The R Project SVN
R
(root)/branches/R-tcl-new/src/include/R_ext/Lapack.h – Rev 25832
Rev 23063 | Blame | Compare with Previous | Last modification | View Log | Download | RSS feed
#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 __cplusplusextern "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 */voidF77_NAME(dbdsqr)(const char* uplo, const int* n, const int* ncvt,const int* nru, const int* ncc, double* d, double* e,double* vt, const int* ldvt, double* u, const int* ldu,double* c, const int* ldc, double* work, int* info);/* 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 */voidF77_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 */voidF77_NAME(dgbbrd)(const char* vect, const int* m, const int* n,const int* ncc, const int* kl, const int* ku,double* ab, const int* ldab,double* d, double* e, double* q,const int* ldq, double* pt, const int* ldpt,double* c, const int* ldc,double* work, int* info);/* DGBCON - estimate the reciprocal of the condition number of a *//* real general band matrix A, in either the 1-norm or the *//* infinity-norm */voidF77_NAME(dgbcon)(const char* norm, const int* n, const int* kl,const int* ku, double* ab, const int* ldab,int* ipiv, const double* anorm, double* rcond,double* work, int* iwork, int* info);/* DGBEQU - compute row and column scalings intended to equilibrate *//* an M-by-N band matrix A and reduce its condition number */voidF77_NAME(dgbequ)(const int* m, const int* n, const int* kl, const int* ku,double* ab, const int* ldab, double* r, double* c,double* rowcnd, double* colcnd, double* amax, int* info);/* DGBRFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is banded, and provides *//* error bounds and backward error estimates for the solution */voidF77_NAME(dgbrfs)(const char* trans, const int* n, const int* kl,const int* ku, const int* nrhs, double* ab,const int* ldab, double* afb, const int* ldafb,int* ipiv, double* b, const int* ldb,double* x, const int* ldx, double* ferr, double* berr,double* work, int* iwork, int* info);/* 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 */voidF77_NAME(dgbsv)(const int* n, const int* kl,const int* ku,const int* nrhs, double* ab, const int* ldab,int* ipiv, double* b, const int* ldb, int* info);/* DGBSVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B or A**T * X = B */voidF77_NAME(dgbsvx)(const int* fact, const char* trans,const int* n, const int* kl,const int* ku,const int* nrhs, double* ab, const int* ldab,double* afb, const int* ldafb, int* ipiv,const char* equed, double* r, double* c,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info);/* DGBTF2 - compute an LU factorization of a real m-by-n band *//* matrix A using partial pivoting with row interchanges */voidF77_NAME(dgbtf2)(const int* m, const int* n, const int* kl,const int* ku,double* ab, const int* ldab, int* ipiv, int* info);/* DGBTRF - compute an LU factorization of a real m-by-n band *//* matrix A using partial pivoting with row interchanges */voidF77_NAME(dgbtrf)(const int* m, const int* n, const int* kl,const int* ku,double* ab, const int* ldab, int* ipiv, int* info);/* DGBTRS - solve a system of linear equations A * X = B or *//* A' * X = B with a general band matrix A using the LU *//* factorization computed by DGBTRF */voidF77_NAME(dgbtrs)(const char* trans, const int* n,const int* kl, const int* ku, const int* nrhs,const double* ab, const int* ldab, const int* ipiv,double* b, const int* ldb, int* info);/* 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 */voidF77_NAME(dgebak)(const char* job, const char* side, const int* n,const int* ilo, const int* ihi, double* scale,const int* m, double* v, const int* ldv, int* info);/* DGEBAL - balance a general real matrix A */voidF77_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 */voidF77_NAME(dgebd2)(const int* m, const int* n, double* a, const int* lda,double* d, double* e, double* tauq, double* taup,double* work, int* info);/* DGEBRD - reduce a general real M-by-N matrix A to upper or *//* lower bidiagonal form B by an orthogonal transformation */voidF77_NAME(dgebrd)(const int* m, const int* n, double* a, const int* lda,double* d, double* e, double* tauq, double* taup,double* work, const int* lwork, int* info);/* DGECON - estimate the reciprocal of the condition number of a *//* general real matrix A, in either the 1-norm or the *//* infinity-norm, using the LU factorization computed by DGETRF */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 */voidF77_NAME(dgeequ)(const int* m, const int* n, double* a, const int* lda,double* r, double* c, double* rowcnd, double* colcnd,double* amax, int* info);/* DGEES - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues, the real Schur form T, and, optionally, the matrix *//* of Schur vectors Z */voidF77_NAME(dgees)(const char* jobvs, const char* sort,int (*select)(const double*, const double*),const int* n, double* a, const int* lda,int* sdim, double* wr, double* wi,double* vs, const int* ldvs,double* work, const int* lwork, int* bwork, int* 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 */voidF77_NAME(dgeesx)(const char* jobvs, const char* sort,int (*select)(const double*, const double*),const char* sense, const int* n, double* a,const int* lda, int* sdim, double* wr, double* wi,double* vs, const int* ldvs, double* rconde,double* rcondv, double* work, const int* lwork,int* iwork, const int* liwork, int* bwork, int* info);/* DGEEV - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues and, optionally, the left and/or right eigenvectors */voidF77_NAME(dgeev)(const char* jobvl, const char* jobvr,const int* n, double* a, const int* lda,double* wr, double* wi, double* vl, const int* ldvl,double* vr, const int* ldvr,double* work, const int* lwork, int* info);/* DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the *//* eigenvalues and, optionally, the left and/or right eigenvectors */voidF77_NAME(dgeevx)(const char* balanc, const char* jobvl, const char* jobvr,const char* sense, const int* n, double* a, const int* lda,double* wr, double* wi, double* vl, const int* ldvl,double* vr, const int* ldvr, int* ilo, int* ihi,double* scale, double* abnrm, double* rconde, double* rcondv,double* work, const int* lwork, int* iwork, int* 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); */voidF77_NAME(dgegv)(const char* jobvl, const char* jobvr,const int* n, double* a, const int* lda,double* b, const int* ldb,double* alphar, double* alphai,const double* beta, double* vl, const int* ldvl,double* vr, const int* ldvr,double* work, const int* lwork, int* info);/* DGEHD2 - reduce a real general matrix A to upper Hessenberg *//* form H by an orthogonal similarity transformation */voidF77_NAME(dgehd2)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, double* tau,double* work, int* info);/* DGEHRD - reduce a real general matrix A to upper Hessenberg *//* form H by an orthogonal similarity transformation */voidF77_NAME(dgehrd)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGELQ2 - compute an LQ factorization of a real m by n matrix A */voidF77_NAME(dgelq2)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, int* info);/* DGELQF - compute an LQ factorization of a real M-by-N matrix A */voidF77_NAME(dgelqf)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGELS - solve overdetermined or underdetermined real linear *//* systems involving an M-by-N matrix A, or its transpose, using a *//* QR or LQ factorization of A */voidF77_NAME(dgels)(const char* trans, const int* m, const int* n,const int* nrhs, double* a, const int* lda,double* b, const int* ldb,double* work, const int* lwork, int* info);/* DGELSS - compute the minimum norm solution to a real linear *//* least squares problem */voidF77_NAME(dgelss)(const int* m, const int* n, const int* nrhs,double* a, const int* lda, double* b, const int* ldb,double* s, double* rcond, int* rank,double* work, const int* lwork, int* info);/* DGELSY - compute the minimum-norm solution to a real linear *//* least squares problem */voidF77_NAME(dgelsy)(const int* m, const int* n, const int* nrhs,double* a, const int* lda, double* b, const int* ldb,int* jpvt, const double* rcond, int* rank,double* work, const int* lwork, int* info);/* DGEQL2 - compute a QL factorization of a real m by n matrix A */voidF77_NAME(dgeql2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGEQLF - compute a QL factorization of a real M-by-N matrix A */voidF77_NAME(dgeqlf)(const int* m, const int* n,double* a, const int* lda, double* tau,double* work, const int* lwork, int* info);/* DGEQP3 - compute a QR factorization with column pivoting of a *//* real M-by-N matrix A using level 3 BLAS */voidF77_NAME(dgeqp3)(const int* m, const int* n, double* a, const int* lda,int* jpvt, double* tau, double* work, const int* lwork,int* info);/* DGEQPF - compute a QR factorization with column pivoting of a *//* real M-by-N matrix A */voidF77_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 */voidF77_NAME(dgeqr2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGEQRF - compute a QR factorization of a real M-by-N matrix A */voidF77_NAME(dgeqrf)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, const int* lwork, int* info);/* DGERFS - improve the computed solution to a system of linear *//* equations and provides error bounds and backward error *//* estimates for the solution */voidF77_NAME(dgerfs)(const char* trans, const int* n, const int* nrhs,double* a, const int* lda, double* af, const int* ldaf,int* ipiv, double* b, const int* ldb,double* x, const int* ldx, double* ferr, double* berr,double* work, int* iwork, int* info);/* DGERQ2 - compute an RQ factorization of a real m by n matrix A */voidF77_NAME(dgerq2)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, int* info);/* DGERQF - compute an RQ factorization of a real M-by-N matrix A */voidF77_NAME(dgerqf)(const int* m, const int* n, double* a, const int* lda,double* tau, double* work, const int* lwork, int* info);/* DGESV - compute the solution to a real system of linear *//* equations A * X = B, */voidF77_NAME(dgesv)(const int* n, const int* nrhs, double* a, const int* lda,int* ipiv, double* b, const int* ldb, int* info);/* DGESVD - compute the singular value decomposition (SVD); of a *//* real M-by-N matrix A, optionally computing the left and/or *//* right singular vectors */voidF77_NAME(dgesvd)(const char* jobu, const char* jobvt, const int* m,const int* n, double* a, const int* lda, double* s,double* u, const int* ldu, double* vt, const int* ldvt,double* work, const int* lwork, int* info);/* DGESVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B, */voidF77_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 */voidF77_NAME(dgetf2)(const int* m, const int* n, double* a, const int* lda,int* ipiv, int* info);/* DGETRF - compute an LU factorization of a general M-by-N *//* matrix A using partial pivoting with row interchanges */voidF77_NAME(dgetrf)(const int* m, const int* n, double* a, const int* lda,int* ipiv, int* info);/* DGETRI - compute the inverse of a matrix using the LU *//* factorization computed by DGETRF */voidF77_NAME(dgetri)(const int* n, double* a, const int* lda,int* ipiv, double* work, const int* lwork, int* info);/* DGETRS - solve a system of linear equations A * X = B or A' * *//* X = B with a general N-by-N matrix A using the LU factorization *//* computed by DGETRF */voidF77_NAME(dgetrs)(const char* trans, const int* n, const int* nrhs,const double* a, const int* lda, const int* ipiv,double* b, const int* ldb, int* info);/* 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 */voidF77_NAME(dggbak)(const char* job, const char* side,const int* n, const int* ilo, const int* ihi,double* lscale, double* rscale, const int* m,double* v, const int* ldv, int* info);/* DGGBAL - balance a pair of general real matrices (A,B); */voidF77_NAME(dggbal)(const char* job, const int* n, double* a, const int* lda,double* b, const int* ldb, int* ilo, int* ihi,double* lscale, double* rscale, double* work, int* 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)*/voidF77_NAME(dgges)(const char* jobvsl, const char* jobvsr, const char* sort,int (*delztg)(double*, double*, double*),const int* n, double* a, const int* lda,double* b, const int* ldb, double* alphar,double* alphai, const double* beta,double* vsl, const int* ldvsl,double* vsr, const int* ldvsr,double* work, const int* lwork, int* bwork, int* info);/* DGGGLM - solve a general Gauss-Markov linear model (GLM) problem */voidF77_NAME(dggglm)(const int* n, const int* m, const int* p,double* a, const int* lda, double* b, const int* ldb,double* d, double* x, double* y,double* work, const int* lwork, int* info);/* DGGHRD - reduce a pair of real matrices (A,B); to generalized *//* upper Hessenberg form using orthogonal transformations, where A *//* is a general matrix and B is upper triangular */voidF77_NAME(dgghrd)(const char* compq, const char* compz, const int* n,const int* ilo, const int* ihi, double* a, const int* lda,double* b, const int* ldb, double* q, const int* ldq,double* z, const int* ldz, int* info);/* DGGLSE - solve the linear equality-constrained least squares *//* (LSE) problem */voidF77_NAME(dgglse)(const int* m, const int* n, const int* p,double* a, const int* lda,double* b, const int* ldb,double* c, double* d, double* x,double* work, const int* lwork, int* info);/* DGGQRF - compute a generalized QR factorization of an N-by-M *//* matrix A and an N-by-P matrix B */voidF77_NAME(dggqrf)(const int* n, const int* m, const int* p,double* a, const int* lda, double* taua,double* b, const int* ldb, double* taub,double* work, const int* lwork, int* info);/* DGGRQF - compute a generalized RQ factorization of an M-by-N *//* matrix A and a P-by-N matrix B */voidF77_NAME(dggrqf)(const int* m, const int* p, const int* n,double* a, const int* lda, double* taua,double* b, const int* ldb, double* taub,double* work, const int* lwork, int* info);/* DGGSVD - compute the generalized singular value decomposition *//* (GSVD) of an M-by-N real matrix A and P-by-N real matrix B */voidF77_NAME(dggsvd)(const char* jobu, const char* jobv, const char* jobq,const int* m, const int* n, const int* p,const int* k, const int* l,double* a, const int* lda,double* b, const int* ldb,const double* alpha, const double* beta,double* u, const int* ldu,double* v, const int* ldv,double* q, const int* ldq,double* work, int* iwork, int* 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 */voidF77_NAME(dgtcon)(const char* norm, const int* n, double* dl, double* d,double* du, double* du2, int* ipiv, const double* anorm,double* rcond, double* work, int* iwork, int* 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 */voidF77_NAME(dgtrfs)(const char* trans, const int* n, const int* nrhs,double* dl, double* d, double* du, double* dlf,double* df, double* duf, double* du2,int* ipiv, double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DGTSV - solve the equation A*X = B, */voidF77_NAME(dgtsv)(const int* n, const int* nrhs,double* dl, double* d, double* du,double* b, const int* ldb, int* info);/* DGTSVX - use the LU factorization to compute the solution to a *//* real system of linear equations A * X = B or A**T * X = B, */voidF77_NAME(dgtsvx)(const int* fact, const char* trans,const int* n, const int* nrhs,double* dl, double* d, double* du,double* dlf, double* df, double* duf,double* du2, int* ipiv,double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info);/* DGTTRF - compute an LU factorization of a real tridiagonal matrix *//* A using elimination with partial pivoting and row interchanges */voidF77_NAME(dgttrf)(const int* n, double* dl, double* d,double* du, double* du2, int* ipiv, int* info);/* DGTTRS - solve one of the systems of equations A*X = B or *//* A'*X = B, */voidF77_NAME(dgttrs)(const char* trans, const int* n, const int* nrhs,double* dl, double* d, double* du, double* du2,int* ipiv, double* b, const int* ldb, int* info);/* 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 */voidF77_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' */voidF77_NAME(dopmtr)(const char* side, const char* uplo,const char* trans, const int* m, const int* n,const double* ap, const double* tau,double* c, const int* ldc,double* work, int* info);/* DORG2L - generate an m by n real matrix Q with orthonormal *//* columns, */voidF77_NAME(dorg2l)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work, int* info);/* DORG2R - generate an m by n real matrix Q with orthonormal *//* columns, */voidF77_NAME(dorg2r)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work, int* info);/* DORGBR - generate one of the real orthogonal matrices Q or *//* P**T determined by DGEBRD when reducing a real matrix A to *//* bidiagonal form */voidF77_NAME(dorgbr)(const char* vect, const int* m,const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info);/* 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 */voidF77_NAME(dorghr)(const int* n, const int* ilo, const int* ihi,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGL2 - generate an m by n real matrix Q with orthonormal *//* rows, */voidF77_NAME(dorgl2)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, int* info);/* DORGLQ - generate an M-by-N real matrix Q with orthonormal *//* rows, */voidF77_NAME(dorglq)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info);/* DORGQL - generate an M-by-N real matrix Q with orthonormal *//* columns, */voidF77_NAME(dorgql)(const int* m, const int* n, const int* k,double* a, const int* lda,const double* tau, double* work,const int* lwork, int* info);/* DORGQR - generate an M-by-N real matrix Q with orthonormal *//* columns, */voidF77_NAME(dorgqr)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGR2 - generate an m by n real matrix Q with orthonormal *//* rows, */voidF77_NAME(dorgr2)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, int* info);/* DORGRQ - generate an M-by-N real matrix Q with orthonormal rows */voidF77_NAME(dorgrq)(const int* m, const int* n, const int* k,double* a, const int* lda, const double* tau,double* work, const int* lwork, int* info);/* DORGTR - generate a real orthogonal matrix Q which is defined *//* as the product of n-1 elementary reflectors of order const int* n, as *//* returned by DSYTRD */voidF77_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', */voidF77_NAME(dorm2l)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, int* info);/* 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', */voidF77_NAME(dorm2r)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc, double* work, int* info);/* DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N *//* matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormbr)(const char* vect, const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc,double* work, const int* lwork, int* info);/* DORMHR - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormhr)(const char* side, const char* trans, const int* m,const int* n, const int* ilo, const int* ihi,const double* a, const int* lda, const double* tau,double* c, const int* ldc,double* work, const int* lwork, int* info);/* 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', */voidF77_NAME(dorml2)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda, const double* tau,double* c, const int* ldc, double* work, int* info);/* DORMLQ - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormlq)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info);/* DORMQL - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormql)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info);/* DORMQR - overwrite the general real M-by-N matrix C with SIDE = *//* 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormqr)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info);/* 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', */voidF77_NAME(dormr2)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, int* info);/* DORMRQ - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormrq)(const char* side, const char* trans,const int* m, const int* n, const int* k,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* info);/* DORMTR - overwrite the general real M-by-N matrix C with *//* SIDE = 'L' SIDE = 'R' TRANS = 'N' */voidF77_NAME(dormtr)(const char* side, const char* uplo,const char* trans, const int* m, const int* n,const double* a, const int* lda,const double* tau, double* c, const int* ldc,double* work, const int* lwork, int* 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 */voidF77_NAME(dpbcon)(const char* uplo, const int* n, const int* kd,const double* ab, const int* ldab,const double* anorm, double* rcond,double* work, int* iwork, int* info);/* 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); */voidF77_NAME(dpbequ)(const char* uplo, const int* n, const int* kd,const double* ab, const int* ldab,double* s, double* scond, double* amax, int* info);/* 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 */voidF77_NAME(dpbrfs)(const char* uplo, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,const double* afb, const int* ldafb,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DPBSTF - compute a split Cholesky factorization of a real *//* symmetric positive definite band matrix A */voidF77_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, */voidF77_NAME(dpbsv)(const char* uplo, const int* n,const int* kd, const int* nrhs,double* ab, const int* ldab,double* b, const int* ldb, int* info);/* 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, */voidF77_NAME(dpbsvx)(const int* fact, const char* uplo, const int* n,const int* kd, const int* nrhs,double* ab, const int* ldab,double* afb, const int* ldafb,char* equed, double* s,double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, int* iwork, int* info);/* DPBTF2 - compute the Cholesky factorization of a real *//* symmetric positive definite band matrix A */voidF77_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 */voidF77_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 */voidF77_NAME(dpbtrs)(const char* uplo, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,double* b, const int* ldb, int* info);/* 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 */voidF77_NAME(dpocon)(const char* uplo, const int* n,const double* a, const int* lda,const double* anorm, double* rcond,double* work, int* iwork, int* info);/* 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); */voidF77_NAME(dpoequ)(const int* n, const double* a, const int* lda,double* s, double* scond, double* amax, int* info);/* DPORFS - improve the computed solution to a system of linear *//* equations when the coefficient matrix is symmetric positive *//* definite, */voidF77_NAME(dporfs)(const char* uplo, const int* n, const int* nrhs,const double* a, const int* lda,const double* af, const int* ldaf,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DPOSV - compute the solution to a real system of linear *//* equations A * X = B, */voidF77_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, */voidF77_NAME(dposvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,double* a, const int* lda,double* af, const int* ldaf, 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 */voidF77_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 */voidF77_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 */voidF77_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 */voidF77_NAME(dpotrs)(const char* uplo, const int* n,const int* nrhs, const double* a, const int* lda,double* b, const int* ldb, int* info);/* 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 */voidF77_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); */voidF77_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 */voidF77_NAME(dpprfs)(const char* uplo, const int* n, const int* nrhs,const double* ap, const double* afp,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DPPSV - compute the solution to a real system of linear *//* equations A * X = B, */voidF77_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, */voidF77_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 */voidF77_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 */voidF77_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 */voidF77_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 */voidF77_NAME(dptcon)(const int* n,const double* d, const double* e,const double* anorm, double* rcond,double* work, int* info);/* DPTEQR - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric positive definite tridiagonal matrix by first *//* factoring the matrix using DPTTRF, and then calling DBDSQR to *//* compute the singular values of the bidiagonal factor */voidF77_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 */voidF77_NAME(dptrfs)(const int* n, const int* nrhs,const double* d, const double* e,const double* df, const double* ef,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* info);/* DPTSV - compute the solution to a real system of linear *//* equations A*X = B, where A is an N-by-N symmetric positive *//* definite tridiagonal matrix, and X and B are N-by-NRHS matrices */voidF77_NAME(dptsv)(const int* n, const int* nrhs, double* d,double* e, double* b, const int* ldb, int* info);/* DPTSVX - use the factorization A = L*D*L**T to compute the *//* solution to a real system of linear equations A*X = B, where A *//* is an N-by-N symmetric positive definite tridiagonal matrix and *//* X and B are N-by-NRHS matrices */voidF77_NAME(dptsvx)(const int* fact, const int* n,const int* nrhs,const double* d, const double* e,double* df, double* ef,const double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, int* info);/* DPTTRF - compute the factorization of a real symmetric *//* positive definite tridiagonal matrix A */voidF77_NAME(dpttrf)(const int* n, double* d, double* e, int* info);/* DPTTRS - solve a system of linear equations A * X = B with a *//* symmetric positive definite tridiagonal matrix A using the *//* factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF */voidF77_NAME(dpttrs)(const int* n, const int* nrhs,const double* d, const double* e,double* b, const int* ldb, int* info);/* DRSCL - multiply an n-element real vector x by the real scalar *//* 1/a */voidF77_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 */voidF77_NAME(dsbev)(const char* jobz, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* w, double* z, const int* ldz,double* work, int* info);/* DSBEVD - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric band matrix A */voidF77_NAME(dsbevd)(const char* jobz, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* w, double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info);/* DSBEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric band matrix A */voidF77_NAME(dsbevx)(const char* jobz, const char* range,const char* uplo, const int* n, const int* kd,double* ab, const int* ldab,double* q, const int* ldq,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info);/* DSBGST - reduce a real symmetric-definite banded generalized *//* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */voidF77_NAME(dsbgst)(const char* vect, const char* uplo,const int* n, const int* ka, const int* kb,double* ab, const int* ldab,double* bb, const int* ldbb,double* x, const int* ldx,double* work, int* info);/* 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 */voidF77_NAME(dsbgv)(const char* jobz, const char* uplo,const int* n, const int* ka, const int* kb,double* ab, const int* ldab,double* bb, const int* ldbb,double* w, double* z, const int* ldz,double* work, int* info);/* DSBTRD - reduce a real symmetric band matrix A to symmetric *//* tridiagonal form T by an orthogonal similarity transformation */voidF77_NAME(dsbtrd)(const char* vect, const char* uplo,const int* n, const int* kd,double* ab, const int* ldab,double* d, double* e,double* q, const int* ldq,double* work, int* info);/* 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 */voidF77_NAME(dspcon)(const char* uplo, const int* n,const double* ap, const int* ipiv,const double* anorm, double* rcond,double* work, int* iwork, int* info);/* DSPEV - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */voidF77_NAME(dspev)(const char* jobz, const char* uplo, const int* n,double* ap, double* w, double* z, const int* ldz,double* work, int* info);/* DSPEVD - compute all the eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */voidF77_NAME(dspevd)(const char* jobz, const char* uplo,const int* n, double* ap, double* w,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info);/* DSPEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A in packed storage */voidF77_NAME(dspevx)(const char* jobz, const char* range,const char* uplo, const int* n, double* ap,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info);/* DSPGST - reduce a real symmetric-definite generalized *//* eigenproblem to standard form, using packed storage */voidF77_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 */voidF77_NAME(dspgv)(const int* itype, const char* jobz,const char* uplo, const int* n,double* ap, double* bp, double* w,double* z, const int* ldz,double* work, int* info);/* 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 */voidF77_NAME(dsprfs)(const char* uplo, const int* n,const int* nrhs, const double* ap,const double* afp, const int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DSPSV - compute the solution to a real system of linear *//* equations A * X = B, */voidF77_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 */voidF77_NAME(dspsvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,const double* ap, double* afp, int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* rcond, double* ferr, double* berr,double* work, int* iwork, int* info);/* DSPTRD - reduce a real symmetric matrix A stored in packed *//* form to symmetric tridiagonal form T by an orthogonal *//* similarity transformation */voidF77_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 */voidF77_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 */voidF77_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 */voidF77_NAME(dsptrs)(const char* uplo, const int* n,const int* nrhs, const double* ap,const int* ipiv, double* b, const int* ldb, int* info);/* Double precision Symmetric Tridiagonal matrices *//* DSTEBZ - compute the eigenvalues of a symmetric tridiagonal *//* matrix T */voidF77_NAME(dstebz)(const char* range, const char* order, const int* n,const double* vl, const double* vu,const int* il, const int* iu,const double *abstol,const double* d, const double* e,int* m, int* nsplit, double* w,int* iblock, int* isplit,double* work, int* iwork,int* info);/* DSTEDC - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric tridiagonal matrix using the divide and conquer *//* method */voidF77_NAME(dstedc)(const char* compz, const int* n,double* d, double* e,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info);/* DSTEIN - compute the eigenvectors of a real symmetric *//* tridiagonal matrix T corresponding to specified eigenvalues, *//* using inverse iteration */voidF77_NAME(dstein)(const int* n, const double* d, const double* e,const int* m, const double* w,const int* iblock, const int* isplit,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info);/* DSTEQR - compute all eigenvalues and, optionally, eigenvectors *//* of a symmetric tridiagonal matrix using the implicit QL or QR *//* method */voidF77_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 */voidF77_NAME(dsterf)(const int* n, double* d, double* e, int* info);/* DSTEV - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric tridiagonal matrix A */voidF77_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 */voidF77_NAME(dstevd)(const char* jobz, const int* n,double* d, double* e,double* z, const int* ldz,double* work, const int* lwork,int* iwork, const int* liwork, int* info);/* DSTEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric tridiagonal matrix A */voidF77_NAME(dstevx)(const char* jobz, const char* range,const int* n, double* d, double* e,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, int* iwork,int* ifail, int* info);/* 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 */voidF77_NAME(dsycon)(const char* uplo, const int* n,const double* a, const int* lda,const int* ipiv,const double* anorm, double* rcond,double* work, int* iwork, int* info);/* DSYEV - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric matrix A */voidF77_NAME(dsyev)(const char* jobz, const char* uplo,const int* n, double* a, const int* lda,double* w, double* work, const int* lwork, int* info);/* DSYEVD - compute all eigenvalues and, optionally, eigenvectors *//* of a real symmetric matrix A */voidF77_NAME(dsyevd)(const char* jobz, const char* uplo,const int* n, double* a, const int* lda,double* w, double* work, const int* lwork,int* iwork, const int* liwork, int* info);/* DSYEVX - compute selected eigenvalues and, optionally, *//* eigenvectors of a real symmetric matrix A */voidF77_NAME(dsyevx)(const char* jobz, const char* range,const char* uplo, const int* n,double* a, const int* lda,const double* vl, const double* vu,const int* il, const int* iu,const double* abstol,int* m, double* w,double* z, const int* ldz,double* work, const int* lwork, int* iwork,int* ifail, int* info);/* DSYGS2 - reduce a real symmetric-definite generalized *//* eigenproblem to standard form */voidF77_NAME(dsygs2)(const int* itype, const char* uplo,const int* n, double* a, const int* lda,const double* b, const int* ldb, int* info);/* DSYGST - reduce a real symmetric-definite generalized *//* eigenproblem to standard form */voidF77_NAME(dsygst)(const int* itype, const char* uplo,const int* n, double* a, const int* lda,const double* b, const int* ldb, int* info);/* 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 */voidF77_NAME(dsygv)(const int* itype, const char* jobz,const char* uplo, const int* n,double* a, const int* lda,double* b, const int* ldb,double* w, double* work, const int* lwork,int* info);/* 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 */voidF77_NAME(dsyrfs)(const char* uplo, const int* n,const int* nrhs,const double* a, const int* lda,const double* af, const int* ldaf,const int* ipiv,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DSYSV - compute the solution to a real system of linear *//* equations A * X = B, */voidF77_NAME(dsysv)(const char* uplo, const int* n,const int* nrhs,double* a, const int* lda, int* ipiv,double* b, const int* ldb,double* work, const int* lwork, int* info);/* DSYSVX - use the diagonal pivoting factorization to compute *//* the solution to a real system of linear equations A * X = B, */voidF77_NAME(dsysvx)(const int* fact, const char* uplo,const int* n, const int* nrhs,const double* a, const int* lda,double* af, const int* ldaf, int* ipiv,const double* b, const int* ldb,double* x, const int* ldx, double* rcond,double* ferr, double* berr,double* work, const int* lwork,int* iwork, int* info);/* DSYTD2 - reduce a real symmetric matrix A to symmetric *//* tridiagonal form T by an orthogonal similarity transformation */voidF77_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 */voidF77_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 */voidF77_NAME(dsytrd)(const char* uplo, const int* n,double* a, const int* lda,double* d, double* e, double* tau,double* work, const int* lwork, int* info);/* DSYTRF - compute the factorization of a real symmetric matrix *//* A using the Bunch-Kaufman diagonal pivoting method */voidF77_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 */voidF77_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 */voidF77_NAME(dsytrs)(const char* uplo, const int* n,const int* nrhs,const double* a, const int* lda,const int* ipiv,double* b, const int* ldb, int* info);/* 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 */voidF77_NAME(dtbcon)(const char* norm, const char* uplo,const char* diag, const int* n, const int* kd,const double* ab, const int* ldab,double* rcond, double* work,int* iwork, int* info);/* DTBRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* band coefficient matrix */voidF77_NAME(dtbrfs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* kd,const int* nrhs,const double* ab, const int* ldab,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* DTBTRS - solve a triangular system of the form A * X = B or *//* A**T * X = B, */voidF77_NAME(dtbtrs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* kd, const int* nrhs,const double* ab, const int* ldab,double* b, const int* ldb, int* info);/* 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); */voidF77_NAME(dtgevc)(const char* side, const char* howmny,const int* select, const int* n,const double* a, const int* lda,const double* b, const int* ldb,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work, int* info);/* DTGSJA - compute the generalized singular value decomposition *//* (GSVD); of two real upper triangular (or trapezoidal); matrices *//* A and B */voidF77_NAME(dtgsja)(const char* jobu, const char* jobv, const char* jobq,const int* m, const int* p, const int* n,const int* k, const int* l,double* a, const int* lda,double* b, const int* ldb,const double* tola, const double* tolb,double* alpha, double* beta,double* u, const int* ldu,double* v, const int* ldv,double* q, const int* ldq,double* work, int* ncycle, int* 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 */voidF77_NAME(dtpcon)(const char* norm, const char* uplo,const char* diag, const int* n,const double* ap, double* rcond,double* work, int* iwork, int* info);/* DTPRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* packed coefficient matrix */voidF77_NAME(dtprfs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* nrhs, const double* ap,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* info);/* Double precision TRiangular matrices *//* DTPTRI - compute the inverse of a real upper or lower *//* triangular matrix A stored in packed format */voidF77_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, */voidF77_NAME(dtptrs)(const char* uplo, const char* trans,const char* diag, const int* n,const int* nrhs, const double* ap,double* b, const int* ldb, int* info);/* DTRCON - estimate the reciprocal of the condition number of a *//* triangular matrix A, in either the 1-norm or the infinity-norm */voidF77_NAME(dtrcon)(const char* norm, const char* uplo,const char* diag, const int* n,const double* a, const int* lda,double* rcond, double* work,int* iwork, int* info);/* DTREVC - compute some or all of the right and/or left *//* eigenvectors of a real upper quasi-triangular matrix T */voidF77_NAME(dtrevc)(const char* side, const char* howmny,const int* select, const int* n,const double* t, const int* ldt,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work, int* 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 */voidF77_NAME(dtrexc)(const char* compq, const int* n,double* t, const int* ldt,double* q, const int* ldq,int* ifst, int* ILST,double* work, int* info);/* DTRRFS - provide error bounds and backward error estimates for *//* the solution to a system of linear equations with a triangular *//* coefficient matrix */voidF77_NAME(dtrrfs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* nrhs,const double* a, const int* lda,const double* b, const int* ldb,double* x, const int* ldx,double* ferr, double* berr,double* work, int* iwork, int* 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, */voidF77_NAME(dtrsen)(const char* job, const char* compq,const int* select, const int* n,double* t, const int* ldt,double* q, const int* ldq,double* wr, double* wi,int* m, double* s, double* sep,double* work, const int* lwork,int* iwork, const int* liwork, int* 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); */voidF77_NAME(dtrsna)(const char* job, const char* howmny,const int* select, const int* n,const double* t, const int* ldt,const double* vl, const int* ldvl,const double* vr, const int* ldvr,double* s, double* sep, const int* mm,int* m, double* work, const int* lwork,int* iwork, int* info);/* DTRSYL - solve the real Sylvester matrix equation */voidF77_NAME(dtrsyl)(const char* trana, const char* tranb,const int* isgn, const int* m, const int* n,const double* a, const int* lda,const double* b, const int* ldb,double* c, const int* ldc,double* scale, int* info);/* DTRTI2 - compute the inverse of a real upper or lower *//* triangular matrix */voidF77_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 */voidF77_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 */voidF77_NAME(dtrtrs)(const char* uplo, const char* trans,const char* diag, const int* n, const int* nrhs,const double* a, const int* lda,double* b, const int* ldb, int* info);/* DTZRQF - reduce the M-by-N ( M<=N ); real upper trapezoidal *//* matrix A to upper triangular form by means of orthogonal *//* transformations */voidF77_NAME(dtzrqf)(const int* m, const int* n,double* a, const int* lda,double* tau, int* info);/* DZSUM1 - take the sum of the absolute values of a complex *//* vector and returns a double precision result */doubleF77_NAME(dzsum1)(const int* n, Rcomplex *CX, const int* incx);/* ZGESV computes the solution to a complex system of linear equations */voidF77_NAME(zgesv)(const int *n, const int *nrhs, Rcomplex *a,const int *lda, int *ipiv, Rcomplex *b,const int *ldb, int *info);/* ZGEQP3 computes a QR factorization with column pivoting */voidF77_NAME(zgeqp3)(const int *m, const int *n,Rcomplex *a, const int *lda,int *jpvt, Rcomplex *tau,Rcomplex *work, const int *lwork,double *rwork, int *info);/* ZUNMQR applies Q or Q**H from the Left or Right */voidF77_NAME(zunmqr)(const char *side, const char *trans,const int *m, const int *n, const int *k,Rcomplex *a, const int *lda,Rcomplex *tau,Rcomplex *c, const int *ldc,Rcomplex *work, const int *lwork, int *info);/* ZTRTRS solves triangular systems */voidF77_NAME(ztrtrs)(const char *uplo, const char *trans, const char *diag,const int *n, const int *nrhs,Rcomplex *a, const int *lda,Rcomplex *b, const int *ldb, int *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 */voidF77_NAME(zgesvd)(const char *jobu, const char *jobvt,const int *m, const int *n,Rcomplex *a, const int *lda, double *s,Rcomplex *u, const int *ldu,Rcomplex *vt, const int *ldvt,Rcomplex *work, const int *lwork, double *rwork,int *info);/* ZGHEEV - compute all eigenvalues and, optionally, eigenvectors *//* of a Hermitian matrix A */voidF77_NAME(zheev)(const char *jobz, const char *uplo,const int *n, Rcomplex *a, const int *lda,double *w, Rcomplex *work, const int *lwork,double *rwork, int *info);/* ZGGEEV - compute all eigenvalues and, optionally, eigenvectors *//* of a complex non-symmetric matrix A */voidF77_NAME(zgeev)(const char *jobvl, const char *jobvr,const int *n, Rcomplex *a, const int *lda,Rcomplex *wr, Rcomplex *vl, const int *ldvl,Rcomplex *vr, const int *ldvr,Rcomplex *work, const int *lwork,double *rwork, int *info);/* 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 */doubleF77_NAME(zlantr)(const char* norm, const char* uplo, const char* diag,const int* m, const int* n, Rcomplex *a,const int* lda, double *work);/* 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 */voidF77_NAME(dhgeqz)(const char* job, const char* compq, const char* compz,const int* n, const int *ILO, const int* IHI,double* a, const int* lda,double* b, const int* ldb,double* alphar, double* alphai, const double* beta,double* q, const int* ldq,double* z, const int* ldz,double* work, const int* lwork, int* info);/* DHSEIN - use inverse iteration to find specified right and/or *//* left eigenvectors of a real upper Hessenberg matrix H */voidF77_NAME(dhsein)(const char* side, const char* eigsrc,const char* initv, int* select,const int* n, double* h, const int* ldh,double* wr, double* wi,double* vl, const int* ldvl,double* vr, const int* ldvr,const int* mm, int* m, double* work,int* ifaill, int* ifailr, int* 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 */voidF77_NAME(dhseqr)(const char* job, const char* compz, const int* n,const int* ilo, const int* ihi,double* h, const int* ldh,double* wr, double* wi,double* z, const int* ldz,double* work, const int* lwork, int* 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 */voidF77_NAME(dlabad)(double* small, double* large);/* DLABRD - reduce the first NB rows and columns of a real *//* general m by n matrix A to upper or lower bidiagonal form by an *//* orthogonal transformation Q' * A * P, and returns the matrices *//* X and Y which are needed to apply the transformation to the *//* unreduced part of A */voidF77_NAME(dlabrd)(const int* m, const int* n, const int* nb,double* a, const int* lda, double* d, double* e,double* tauq, double* taup,double* x, const int* ldx, double* y, const int* ldy);/* DLACON - estimate the 1-norm of a square, real matrix A */voidF77_NAME(dlacon)(const int* n, double* v, double* x,int* isgn, double* est, int* kase);/* DLACPY - copy all or part of a two-dimensional matrix A to *//* another matrix B */voidF77_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 */voidF77_NAME(dladiv)(const double* a, const double* b,const double* c, const double* d,double* p, double* q);/* DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] *//* [ B C ] */voidF77_NAME(dlae2)(const double* a, const double* b, const double* c,double* rt1, double* rt2);/* DLAEBZ - contain the iteration loops which compute and use the *//* function N(w);, which is the count of eigenvalues of a *//* symmetric tridiagonal matrix T less than or equal to its *//* argument w */voidF77_NAME(dlaebz)(const int* ijob, const int* nitmax, const int* n,const int* mmax, const int* minp, const int* nbmin,const double* abstol, const double* reltol,const double* pivmin, double* d, double* e,double* e2, int* nval, double* ab, double* c,int* mout, int* nab, double* work, int* iwork,int* info);/* DLAED0 - compute all eigenvalues and corresponding *//* eigenvectors of a symmetric tridiagonal matrix using the divide *//* and conquer method */voidF77_NAME(dlaed0)(const int* icompq, const int* qsiz, const int* n,double* d, double* e, double* q, const int* ldq,double* qstore, const int* ldqs,double* work, int* iwork, int* info);/* DLAED1 - compute the updated eigensystem of a diagonal matrix *//* after modification by a rank-one symmetric matrix */voidF77_NAME(dlaed1)(const int* n, double* d, double* q, const int* ldq,int* indxq, const double* rho, const int* cutpnt,double* work, int* iwork, int* info);/* DLAED2 - merge the two sets of eigenvalues together into a *//* single sorted set */voidF77_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 */voidF77_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 */voidF77_NAME(dlaed4)(const int* n, const int* i, const double* d,const double* z, const double* delta,const double* rho, double* dlam, int* info);/* DLAED5 - subroutine computes the I-th eigenvalue of a *//* symmetric rank-one modification of a 2-by-2 diagonal matrix *//* diag( D ); + RHO The diagonal elements in the array D are *//* assumed to satisfy D(i); < D(j); for i < j */voidF77_NAME(dlaed5)(const int* i, const double* d, const double* z,double* delta, const double* rho, double* dlam);/* DLAED6 - compute the positive or negative root (closest to the *//* origin); of z(1); z(2); z(3); f(x); = rho + --------- + *//* ---------- + --------- d(1);-x d(2);-x d(3);-x It is assumed *//* that if ORGATI = .true */voidF77_NAME(dlaed6)(const int* kniter, const int* orgati,const double* rho, const double* d,const double* z, const double* finit,double* tau, int* info);/* DLAED7 - compute the updated eigensystem of a diagonal matrix *//* after modification by a rank-one symmetric matrix */voidF77_NAME(dlaed7)(const int* icompq, const int* n,const int* qsiz, const int* tlvls,const int* curlvl, const int* curpbm,double* d, double* q, const int* ldq,int* indxq, const double* rho, const int* cutpnt,double* qstore, double* qptr, const int* prmptr,const int* perm, const int* givptr,const int* givcol, const double* givnum,double* work, int* iwork, int* info);/* DLAED8 - merge the two sets of eigenvalues together into a *//* single sorted set */voidF77_NAME(dlaed8)(const int* icompq, const int* k,const int* n, const int* qsiz,double* d, double* q, const int* ldq,const int* indxq, double* rho,const int* cutpnt, const double* z,double* dlamda, double* q2, const int* ldq2,double* w, int* perm, int* givptr,int* givcol, double* givnum, int* indxp,int* indx, int* info);/* DLAED9 - find the roots of the secular equation, as defined by *//* the values in double* d, Z, and RHO, between KSTART and KSTOP */voidF77_NAME(dlaed9)(const int* k, const int* kstart, const int* kstop,const int* n, double* d, double* q, const int* ldq,const double* rho, const double* dlamda,const double* w, double* s, const int* lds, int* info);/* DLAEDA - compute the Z vector corresponding to the merge step *//* in the CURLVLth step of the merge process with TLVLS steps for *//* the CURPBMth problem */voidF77_NAME(dlaeda)(const int* n, const int* tlvls, const int* curlvl,const int* curpbm, const int* prmptr, const int* perm,const int* givptr, const int* givcol,const double* givnum, const double* q,const int* qptr, double* z, double* ztemp, int* info);/* DLAEIN - use inverse iteration to find a right or left *//* eigenvector corresponding to the eigenvalue (WR,WI); of a real *//* upper Hessenberg matrix H */voidF77_NAME(dlaein)(const int* rightv, const int* noinit, const int* n,const double* h, const int* ldh,const double* wr, const double* wi,double* vr, double* vi,double* b, const int* ldb, double* work,const double* eps3, const double* smlnum,const double* bignum, int* info);/* DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric *//* matrix [ A B ] [ B C ] */voidF77_NAME(dlaev2)(const double* a, const double* b, const double* c,double* rt1, double* rt2, double* cs1, double *sn1);/* DLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 *//* or 2 in an upper quasi-triangular matrix T by an orthogonal *//* similarity transformation */voidF77_NAME(dlaexc)(const int* wantq, const int* n, double* t, const int* ldt,double* q, const int* ldq, const int* j1,const int* n1, const int* n2, double* work, int* info);/* DLAG2 - compute the eigenvalues of a 2 x 2 generalized *//* eigenvalue problem A - w B, with scaling as necessary to avoid *//* over-/underflow */voidF77_NAME(dlag2)(const double* a, const int* lda, const double* b,const int* ldb, const double* safmin,double* scale1, double* scale2,double* wr1, double* wr2, double* wi);/* DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such *//* that if ( UPPER ); then U'*A*Q = U'*( A1 A2 );*Q = ( x 0 ); *//* ( 0 A3 ); ( x x ); and V'*B*Q = V'*( B1 B2 );*Q = ( x 0 ); ( *//* 0 B3 ); ( x x ); or if ( .NOT.UPPER ); then U'*A*Q = U'*( A1 *//* 0 );*Q = ( x x ); ( A2 A3 ); ( 0 x ); and V'*B*Q = V'*( B1 0 *//* );*Q = ( x x ); ( B2 B3 ); ( 0 x ); The rows of the *//* transformed A and B are parallel, where U = ( CSU SNU );, V = *//* ( CSV SNV );, Q = ( CSQ SNQ ); ( -SNU CSU ); ( -SNV CSV ); ( *//* -SNQ CSQ ); Z' denotes the transpose of Z */voidF77_NAME(dlags2)(const int* upper,const double* a1, const double* a2, const double* a3,const double* b1, const double* b2, const double* b3,double* csu, double* snu,double* csv, double* snv, double *csq, double *snq);/* DLAGTF - factorize the matrix (T - lambda*I);, where T is an n *//* by n tridiagonal matrix and lambda is a scalar, as T - *//* lambda*I = PLU, */voidF77_NAME(dlagtf)(const int* n, double* a, const double* lambda,double* b, double* c, const double *tol,double* d, int* in, int* info);/* DLAGTM - perform a matrix-vector product of the form B := *//* alpha * A * X + beta * B where A is a tridiagonal matrix of *//* order N, B and X are N by NRHS matrices, and alpha and beta are *//* real scalars, each of which may be 0., 1., or -1 */voidF77_NAME(dlagtm)(const char* trans, const int* n, const int* nrhs,const double* alpha, const double* dl,const double* d, const double* du,const double* x, const int* ldx, const double* beta,double* b, const int* ldb);/* DLAGTS - may be used to solve one of the systems of equations *//* (T - lambda*I);*x = y or (T - lambda*I);'*x = y, */voidF77_NAME(dlagts)(const int* job, const int* n,const double* a, const double* b,const double* c, const double* d,const int* in, double* y, double* tol, int* info);/* DLAHQR - an auxiliary routine called by DHSEQR to update the *//* eigenvalues and Schur decomposition already computed by DHSEQR, *//* by dealing with the Hessenberg submatrix in rows and columns *//* ILO to IHI */voidF77_NAME(dlahqr)(const int* wantt, const int* wantz, const int* n,const int* ilo, const int* ihi,double* H, const int* ldh, double* wr, double* wi,const int* iloz, const int* ihiz,double* z, const int* ldz, int* info);/* 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 */voidF77_NAME(dlahrd)(const int* n, const int* k, const int* nb,double* a, const int* lda,double* tau, double* t, const int* ldt,double* y, const int* ldy);/* DLAIC1 - apply one step of incremental condition estimation in *//* its simplest version */voidF77_NAME(dlaic1)(const int* job, const int* j, const double* x,const double* sest, const double* w,const double* gamma, double* sestpr,double* s, double* c);/* DLALN2 - solve a system of the form (ca A - w D ); X = s B or *//* (ca A' - w D); X = s B with possible scaling ("s"); and *//* perturbation of A */voidF77_NAME(dlaln2)(const int* ltrans, const int* na, const int* nw,const double* smin, const double* ca,const double* a, const int* lda,const double* d1, const double* d2,const double* b, const int* ldb,const double* wr, const double* wi,double* x, const int* ldx, double* scale,double* xnorm, int* info);/* DLAMCH - determine double precision machine parameters */doubleF77_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 */voidF77_NAME(dlamrg)(const int* n1, const int* n2, const double* a,const int* dtrd1, const int* dtrd2, int* index);/* DLANGB - return the value of the one norm, or the Frobenius *//* norm, or the infinity norm, or the element of largest absolute *//* value of an n by n band matrix A, with kl sub-diagonals and ku *//* super-diagonals */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_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 */doubleF77_NAME(dlantb)(const char* norm, const char* uplo,const char* diag, const int* n, const int* k,const double* ab, const int* ldab, double* 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 */doubleF77_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 */doubleF77_NAME(dlantr)(const char* norm, const char* uplo,const char* diag, const int* m, const int* n,const double* a, const int* lda, double* work);/* DLANV2 - compute the Schur factorization of a real 2-by-2 *//* nonsymmetric matrix in standard form */voidF77_NAME(dlanv2)(double* a, double* b, double* c, double* d,double* rt1r, double* rt1i, double* rt2r, double* rt2i,double* cs, double *sn);/* DLAPLL - two column vectors X and Y, let A = ( X Y ); */voidF77_NAME(dlapll)(const int* n, double* x, const int* incx,double* y, const int* incy, double* ssmin);/* DLAPMT - rearrange the columns of the M by N matrix X as *//* specified by the permutation K(1);,K(2);,...,K(N); of the *//* integers 1,...,N */voidF77_NAME(dlapmt)(const int* forwrd, const int* m, const int* n,double* x, const int* ldx, const int* k);/* DLAPY2 - return sqrt(x**2+y**2);, taking care not to cause *//* unnecessary overflow */doubleF77_NAME(dlapy2)(const double* x, const double* y);/* DLAPY3 - return sqrt(x**2+y**2+z**2);, taking care not to *//* cause unnecessary overflow */doubleF77_NAME(dlapy3)(const double* x, const double* y, const double* z);/* DLAQGB - equilibrate a general M by N band matrix A with KL *//* subdiagonals and KU superdiagonals using the row and scaling *//* factors in the vectors R and C */voidF77_NAME(dlaqgb)(const int* m, const int* n,const int* kl, const int* ku,double* ab, const int* ldab,double* r, double* c,double* rowcnd, double* colcnd,const double* amax, char* equed);/* DLAQGE - equilibrate a general M by N matrix A using the row *//* and scaling factors in the vectors R and C */voidF77_NAME(dlaqge)(const int* m, const int* n,double* a, const int* lda,double* r, double* c,double* rowcnd, double* colcnd,const double* amax, char* equed);/* DLAQSB - equilibrate a symmetric band matrix A using the *//* scaling factors in the vector S */voidF77_NAME(dlaqsb)(const char* uplo, const int* n, const int* kd,double* ab, const int* ldab, const double* s,const double* scond, const double* amax, char* equed);/* DLAQSP - equilibrate a symmetric matrix A using the scaling *//* factors in the vector S */voidF77_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 */voidF77_NAME(dlaqsy)(const char* uplo, const int* n,double* a, const int* lda,const double* s, const double* scond,const double* amax, int* equed);/* DLAQTR - solve the real quasi-triangular system *//* op(T) * p = scale*c */voidF77_NAME(dlaqtr)(const int* ltran, const int* lreal, const int* n,const double* t, const int* ldt,const double* b, const double* w,double* scale, double* x, double* work, int* info);/* DLAR2V - apply a vector of real plane rotations from both *//* sides to a sequence of 2-by-2 real symmetric matrices, defined *//* by the elements of the vectors x, y and z */voidF77_NAME(dlar2v)(const int* n, double* x, double* y,double* z, const int* incx,const double* c, const double* s,const int* incc);/* DLARF - apply a real elementary reflector H to a real m by n *//* matrix C, from either the left or the right */voidF77_NAME(dlarf)(const char* side, const int* m, const int* n,const double* v, const int* incv, const double* tau,double* c, const int* ldc, double* work);/* 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 */voidF77_NAME(dlarfb)(const char* side, const char* trans,const char* direct, const char* storev,const int* m, const int* n, const int* k,const double* v, const int* ldv,const double* t, const int* ldt,double* c, const int* ldc,double* work, const int* lwork);/* DLARFG - generate a real elementary reflector H of order n, *//* such that H * ( alpha ) = ( beta ), H' * H = I */voidF77_NAME(dlarfg)(const int* n, const double* alpha,double* x, const int* incx, double* tau);/* DLARFT - form the triangular factor T of a real block *//* reflector H of order n, which is defined as a product of k *//* elementary reflectors */voidF77_NAME(dlarft)(const char* direct, const char* storev,const int* n, const int* k, double* v, const int* ldv,const double* tau, double* t, const int* ldt);/* DLARFX - apply a real elementary reflector H to a real m by n *//* matrix C, from either the left or the right */voidF77_NAME(dlarfx)(const char* side, const int* m, const int* n,const double* v, const double* tau,double* c, const int* ldc, double* work);/* DLARGV - generate a vector of real plane rotations, determined *//* by elements of the real vectors x and y */voidF77_NAME(dlargv)(const int* n, double* x, const int* incx,double* y, const int* incy, double* c, const int* incc);/* DLARNV - return a vector of n random real numbers from a *//* uniform or normal distribution */voidF77_NAME(dlarnv)(const int* idist, int* iseed, const int* n, double* x);/* DLARTG - generate a plane rotation so that [ CS SN ] */voidF77_NAME(dlartg)(const double* f, const double* g, double* cs,double* sn, double *r);/* DLARTV - apply a vector of real plane rotations to elements of *//* the real vectors x and y */voidF77_NAME(dlartv)(const int* n, double* x, const int* incx,double* y, const int* incy,const double* c, const double* s,const int* incc);/* DLARUV - return a vector of n random real numbers from a *//* uniform (0,1); */voidF77_NAME(dlaruv)(int* iseed, const int* n, double* x);/* DLAS2 - compute the singular values of the 2-by-2 matrix *//* [ F G ] [ 0 H ] */voidF77_NAME(dlas2)(const double* f, const double* g, const double* h,double* ssmin, double* ssmax);/* DLASCL - multiply the M by N real matrix A by the real scalar *//* CTO/CFROM */voidF77_NAME(dlascl)(const char* type,const int* kl,const int* ku,double* cfrom, double* cto,const int* m, const int* n,double* a, const int* lda, int* info);/* DLASET - initialize an m-by-n matrix A to BETA on the diagonal *//* and ALPHA on the offdiagonals */voidF77_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 */voidF77_NAME(dlasq1)(const int* n, double* d, double* e,double* work, int* info);/* DLASQ2 - DLASQ2 computes the singular values of a real N-by-N *//* unreduced bidiagonal matrix with squared diagonal elements in *//* Q and squared off-diagonal elements in E */voidF77_NAME(dlasq2)(const int* m, double* q, double* e,double* qq, double* ee, const double* eps,const double* tol2, const double* small2,double* sup, int* kend, int* info);/* DLASQ3 - DLASQ3 is the workhorse of the whole bidiagonal SVD *//* algorithm */voidF77_NAME(dlasq3)(int* n, double* q, double* e, double* qq,double* ee, double* sup, double *sigma,int* kend, int* off, int* iphase,const int* iconv, const double* eps,const double* tol2, const double* small2);/* DLASQ4 - DLASQ4 estimates TAU, the smallest eigenvalue of a *//* matrix */voidF77_NAME(dlasq4)(const int* n, const double* q, const double* e,double* tau, double* sup);/* DLASR - perform the transformation A := P*A, when SIDE = 'L' *//* or 'l' ( Left-hand side ); A := A*P', when SIDE = 'R' or 'r' *//* ( Right-hand side ); where A is an m by n real matrix and P is *//* an orthogonal matrix, */voidF77_NAME(dlasr)(const char* side, const char* pivot,const char* direct, const int* m, const int* n,const double* c, const double* s,double* a, const int* lda);/* DLASRT - the numbers in D in increasing order (if ID = 'I'); *//* or in decreasing order (if ID = 'D' ); */voidF77_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, */voidF77_NAME(dlassq)(const int* n, const double* x, const int* incx,double* scale, double* sumsq);/* DLASV2 - compute the singular value decomposition of a 2-by-2 *//* triangular matrix [ F G ] [ 0 H ] */voidF77_NAME(dlasv2)(const double* f, const double* g, const double* h,double* ssmin, double* ssmax, double* snr, double* csr,double* snl, double* csl);/* DLASWP - perform a series of row interchanges on the matrix A */voidF77_NAME(dlaswp)(const int* n, double* a, const int* lda,const int* k1, const int* k2,const int* ipiv, const int* incx);/* DLASY2 - solve for the N1 by N2 matrix double* x, 1 <= N1,N2 <= 2, in *//* op(TL);*X + ISGN*X*op(TR); = SCALE*B, */voidF77_NAME(dlasy2)(const int* ltranl, const int* ltranr,const int* isgn, const int* n1, const int* n2,const double* tl, const int* ldtl,const double* tr, const int* ldtr,const double* b, const int* ldb,double* scale, double* x, const int* ldx,double* xnorm, int* info);/* DLASYF - compute a partial factorization of a real symmetric *//* matrix A using the Bunch-Kaufman diagonal pivoting method */voidF77_NAME(dlasyf)(const char* uplo, const int* n,const int* nb, const int* kb,double* a, const int* lda, int* ipiv,double* w, const int* ldw, int* info);/* 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 */voidF77_NAME(dlatbs)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const int* kd,const double* ab, const int* ldab,double* x, double* scale, double* cnorm, int* 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 */voidF77_NAME(dlatps)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const double* ap,double* x, double* scale, double* cnorm, int* 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 */voidF77_NAME(dlatrd)(const char* uplo, const int* n, const int* nb,double* a, const int* lda, double* e, double* tau,double* w, const int* ldw);/* DLATRS - solve one of the triangular systems A *x = s*b or *//* A'*x = s*b with scaling to prevent overflow */voidF77_NAME(dlatrs)(const char* uplo, const char* trans,const char* diag, const char* normin,const int* n, const double* a, const int* lda,double* x, double* scale, double* cnorm, int* info);/* DLATZM - apply a Householder matrix generated by DTZRQF to a *//* matrix */voidF77_NAME(dlatzm)(const char* side, const int* m, const int* n,const double* v, const int* incv,const double* tau, double* c1, double* c2,const int* ldc, double* work);/* 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 */voidF77_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 */voidF77_NAME(dlauum)(const char* uplo, const int* n,double* a, const int* lda, int* info);/* DSECND - return the user time for a process in seconds */doubleF77_NAME(dsecnd)(void);#ifdef __cplusplus}#endif#endif /* R_LAPACK_H */