Rcomplex *w,
      Rcomplex *z, int *ldz, Rcomplex *work, int *lwork,
       int *info);

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);

void
F77_NAME(zlacgv)(int *n, Rcomplex *x, int *incx);

void
F77_NAME(zlacpy)(char *uplo, int *m, int *n,
      Rcomplex *a, int *lda, Rcomplex *b, int *ldb);

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);

void
F77_NAME(zlahrd)(int *n, int *k, int *nb,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *t,
      int *ldt, Rcomplex *y, int *ldy);

void
F77_NAME(zlange)(char *norm, int *m, int *n, Rcomplex *a, int *lda, 
             double *work);

void
F77_NAME(zlanhe)(char *norm,  char *uplo, int *n, Rcomplex *a,
               int *lda, double *work);

void
F77_NAME(zlanhs)(char *norm, int *n, Rcomplex *a, int *lda, double *work);


void
F77_NAME(zlaqp2)(int *m, int *n, int *offset,
      Rcomplex *a, int *lda, int *jpvt, Rcomplex *tau,
      double *vn1, double *vn2, Rcomplex *work);

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);

void
F77_NAME(zlarf)(char *side, int *m, int *n, Rcomplex
      *v, int *incv, Rcomplex *tau, Rcomplex *c, int *
      ldc, Rcomplex *work);

void
F77_NAME(zlarfb)(char *side, char *trans, char *direct, char *
      storev, int *m, int *n, int *k, Rcomplex *v, int
      *ldv, Rcomplex *t, int *ldt, Rcomplex *c, int *
      ldc, Rcomplex *work, int *ldwork);

void
F77_NAME(zlarfg)(int *n, Rcomplex *alpha, Rcomplex *
      x, int *incx, Rcomplex *tau);

void
F77_NAME(zlarft)(char *direct, char *storev, int *n, int *
      k, Rcomplex *v, int *ldv, Rcomplex *tau, Rcomplex *
      t, int *ldt);

void
F77_NAME(zlarfx)(char *side, int *m, int *n,
      Rcomplex *v, Rcomplex *tau, Rcomplex *c, int *
      ldc, Rcomplex *work);

void
F77_NAME(zlascl)(char *type, int *kl, int *ku,
      double *cfrom, double *cto, int *m, int *n,
      Rcomplex *a, int *lda, int *info);

void
F77_NAME(zlaset)(char *uplo, int *m, int *n,
      Rcomplex *alpha, Rcomplex *beta, Rcomplex *a, int *
      lda);

void
F77_NAME(zlasr)(char *side, char *pivot, char *direct, int *m,
       int *n, double *c, double *s, Rcomplex *a,
      int *lda);

void
F77_NAME(zlassq)(int *n, Rcomplex *x, int *incx,
      double *scale, double *sumsq);

void
F77_NAME(zlaswp)(int *n, Rcomplex *a, int *lda,
      int *k1, int *k2, int *ipiv, int *incx);

void
F77_NAME(zlatrd)(char *uplo, int *n, int *nb,
      Rcomplex *a, int *lda, double *e, Rcomplex *tau,
      Rcomplex *w, int *ldw);

void
F77_NAME(zlatrs)(char *uplo, char *trans, char *diag, char *
      normin, int *n, Rcomplex *a, int *lda, Rcomplex *x,
      double *scale, double *cnorm, int *info);

void
F77_NAME(zsteqr)(char *compz, int *n, double *d,
      double *e, Rcomplex *z, int *ldz, double *work,
      int *info);

void
F77_NAME(ztrevc)(char *side, 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);

void
F77_NAME(zung2l)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *info);

void
F77_NAME(zung2r)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *info);

void
F77_NAME(zungbr)(char *vect, int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zunghr)(int *n, int *ilo, int *ihi,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zungl2)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *info);

void
F77_NAME(zunglq)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zungql)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zungqr)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zungr2)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *info);

void
F77_NAME(zungrq)(int *m, int *n, int *k,
      Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *
      work, int *lwork, int *info);

void
F77_NAME(zungtr)(char *uplo, int *n, Rcomplex *a,
      int *lda, Rcomplex *tau, Rcomplex *work, int *lwork,
       int *info);

void
F77_NAME(zunm2r)(char *side, char *trans, int *m, int *n,
      int *k, Rcomplex *a, int *lda, Rcomplex *tau,
      Rcomplex *c, int *ldc, Rcomplex *work, int *info);

void
F77_NAME(zunmbr)(char *vect, char *side, char *trans, int *m,
      int *n, int *k, Rcomplex *a, int *lda, Rcomplex
      *tau, Rcomplex *c, int *ldc, Rcomplex *work, int *
      lwork, int *info);

void
F77_NAME(zunml2)(char *side, char *trans, int *m, int *n,
      int *k, Rcomplex *a, int *lda, Rcomplex *tau,
      Rcomplex *c, int *ldc, Rcomplex *work, int *info);

void
F77_NAME(zunmlq)(char *side, char *trans, int *m, int *n,
      int *k, Rcomplex *a, int *lda, Rcomplex *tau,
      Rcomplex *c, int *ldc, Rcomplex *work, int *lwork,
       int *info);

#ifdef  __cplusplus
}
#endif

#endif /* R_LAPACK_H */

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