diff options
Diffstat (limited to 'sourcecodes/localscore/Lapack.h')
| -rw-r--r-- | sourcecodes/localscore/Lapack.h | 3072 |
1 files changed, 0 insertions, 3072 deletions
diff --git a/sourcecodes/localscore/Lapack.h b/sourcecodes/localscore/Lapack.h deleted file mode 100644 index ad044ef7..00000000 --- a/sourcecodes/localscore/Lapack.h +++ /dev/null @@ -1,3072 +0,0 @@ -/* - * R : A Computer Language for Statistical Data Analysis - * Copyright (C) 2003-12 The R Core Team. - * Copyright (C) 2008 The R Foundation - * - * 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, a copy is available at - * http://www.r-project.org/Licenses/ - */ - -/* - C declarations of LAPACK Fortran subroutines included in R. - Just those used (currently or previously) by C routines in R itself. - - Part of the API. - - R packages that use these should have PKG_LIBS in src/Makevars include - $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) - */ - - -#ifndef R_LAPACK_H -#define R_LAPACK_H - -#include <R_ext/RS.h> /* for F77_... */ -#include <R_ext/Complex.h> /* for Rcomplex */ -#include <R_ext/BLAS.h> - -/* - LAPACK function names are [dz]<name>(), where d denotes the real - version of the function, z the complex version. (Only - double-precision versions are used in R.) -*/ - -#ifdef __cplusplus -extern "C" { -#endif - -// Never defined by R itself. -#ifndef La_extern -#define La_extern extern -#endif - -/* Utilities for Lapack-using packages : */ - -/* matrix norms: converting typstr[] to one of {'M', 'O', 'I', 'F'} - * or signal error(): */ -La_extern char La_norm_type(const char *typstr); - -/* matrix (reciprocal) condition numbers: convert typstr[] to 'O'(ne) or 'I'(nf) - * or signal error(): */ -La_extern char La_rcond_type(const char *typstr); - - - -/* Selected Double Precision Lapack Routines - ======== - */ - -/* Double precision BiDiagonal matrices */ - -/* DBDSQR - compute the singular value decomposition (SVD) of a real */ -/* N-by-N (upper or lower) bidiagonal matrix B */ -La_extern void -F77_NAME(dbdsqr)(const char* uplo, const int* n, const int* ncvt, - const int* nru, const int* ncc, double* d, double* e, - double* vt, const int* ldvt, double* u, const int* ldu, - double* c, const int* ldc, double* work, int* info); -/* DDISNA - compute the reciprocal condition numbers for the */ -/* eigenvectors of a real symmetric or complex Hermitian matrix or */ -/* for the left or right singular vectors of a general m-by-n */ -/* matrix */ -La_extern void -F77_NAME(ddisna)(const char* job, const int* m, const int* n, - double* d, double* sep, int* info); - -/* Double precision General Banded matrices */ - -/* DGBBRD - reduce a real general m-by-n band matrix A to upper */ -/* bidiagonal form B by an orthogonal transformation */ -La_extern void -F77_NAME(dgbbrd)(const char* vect, const int* m, const int* n, - const int* ncc, const int* kl, const int* ku, - double* ab, const int* ldab, - double* d, double* e, double* q, - const int* ldq, double* pt, const int* ldpt, - double* c, const int* ldc, - double* work, int* info); -/* DGBCON - estimate the reciprocal of the condition number of a */ -/* real general band matrix A, in either the 1-norm or the */ -/* infinity-norm */ -La_extern void -F77_NAME(dgbcon)(const char* norm, const int* n, const int* kl, - const int* ku, double* ab, const int* ldab, - int* ipiv, const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DGBEQU - compute row and column scalings intended to equilibrate */ -/* an M-by-N band matrix A and reduce its condition number */ -La_extern void -F77_NAME(dgbequ)(const int* m, const int* n, const int* kl, const int* ku, - double* ab, const int* ldab, double* r, double* c, - double* rowcnd, double* colcnd, double* amax, int* info); -/* DGBRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is banded, and provides */ -/* error bounds and backward error estimates for the solution */ -La_extern void -F77_NAME(dgbrfs)(const char* trans, const int* n, const int* kl, - const int* ku, const int* nrhs, double* ab, - const int* ldab, double* afb, const int* ldafb, - int* ipiv, double* b, const int* ldb, - double* x, const int* ldx, double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DGBSV - compute the solution to a real system of linear */ -/* equations A * X = B, where A is a band matrix of order N with */ -/* KL subdiagonals and KU superdiagonals, and X and B are */ -/* N-by-NRHS matrices */ -La_extern void -F77_NAME(dgbsv)(const int* n, const int* kl,const int* ku, - const int* nrhs, double* ab, const int* ldab, - int* ipiv, double* b, const int* ldb, int* info); -/* DGBSVX - use the LU factorization to compute the solution to a */ -/* real system of linear equations A * X = B or A**T * X = B */ -La_extern void -F77_NAME(dgbsvx)(const int* fact, const char* trans, - const int* n, const int* kl,const int* ku, - const int* nrhs, double* ab, const int* ldab, - double* afb, const int* ldafb, int* ipiv, - const char* equed, double* r, double* c, - double* b, const int* ldb, - double* x, const int* ldx, - double* rcond, double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DGBTF2 - compute an LU factorization of a real m-by-n band */ -/* matrix A using partial pivoting with row interchanges */ -La_extern void -F77_NAME(dgbtf2)(const int* m, const int* n, const int* kl,const int* ku, - double* ab, const int* ldab, int* ipiv, int* info); -/* DGBTRF - compute an LU factorization of a real m-by-n band */ -/* matrix A using partial pivoting with row interchanges */ -La_extern void -F77_NAME(dgbtrf)(const int* m, const int* n, const int* kl,const int* ku, - double* ab, const int* ldab, int* ipiv, int* info); -/* DGBTRS - solve a system of linear equations A * X = B or */ -/* A' * X = B with a general band matrix A using the LU */ -/* factorization computed by DGBTRF */ -La_extern void -F77_NAME(dgbtrs)(const char* trans, const int* n, - const int* kl, const int* ku, const int* nrhs, - const double* ab, const int* ldab, const int* ipiv, - double* b, const int* ldb, int* info); - -/* Double precision GEneral matrices */ - -/* DGEBAK - form the right or left eigenvectors of a real general */ -/* matrix by backward transformation on the computed eigenvectors */ -/* of the balanced matrix output by DGEBAL */ -La_extern void -F77_NAME(dgebak)(const char* job, const char* side, const int* n, - const int* ilo, const int* ihi, double* scale, - const int* m, double* v, const int* ldv, int* info); -/* DGEBAL - balance a general real matrix A */ -La_extern void -F77_NAME(dgebal)(const char* job, const int* n, double* a, const int* lda, - int* ilo, int* ihi, double* scale, int* info); -/* DGEBD2 - reduce a real general m by n matrix A to upper or */ -/* lower bidiagonal form B by an orthogonal transformation */ -La_extern void -F77_NAME(dgebd2)(const int* m, const int* n, double* a, const int* lda, - double* d, double* e, double* tauq, double* taup, - double* work, int* info); -/* DGEBRD - reduce a general real M-by-N matrix A to upper or */ -/* lower bidiagonal form B by an orthogonal transformation */ -La_extern void -F77_NAME(dgebrd)(const int* m, const int* n, double* a, const int* lda, - double* d, double* e, double* tauq, double* taup, - double* work, const int* lwork, int* info); -/* DGECON - estimate the reciprocal of the condition number of a */ -/* general real matrix A, in either the 1-norm or the */ -/* infinity-norm, using the LU factorization computed by DGETRF */ -La_extern void -F77_NAME(dgecon)(const char* norm, const int* n, - const double* a, const int* lda, - const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DGEEQU - compute row and column scalings intended to equilibrate */ -/* an M-by-N matrix A and reduce its condition number */ -La_extern void -F77_NAME(dgeequ)(const int* m, const int* n, double* a, const int* lda, - double* r, double* c, double* rowcnd, double* colcnd, - double* amax, int* info); -/* DGEES - compute for an N-by-N real nonsymmetric matrix A, the */ -/* eigenvalues, the real Schur form T, and, optionally, the matrix */ -/* of Schur vectors Z */ -La_extern void -F77_NAME(dgees)(const char* jobvs, const char* sort, - int (*select)(const double*, const double*), - const int* n, double* a, const int* lda, - int* sdim, double* wr, double* wi, - double* vs, const int* ldvs, - double* work, const int* lwork, int* bwork, int* info); -/* DGEESX - compute for an N-by-N real nonsymmetric matrix A, the */ -/* eigenvalues, the real Schur form T, and, optionally, the matrix */ -/* of Schur vectors Z */ -La_extern void -F77_NAME(dgeesx)(const char* jobvs, const char* sort, - int (*select)(const double*, const double*), - const char* sense, const int* n, double* a, - const int* lda, int* sdim, double* wr, double* wi, - double* vs, const int* ldvs, double* rconde, - double* rcondv, double* work, const int* lwork, - int* iwork, const int* liwork, int* bwork, int* info); -/* DGEEV - compute for an N-by-N real nonsymmetric matrix A, the */ -/* eigenvalues and, optionally, the left and/or right eigenvectors */ -La_extern void -F77_NAME(dgeev)(const char* jobvl, const char* jobvr, - const int* n, double* a, const int* lda, - double* wr, double* wi, double* vl, const int* ldvl, - double* vr, const int* ldvr, - double* work, const int* lwork, int* info); -/* DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the */ -/* eigenvalues and, optionally, the left and/or right eigenvectors */ -La_extern void -F77_NAME(dgeevx)(const char* balanc, const char* jobvl, const char* jobvr, - const char* sense, const int* n, double* a, const int* lda, - double* wr, double* wi, double* vl, const int* ldvl, - double* vr, const int* ldvr, int* ilo, int* ihi, - double* scale, double* abnrm, double* rconde, double* rcondv, - double* work, const int* lwork, int* iwork, int* info); -/* DGEGV - compute for a pair of n-by-n real nonsymmetric */ -/* matrices A and B, the generalized eigenvalues (alphar +/- */ -/* alphai*i, beta);, and optionally, the left and/or right */ -/* generalized eigenvectors (VL and VR); */ -La_extern void -F77_NAME(dgegv)(const char* jobvl, const char* jobvr, - const int* n, double* a, const int* lda, - double* b, const int* ldb, - double* alphar, double* alphai, - const double* beta, double* vl, const int* ldvl, - double* vr, const int* ldvr, - double* work, const int* lwork, int* info); -/* DGEHD2 - reduce a real general matrix A to upper Hessenberg */ -/* form H by an orthogonal similarity transformation */ -La_extern void -F77_NAME(dgehd2)(const int* n, const int* ilo, const int* ihi, - double* a, const int* lda, double* tau, - double* work, int* info); -/* DGEHRD - reduce a real general matrix A to upper Hessenberg */ -/* form H by an orthogonal similarity transformation */ -La_extern void -F77_NAME(dgehrd)(const int* n, const int* ilo, const int* ihi, - double* a, const int* lda, double* tau, - double* work, const int* lwork, int* info); -/* DGELQ2 - compute an LQ factorization of a real m by n matrix A */ -La_extern void -F77_NAME(dgelq2)(const int* m, const int* n, - double* a, const int* lda, double* tau, - double* work, int* info); -/* DGELQF - compute an LQ factorization of a real M-by-N matrix A */ -La_extern void -F77_NAME(dgelqf)(const int* m, const int* n, - double* a, const int* lda, double* tau, - double* work, const int* lwork, int* info); -/* DGELS - solve overdetermined or underdetermined real linear */ -/* systems involving an M-by-N matrix A, or its transpose, using a */ -/* QR or LQ factorization of A */ -La_extern void -F77_NAME(dgels)(const char* trans, const int* m, const int* n, - const int* nrhs, double* a, const int* lda, - double* b, const int* ldb, - double* work, const int* lwork, int* info); -/* DGELSS - compute the minimum norm solution to a real linear */ -/* least squares problem */ -La_extern void -F77_NAME(dgelss)(const int* m, const int* n, const int* nrhs, - double* a, const int* lda, double* b, const int* ldb, - double* s, double* rcond, int* rank, - double* work, const int* lwork, int* info); -/* DGELSY - compute the minimum-norm solution to a real linear */ -/* least squares problem */ -La_extern void -F77_NAME(dgelsy)(const int* m, const int* n, const int* nrhs, - double* a, const int* lda, double* b, const int* ldb, - int* jpvt, const double* rcond, int* rank, - double* work, const int* lwork, int* info); -/* DGEQL2 - compute a QL factorization of a real m by n matrix A */ -La_extern void -F77_NAME(dgeql2)(const int* m, const int* n, double* a, const int* lda, - double* tau, double* work, int* info); -/* DGEQLF - compute a QL factorization of a real M-by-N matrix A */ -La_extern void -F77_NAME(dgeqlf)(const int* m, const int* n, - double* a, const int* lda, double* tau, - double* work, const int* lwork, int* info); -/* DGEQP3 - compute a QR factorization with column pivoting of a */ -/* real M-by-N matrix A using level 3 BLAS */ -La_extern void -F77_NAME(dgeqp3)(const int* m, const int* n, double* a, const int* lda, - int* jpvt, double* tau, double* work, const int* lwork, - int* info); -/* DGEQPF - compute a QR factorization with column pivoting of a */ -/* real M-by-N matrix A */ -La_extern void -F77_NAME(dgeqpf)(const int* m, const int* n, double* a, const int* lda, - int* jpvt, double* tau, double* work, int* info); -/* DGEQR2 - compute a QR factorization of a real m by n matrix A */ -La_extern void -F77_NAME(dgeqr2)(const int* m, const int* n, double* a, const int* lda, - double* tau, double* work, int* info); -/* DGEQRF - compute a QR factorization of a real M-by-N matrix A */ -La_extern void -F77_NAME(dgeqrf)(const int* m, const int* n, double* a, const int* lda, - double* tau, double* work, const int* lwork, int* info); -/* DGERFS - improve the computed solution to a system of linear */ -/* equations and provides error bounds and backward error */ -/* estimates for the solution */ -La_extern void -F77_NAME(dgerfs)(const char* trans, const int* n, const int* nrhs, - double* a, const int* lda, double* af, const int* ldaf, - int* ipiv, double* b, const int* ldb, - double* x, const int* ldx, double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DGERQ2 - compute an RQ factorization of a real m by n matrix A */ -La_extern void -F77_NAME(dgerq2)(const int* m, const int* n, double* a, const int* lda, - double* tau, double* work, int* info); -/* DGERQF - compute an RQ factorization of a real M-by-N matrix A */ -La_extern void -F77_NAME(dgerqf)(const int* m, const int* n, double* a, const int* lda, - double* tau, double* work, const int* lwork, int* info); -/* DGESV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dgesv)(const int* n, const int* nrhs, double* a, const int* lda, - int* ipiv, double* b, const int* ldb, int* info); -/* DGESVD - compute the singular value decomposition (SVD); of a */ -/* real M-by-N matrix A, optionally computing the left and/or */ -/* right singular vectors */ -La_extern void -F77_NAME(dgesvd)(const char* jobu, const char* jobvt, const int* m, - const int* n, double* a, const int* lda, double* s, - double* u, const int* ldu, double* vt, const int* ldvt, - double* work, const int* lwork, int* info); -/* DGESVX - use the LU factorization to compute the solution to a */ -/* real system of linear equations A * X = B, */ -La_extern void -F77_NAME(dgesvx)(const 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 */ -La_extern void -F77_NAME(dgetf2)(const int* m, const int* n, double* a, const int* lda, - int* ipiv, int* info); -/* DGETRF - compute an LU factorization of a general M-by-N */ -/* matrix A using partial pivoting with row interchanges */ -La_extern void -F77_NAME(dgetrf)(const int* m, const int* n, double* a, const int* lda, - int* ipiv, int* info); -/* DGETRI - compute the inverse of a matrix using the LU */ -/* factorization computed by DGETRF */ -La_extern void -F77_NAME(dgetri)(const int* n, double* a, const int* lda, - int* ipiv, double* work, const int* lwork, int* info); -/* DGETRS - solve a system of linear equations A * X = B or A' * */ -/* X = B with a general N-by-N matrix A using the LU factorization */ -/* computed by DGETRF */ -La_extern void -F77_NAME(dgetrs)(const char* trans, const int* n, const int* nrhs, - const double* a, const int* lda, const int* ipiv, - double* b, const int* ldb, int* info); - -/* Double precision General matrices Generalized problems */ - -/* DGGBAK - form the right or left eigenvectors of a real */ -/* generalized eigenvalue problem A*x = lambda*B*x, by backward */ -/* transformation on the computed eigenvectors of the balanced */ -/* pair of matrices output by DGGBAL */ -La_extern void -F77_NAME(dggbak)(const char* job, const char* side, - const int* n, const int* ilo, const int* ihi, - double* lscale, double* rscale, const int* m, - double* v, const int* ldv, int* info); -/* DGGBAL - balance a pair of general real matrices (A,B); */ -La_extern void -F77_NAME(dggbal)(const char* job, const int* n, double* a, const int* lda, - double* b, const int* ldb, int* ilo, int* ihi, - double* lscale, double* rscale, double* work, int* info); -/* DGGES - compute for a pair of N-by-N real nonsymmetric */ -/* matrices A, B the generalized eigenvalues, the generalized */ -/* real Schur form (S,T), optionally, the left and/or right matrices */ -/* of Schur vectors (VSL and VSR)*/ -La_extern void -F77_NAME(dgges)(const char* jobvsl, const char* jobvsr, const char* sort, - int (*delztg)(double*, double*, double*), - const int* n, double* a, const int* lda, - double* b, const int* ldb, double* alphar, - double* alphai, const double* beta, - double* vsl, const int* ldvsl, - double* vsr, const int* ldvsr, - double* work, const int* lwork, int* bwork, int* info); - -/* DGGGLM - solve a general Gauss-Markov linear model (GLM) problem */ -La_extern void -F77_NAME(dggglm)(const int* n, const int* m, const int* p, - double* a, const int* lda, double* b, const int* ldb, - double* d, double* x, double* y, - double* work, const int* lwork, int* info); -/* DGGHRD - reduce a pair of real matrices (A,B); to generalized */ -/* upper Hessenberg form using orthogonal transformations, where A */ -/* is a general matrix and B is upper triangular */ -La_extern void -F77_NAME(dgghrd)(const char* compq, const char* compz, const int* n, - const int* ilo, const int* ihi, double* a, const int* lda, - double* b, const int* ldb, double* q, const int* ldq, - double* z, const int* ldz, int* info); -/* DGGLSE - solve the linear equality-constrained least squares */ -/* (LSE) problem */ -La_extern void -F77_NAME(dgglse)(const int* m, const int* n, const int* p, - double* a, const int* lda, - double* b, const int* ldb, - double* c, double* d, double* x, - double* work, const int* lwork, int* info); -/* DGGQRF - compute a generalized QR factorization of an N-by-M */ -/* matrix A and an N-by-P matrix B */ -La_extern void -F77_NAME(dggqrf)(const int* n, const int* m, const int* p, - double* a, const int* lda, double* taua, - double* b, const int* ldb, double* taub, - double* work, const int* lwork, int* info); -/* DGGRQF - compute a generalized RQ factorization of an M-by-N */ -/* matrix A and a P-by-N matrix B */ -La_extern void -F77_NAME(dggrqf)(const int* m, const int* p, const int* n, - double* a, const int* lda, double* taua, - double* b, const int* ldb, double* taub, - double* work, const int* lwork, int* info); -/* DGGSVD - compute the generalized singular value decomposition */ -/* (GSVD) of an M-by-N real matrix A and P-by-N real matrix B */ -La_extern void -F77_NAME(dggsvd)(const char* jobu, const char* jobv, const char* jobq, - const int* m, const int* n, const int* p, - const int* k, const int* l, - double* a, const int* lda, - double* b, const int* ldb, - const double* alpha, const double* beta, - double* u, const int* ldu, - double* v, const int* ldv, - double* q, const int* ldq, - double* work, int* iwork, int* info); - -/* 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 */ -La_extern void -F77_NAME(dgtcon)(const char* norm, const int* n, double* dl, double* d, - double* du, double* du2, int* ipiv, const double* anorm, - double* rcond, double* work, int* iwork, int* info); -/* DGTRFS - improve the computed solution to a system of linear equations */ -/* when the coefficient matrix is tridiagonal, and provides error bounds */ -/* and backward error estimates for the solution */ -La_extern void -F77_NAME(dgtrfs)(const char* trans, const int* n, const int* nrhs, - double* dl, double* d, double* du, double* dlf, - double* df, double* duf, double* du2, - int* ipiv, double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DGTSV - solve the equation A*X = B, */ -La_extern void -F77_NAME(dgtsv)(const int* n, const int* nrhs, - double* dl, double* d, double* du, - double* b, const int* ldb, int* info); -/* DGTSVX - use the LU factorization to compute the solution to a */ -/* real system of linear equations A * X = B or A**T * X = B, */ -La_extern void -F77_NAME(dgtsvx)(const int* fact, const char* trans, - const int* n, const int* nrhs, - double* dl, double* d, double* du, - double* dlf, double* df, double* duf, - double* du2, int* ipiv, - double* b, const int* ldb, - double* x, const int* ldx, - double* rcond, double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DGTTRF - compute an LU factorization of a real tridiagonal matrix */ -/* A using elimination with partial pivoting and row interchanges */ -La_extern void -F77_NAME(dgttrf)(const int* n, double* dl, double* d, - double* du, double* du2, int* ipiv, int* info); -/* DGTTRS - solve one of the systems of equations A*X = B or */ -/* A'*X = B, */ -La_extern void -F77_NAME(dgttrs)(const char* trans, const int* n, const int* nrhs, - double* dl, double* d, double* du, double* du2, - int* ipiv, double* b, const int* ldb, int* info); - -/* Double precision Orthogonal matrices */ - -/* DOPGTR - generate a real orthogonal matrix Q which is defined */ -/* as the product of n-1 elementary reflectors H(i); of order n, */ -/* as returned by DSPTRD using packed storage */ -La_extern void -F77_NAME(dopgtr)(const char* uplo, const int* n, - const double* ap, const double* tau, - double* q, const int* ldq, - double* work, int* info); -/* DOPMTR - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dopmtr)(const char* side, const char* uplo, - const char* trans, const int* m, const int* n, - const double* ap, const double* tau, - double* c, const int* ldc, - double* work, int* info); -/* DORG2L - generate an m by n real matrix Q with orthonormal */ -/* columns, */ -La_extern void -F77_NAME(dorg2l)(const int* m, const int* n, const int* k, - double* a, const int* lda, - const double* tau, double* work, int* info); -/* DORG2R - generate an m by n real matrix Q with orthonormal */ -/* columns, */ -La_extern void -F77_NAME(dorg2r)(const int* m, const int* n, const int* k, - double* a, const int* lda, - const double* tau, double* work, int* info); -/* DORGBR - generate one of the real orthogonal matrices Q or */ -/* P**T determined by DGEBRD when reducing a real matrix A to */ -/* bidiagonal form */ -La_extern void -F77_NAME(dorgbr)(const char* vect, const int* m, - const int* n, const int* k, - double* a, const int* lda, - const double* tau, double* work, - const int* lwork, int* info); -/* DORGHR - generate a real orthogonal matrix Q which is defined */ -/* as the product of IHI-ILO elementary reflectors of order N, as */ -/* returned by DGEHRD */ -La_extern void -F77_NAME(dorghr)(const int* n, const int* ilo, const int* ihi, - double* a, const int* lda, const double* tau, - double* work, const int* lwork, int* info); -/* DORGL2 - generate an m by n real matrix Q with orthonormal */ -/* rows, */ -La_extern void -F77_NAME(dorgl2)(const int* m, const int* n, const int* k, - double* a, const int* lda, const double* tau, - double* work, int* info); -/* DORGLQ - generate an M-by-N real matrix Q with orthonormal */ -/* rows, */ -La_extern void -F77_NAME(dorglq)(const int* m, const int* n, const int* k, - double* a, const int* lda, - const double* tau, double* work, - const int* lwork, int* info); -/* DORGQL - generate an M-by-N real matrix Q with orthonormal */ -/* columns, */ -La_extern void -F77_NAME(dorgql)(const int* m, const int* n, const int* k, - double* a, const int* lda, - const double* tau, double* work, - const int* lwork, int* info); -/* DORGQR - generate an M-by-N real matrix Q with orthonormal */ -/* columns, */ -La_extern void -F77_NAME(dorgqr)(const int* m, const int* n, const int* k, - double* a, const int* lda, const double* tau, - double* work, const int* lwork, int* info); -/* DORGR2 - generate an m by n real matrix Q with orthonormal */ -/* rows, */ -La_extern void -F77_NAME(dorgr2)(const int* m, const int* n, const int* k, - double* a, const int* lda, const double* tau, - double* work, int* info); -/* DORGRQ - generate an M-by-N real matrix Q with orthonormal rows */ -La_extern void -F77_NAME(dorgrq)(const int* m, const int* n, const int* k, - double* a, const int* lda, const double* tau, - double* work, const int* lwork, int* info); -/* DORGTR - generate a real orthogonal matrix Q which is defined */ -/* as the product of n-1 elementary reflectors of order const int* n, as */ -/* returned by DSYTRD */ -La_extern void -F77_NAME(dorgtr)(const char* uplo, const int* n, - double* a, const int* lda, const double* tau, - double* work, const int* lwork, int* info); -/* DORM2L - overwrite the general real m by n matrix C with Q * */ -/* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and */ -/* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * */ -/* Q' if SIDE = 'R' and TRANS = 'T', */ -La_extern void -F77_NAME(dorm2l)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, int* info); -/* DORM2R - overwrite the general real m by n matrix C with Q * C */ -/* if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and */ -/* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * */ -/* Q' if SIDE = 'R' and TRANS = 'T', */ -La_extern void -F77_NAME(dorm2r)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, const double* tau, - double* c, const int* ldc, double* work, int* info); -/* DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N */ -/* matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormbr)(const char* vect, const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, const double* tau, - double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORMHR - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormhr)(const char* side, const char* trans, const int* m, - const int* n, const int* ilo, const int* ihi, - const double* a, const int* lda, const double* tau, - double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORML2 - overwrite the general real m by n matrix C with Q * */ -/* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and */ -/* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * */ -/* Q' if SIDE = 'R' and TRANS = 'T', */ -La_extern void -F77_NAME(dorml2)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, const double* tau, - double* c, const int* ldc, double* work, int* info); -/* DORMLQ - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormlq)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORMQL - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormql)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORMQR - overwrite the general real M-by-N matrix C with SIDE = */ -/* 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormqr)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORMR2 - overwrite the general real m by n matrix C with Q * */ -/* C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and */ -/* TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * */ -/* Q' if SIDE = 'R' and TRANS = 'T', */ -La_extern void -F77_NAME(dormr2)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, int* info); -/* DORMRQ - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormrq)(const char* side, const char* trans, - const int* m, const int* n, const int* k, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, const int* lwork, int* info); -/* DORMTR - overwrite the general real M-by-N matrix C with */ -/* SIDE = 'L' SIDE = 'R' TRANS = 'N' */ -La_extern void -F77_NAME(dormtr)(const char* side, const char* uplo, - const char* trans, const int* m, const int* n, - const double* a, const int* lda, - const double* tau, double* c, const int* ldc, - double* work, const int* lwork, int* info); - -/* Double precision Positive definite Band matrices */ - -/* DPBCON - estimate the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric positive definite band matrix */ -/* using the Cholesky factorization A = U**T*U or A = L*L**T */ -/* computed by DPBTRF */ -La_extern void -F77_NAME(dpbcon)(const char* uplo, const int* n, const int* kd, - const double* ab, const int* ldab, - const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DPBEQU - compute row and column scalings intended to */ -/* equilibrate a symmetric positive definite band matrix A and */ -/* reduce its condition number (with respect to the two-norm); */ -La_extern void -F77_NAME(dpbequ)(const char* uplo, const int* n, const int* kd, - const double* ab, const int* ldab, - double* s, double* scond, double* amax, int* info); -/* DPBRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric positive */ -/* definite and banded, and provides error bounds and backward */ -/* error estimates for the solution */ -La_extern void -F77_NAME(dpbrfs)(const char* uplo, const int* n, - const int* kd, const int* nrhs, - const double* ab, const int* ldab, - const double* afb, const int* ldafb, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DPBSTF - compute a split Cholesky factorization of a real */ -/* symmetric positive definite band matrix A */ -La_extern void -F77_NAME(dpbstf)(const char* uplo, const int* n, const int* kd, - double* ab, const int* ldab, int* info); -/* DPBSV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dpbsv)(const char* uplo, const int* n, - const int* kd, const int* nrhs, - double* ab, const int* ldab, - double* b, const int* ldb, int* info); -/* DPBSVX - use the Cholesky factorization A = U**T*U or A = */ -/* L*L**T to compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dpbsvx)(const int* fact, const char* uplo, const int* n, - const int* kd, const int* nrhs, - double* ab, const int* ldab, - double* afb, const int* ldafb, - char* equed, double* s, - double* b, const int* ldb, - double* x, const int* ldx, double* rcond, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DPBTF2 - compute the Cholesky factorization of a real */ -/* symmetric positive definite band matrix A */ -La_extern void -F77_NAME(dpbtf2)(const char* uplo, const int* n, const int* kd, - double* ab, const int* ldab, int* info); -/* DPBTRF - compute the Cholesky factorization of a real */ -/* symmetric positive definite band matrix A */ -La_extern void -F77_NAME(dpbtrf)(const char* uplo, const int* n, const int* kd, - double* ab, const int* ldab, int* info); -/* DPBTRS - solve a system of linear equations A*X = B with a */ -/* symmetric positive definite band matrix A using the Cholesky */ -/* factorization A = U**T*U or A = L*L**T computed by DPBTRF */ -La_extern void -F77_NAME(dpbtrs)(const char* uplo, const int* n, - const int* kd, const int* nrhs, - const double* ab, const int* ldab, - double* b, const int* ldb, int* info); - -/* Double precision Positive definite matrices */ - -/* DPOCON - estimate the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric positive definite matrix using */ -/* the Cholesky factorization A = U**T*U or A = L*L**T computed by */ -/* DPOTRF */ -La_extern void -F77_NAME(dpocon)(const char* uplo, const int* n, - const double* a, const int* lda, - const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DPOEQU - compute row and column scalings intended to */ -/* equilibrate a symmetric positive definite matrix A and reduce */ -/* its condition number (with respect to the two-norm); */ -La_extern void -F77_NAME(dpoequ)(const int* n, const double* a, const int* lda, - double* s, double* scond, double* amax, int* info); -/* DPORFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric positive */ -/* definite, */ -La_extern void -F77_NAME(dporfs)(const char* uplo, const int* n, const int* nrhs, - const double* a, const int* lda, - const double* af, const int* ldaf, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DPOSV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dposv)(const char* uplo, const int* n, const int* nrhs, - double* a, const int* lda, - double* b, const int* ldb, int* info); -/* DPOSVX - use the Cholesky factorization A = U**T*U or A = */ -/* L*L**T to compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dposvx)(const int* fact, const char* uplo, - const int* n, const int* nrhs, - double* a, const int* lda, - double* af, const int* ldaf, char* equed, - double* s, double* b, const int* ldb, - double* x, const int* ldx, double* rcond, - double* ferr, double* berr, double* work, - int* iwork, int* info); -/* DPOTF2 - compute the Cholesky factorization of a real */ -/* symmetric positive definite matrix A */ -La_extern void -F77_NAME(dpotf2)(const char* uplo, const int* n, - double* a, const int* lda, int* info); -/* DPOTRF - compute the Cholesky factorization of a real */ -/* symmetric positive definite matrix A */ -La_extern void -F77_NAME(dpotrf)(const char* uplo, const int* n, - double* a, const int* lda, int* info); -/* DPOTRI - compute the inverse of a real symmetric positive */ -/* definite matrix A using the Cholesky factorization A = U**T*U */ -/* or A = L*L**T computed by DPOTRF */ -La_extern void -F77_NAME(dpotri)(const char* uplo, const int* n, - double* a, const int* lda, int* info); -/* DPOTRS - solve a system of linear equations A*X = B with a */ -/* symmetric positive definite matrix A using the Cholesky */ -/* factorization A = U**T*U or A = L*L**T computed by DPOTRF */ -La_extern void -F77_NAME(dpotrs)(const char* uplo, const int* n, - const int* nrhs, const double* a, const int* lda, - double* b, const int* ldb, int* info); -/* DPPCON - estimate the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric positive definite packed */ -/* matrix using the Cholesky factorization A = U**T*U or A = */ -/* L*L**T computed by DPPTRF */ -La_extern void -F77_NAME(dppcon)(const char* uplo, const int* n, - const double* ap, const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DPPEQU - compute row and column scalings intended to */ -/* equilibrate a symmetric positive definite matrix A in packed */ -/* storage and reduce its condition number (with respect to the */ -/* two-norm); */ -La_extern void -F77_NAME(dppequ)(const char* uplo, const int* n, - const double* ap, double* s, double* scond, - double* amax, int* info); - -/* Double precision Positive definite matrices in Packed storage */ - -/* DPPRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric positive */ -/* definite and packed, and provides error bounds and backward */ -/* error estimates for the solution */ -La_extern void -F77_NAME(dpprfs)(const char* uplo, const int* n, const int* nrhs, - const double* ap, const double* afp, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DPPSV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dppsv)(const char* uplo, const int* n, - const int* nrhs, const double* ap, - double* b, const int* ldb, int* info); -/* DPPSVX - use the Cholesky factorization A = U**T*U or A = */ -/* L*L**T to compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dppsvx)(const 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 */ -La_extern void -F77_NAME(dpptrf)(const char* uplo, const int* n, double* ap, int* info); -/* DPPTRI - compute the inverse of a real symmetric positive */ -/* definite matrix A using the Cholesky factorization A = U**T*U */ -/* or A = L*L**T computed by DPPTRF */ -La_extern void -F77_NAME(dpptri)(const char* uplo, const int* n, double* ap, int* info); -/* DPPTRS - solve a system of linear equations A*X = B with a */ -/* symmetric positive definite matrix A in packed storage using */ -/* the Cholesky factorization A = U**T*U or A = L*L**T computed by */ -/* DPPTRF */ -La_extern void -F77_NAME(dpptrs)(const char* uplo, const int* n, - const int* nrhs, const double* ap, - double* b, const int* ldb, int* info); - -/* Double precision symmetric Positive definite Tridiagonal matrices */ - -/* DPTCON - compute the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric positive definite tridiagonal */ -/* matrix using the factorization A = L*D*L**T or A = U**T*D*U */ -/* computed by DPTTRF */ -La_extern void -F77_NAME(dptcon)(const int* n, - const double* d, const double* e, - const double* anorm, double* rcond, - double* work, int* info); -/* DPTEQR - compute all eigenvalues and, optionally, eigenvectors */ -/* of a symmetric positive definite tridiagonal matrix by first */ -/* factoring the matrix using DPTTRF, and then calling DBDSQR to */ -/* compute the singular values of the bidiagonal factor */ -La_extern void -F77_NAME(dpteqr)(const char* compz, const int* n, double* d, - double* e, double* z, const int* ldz, - double* work, int* info); -/* DPTRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric positive */ -/* definite and tridiagonal, and provides error bounds and */ -/* backward error estimates for the solution */ -La_extern void -F77_NAME(dptrfs)(const int* n, const int* nrhs, - const double* d, const double* e, - const double* df, const double* ef, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* info); -/* DPTSV - compute the solution to a real system of linear */ -/* equations A*X = B, where A is an N-by-N symmetric positive */ -/* definite tridiagonal matrix, and X and B are N-by-NRHS matrices */ -La_extern void -F77_NAME(dptsv)(const int* n, const int* nrhs, double* d, - double* e, double* b, const int* ldb, int* info); -/* DPTSVX - use the factorization A = L*D*L**T to compute the */ -/* solution to a real system of linear equations A*X = B, where A */ -/* is an N-by-N symmetric positive definite tridiagonal matrix and */ -/* X and B are N-by-NRHS matrices */ -La_extern void -F77_NAME(dptsvx)(const int* fact, const int* n, - const int* nrhs, - const double* d, const double* e, - double* df, double* ef, - const double* b, const int* ldb, - double* x, const int* ldx, double* rcond, - double* ferr, double* berr, - double* work, int* info); -/* DPTTRF - compute the factorization of a real symmetric */ -/* positive definite tridiagonal matrix A */ -La_extern void -F77_NAME(dpttrf)(const int* n, double* d, double* e, int* info); -/* DPTTRS - solve a system of linear equations A * X = B with a */ -/* symmetric positive definite tridiagonal matrix A using the */ -/* factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF */ -La_extern void -F77_NAME(dpttrs)(const int* n, const int* nrhs, - const double* d, const double* e, - double* b, const int* ldb, int* info); -/* DRSCL - multiply an n-element real vector x by the real scalar */ -/* 1/a */ -La_extern void -F77_NAME(drscl)(const int* n, const double* da, - double* x, const int* incx); - -/* Double precision Symmetric Band matrices */ - -/* DSBEV - compute all the eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric band matrix A */ -La_extern void -F77_NAME(dsbev)(const char* jobz, const char* uplo, - const int* n, const int* kd, - double* ab, const int* ldab, - double* w, double* z, const int* ldz, - double* work, int* info); -/* DSBEVD - compute all the eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric band matrix A */ -La_extern void -F77_NAME(dsbevd)(const char* jobz, const char* uplo, - const int* n, const int* kd, - double* ab, const int* ldab, - double* w, double* z, const int* ldz, - double* work, const int* lwork, - int* iwork, const int* liwork, int* info); -/* DSBEVX - compute selected eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric band matrix A */ -La_extern void -F77_NAME(dsbevx)(const char* jobz, const char* range, - const char* uplo, const int* n, const int* kd, - double* ab, const int* ldab, - double* q, const int* ldq, - const double* vl, const double* vu, - const int* il, const int* iu, - const double* abstol, - int* m, double* w, - double* z, const int* ldz, - double* work, int* iwork, - int* ifail, int* info); -/* DSBGST - reduce a real symmetric-definite banded generalized */ -/* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */ -La_extern void -F77_NAME(dsbgst)(const char* vect, const char* uplo, - const int* n, const int* ka, const int* kb, - double* ab, const int* ldab, - double* bb, const int* ldbb, - double* x, const int* ldx, - double* work, int* info); -/* DSBGV - compute all the eigenvalues, and optionally, the */ -/* eigenvectors of a real generalized symmetric-definite banded */ -/* eigenproblem, of the form A*x=(lambda);*B*x */ -La_extern void -F77_NAME(dsbgv)(const char* jobz, const char* uplo, - const int* n, const int* ka, const int* kb, - double* ab, const int* ldab, - double* bb, const int* ldbb, - double* w, double* z, const int* ldz, - double* work, int* info); -/* DSBTRD - reduce a real symmetric band matrix A to symmetric */ -/* tridiagonal form T by an orthogonal similarity transformation */ -La_extern void -F77_NAME(dsbtrd)(const char* vect, const char* uplo, - const int* n, const int* kd, - double* ab, const int* ldab, - double* d, double* e, - double* q, const int* ldq, - double* work, int* info); - -/* Double precision Symmetric Packed matrices */ - -/* DSPCON - estimate the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric packed matrix A using the */ -/* factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF */ -La_extern void -F77_NAME(dspcon)(const char* uplo, const int* n, - const double* ap, const int* ipiv, - const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DSPEV - compute all the eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric matrix A in packed storage */ -La_extern void -F77_NAME(dspev)(const char* jobz, const char* uplo, const int* n, - double* ap, double* w, double* z, const int* ldz, - double* work, int* info); -/* DSPEVD - compute all the eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric matrix A in packed storage */ -La_extern void -F77_NAME(dspevd)(const char* jobz, const char* uplo, - const int* n, double* ap, double* w, - double* z, const int* ldz, - double* work, const int* lwork, - int* iwork, const int* liwork, int* info); -/* DSPEVX - compute selected eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric matrix A in packed storage */ -La_extern void -F77_NAME(dspevx)(const char* jobz, const char* range, - const char* uplo, const int* n, double* ap, - const double* vl, const double* vu, - const int* il, const int* iu, - const double* abstol, - int* m, double* w, - double* z, const int* ldz, - double* work, int* iwork, - int* ifail, int* info); -/* DSPGST - reduce a real symmetric-definite generalized */ -/* eigenproblem to standard form, using packed storage */ -La_extern void -F77_NAME(dspgst)(const int* itype, const char* uplo, - const int* n, double* ap, double* bp, int* info); -/* DSPGV - compute all the eigenvalues and, optionally, the */ -/* eigenvectors of a real generalized symmetric-definite */ -/* eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, */ -/* or B*A*x=(lambda)*x */ -La_extern void -F77_NAME(dspgv)(const int* itype, const char* jobz, - const char* uplo, const int* n, - double* ap, double* bp, double* w, - double* z, const int* ldz, - double* work, int* info); - -/* DSPRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric indefinite */ -/* and packed, and provides error bounds and backward error */ -/* estimates for the solution */ -La_extern void -F77_NAME(dsprfs)(const char* uplo, const int* n, - const int* nrhs, const double* ap, - const double* afp, const int* ipiv, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); - -/* DSPSV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dspsv)(const char* uplo, const int* n, - const int* nrhs, double* ap, int* ipiv, - double* b, const int* ldb, int* info); - -/* DSPSVX - use the diagonal pivoting factorization A = U*D*U**T */ -/* or A = L*D*L**T to compute the solution to a real system of */ -/* linear equations A * X = B, where A is an N-by-N symmetric */ -/* matrix stored in packed format and X and B are N-by-NRHS */ -/* matrices */ -La_extern void -F77_NAME(dspsvx)(const int* fact, const char* uplo, - const int* n, const int* nrhs, - const double* ap, double* afp, int* ipiv, - const double* b, const int* ldb, - double* x, const int* ldx, - double* rcond, double* ferr, double* berr, - double* work, int* iwork, int* info); - -/* DSPTRD - reduce a real symmetric matrix A stored in packed */ -/* form to symmetric tridiagonal form T by an orthogonal */ -/* similarity transformation */ -La_extern void -F77_NAME(dsptrd)(const char* uplo, const int* n, - double* ap, double* d, double* e, - double* tau, int* info); - -/* DSPTRF - compute the factorization of a real symmetric matrix */ -/* A stored in packed format using the Bunch-Kaufman diagonal */ -/* pivoting method */ -La_extern void -F77_NAME(dsptrf)(const char* uplo, const int* n, - double* ap, int* ipiv, int* info); - -/* DSPTRI - compute the inverse of a real symmetric indefinite */ -/* matrix A in packed storage using the factorization A = U*D*U**T */ -/* or A = L*D*L**T computed by DSPTRF */ -La_extern void -F77_NAME(dsptri)(const char* uplo, const int* n, - double* ap, const int* ipiv, - double* work, int* info); - -/* DSPTRS - solve a system of linear equations A*X = B with a */ -/* real symmetric matrix A stored in packed format using the */ -/* factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF */ -La_extern void -F77_NAME(dsptrs)(const char* uplo, const int* n, - const int* nrhs, const double* ap, - const int* ipiv, double* b, const int* ldb, int* info); - -/* Double precision Symmetric Tridiagonal matrices */ - -/* DSTEBZ - compute the eigenvalues of a symmetric tridiagonal */ -/* matrix T */ -La_extern void -F77_NAME(dstebz)(const char* range, const char* order, const int* n, - const double* vl, const double* vu, - const int* il, const int* iu, - const double *abstol, - const double* d, const double* e, - int* m, int* nsplit, double* w, - int* iblock, int* isplit, - double* work, int* iwork, - int* info); -/* DSTEDC - compute all eigenvalues and, optionally, eigenvectors */ -/* of a symmetric tridiagonal matrix using the divide and conquer */ -/* method */ -La_extern void -F77_NAME(dstedc)(const char* compz, const int* n, - double* d, double* e, - double* z, const int* ldz, - double* work, const int* lwork, - int* iwork, const int* liwork, int* info); -/* DSTEIN - compute the eigenvectors of a real symmetric */ -/* tridiagonal matrix T corresponding to specified eigenvalues, */ -/* using inverse iteration */ -La_extern void -F77_NAME(dstein)(const int* n, const double* d, const double* e, - const int* m, const double* w, - const int* iblock, const int* isplit, - double* z, const int* ldz, - double* work, int* iwork, - int* ifail, int* info); -/* DSTEQR - compute all eigenvalues and, optionally, eigenvectors */ -/* of a symmetric tridiagonal matrix using the implicit QL or QR */ -/* method */ -La_extern void -F77_NAME(dsteqr)(const char* compz, const int* n, double* d, double* e, - double* z, const int* ldz, double* work, int* info); -/* DSTERF - compute all eigenvalues of a symmetric tridiagonal */ -/* matrix using the Pal-Walker-Kahan variant of the QL or QR */ -/* algorithm */ -La_extern void -F77_NAME(dsterf)(const int* n, double* d, double* e, int* info); -/* DSTEV - compute all eigenvalues and, optionally, eigenvectors */ -/* of a real symmetric tridiagonal matrix A */ -La_extern void -F77_NAME(dstev)(const char* jobz, const int* n, - double* d, double* e, - double* z, const int* ldz, - double* work, int* info); -/* DSTEVD - compute all eigenvalues and, optionally, eigenvectors */ -/* of a real symmetric tridiagonal matrix */ -La_extern void -F77_NAME(dstevd)(const char* jobz, const int* n, - double* d, double* e, - double* z, const int* ldz, - double* work, const int* lwork, - int* iwork, const int* liwork, int* info); -/* DSTEVX - compute selected eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric tridiagonal matrix A */ -La_extern void -F77_NAME(dstevx)(const char* jobz, const char* range, - const int* n, double* d, double* e, - const double* vl, const double* vu, - const int* il, const int* iu, - const double* abstol, - int* m, double* w, - double* z, const int* ldz, - double* work, int* iwork, - int* ifail, int* info); - -/* Double precision SYmmetric matrices */ - -/* DSYCON - estimate the reciprocal of the condition number (in */ -/* the 1-norm); of a real symmetric matrix A using the */ -/* factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF */ -La_extern void -F77_NAME(dsycon)(const char* uplo, const int* n, - const double* a, const int* lda, - const int* ipiv, - const double* anorm, double* rcond, - double* work, int* iwork, int* info); -/* DSYEV - compute all eigenvalues and, optionally, eigenvectors */ -/* of a real symmetric matrix A */ -La_extern void -F77_NAME(dsyev)(const char* jobz, const char* uplo, - const int* n, double* a, const int* lda, - double* w, double* work, const int* lwork, int* info); -/* DSYEVD - compute all eigenvalues and, optionally, eigenvectors */ -/* of a real symmetric matrix A */ -La_extern void -F77_NAME(dsyevd)(const char* jobz, const char* uplo, - const int* n, double* a, const int* lda, - double* w, double* work, const int* lwork, - int* iwork, const int* liwork, int* info); -/* DSYEVX - compute selected eigenvalues and, optionally, */ -/* eigenvectors of a real symmetric matrix A */ -La_extern void -F77_NAME(dsyevx)(const char* jobz, const char* range, - const char* uplo, const int* n, - double* a, const int* lda, - const double* vl, const double* vu, - const int* il, const int* iu, - const double* abstol, - int* m, double* w, - double* z, const int* ldz, - double* work, const int* lwork, int* iwork, - int* ifail, int* info); -/* DSYEVR - compute all eigenvalues and, optionally, eigenvectors */ -/* of a real symmetric matrix A */ -La_extern void -F77_NAME(dsyevr)(const char *jobz, const char *range, const char *uplo, - const int *n, double *a, const int *lda, - const double *vl, const double *vu, - const int *il, const int *iu, - const double *abstol, int *m, double *w, - double *z, const int *ldz, int *isuppz, - double *work, const int *lwork, - int *iwork, const int *liwork, - int *info); -/* DSYGS2 - reduce a real symmetric-definite generalized */ -/* eigenproblem to standard form */ -La_extern void -F77_NAME(dsygs2)(const int* itype, const char* uplo, - const int* n, double* a, const int* lda, - const double* b, const int* ldb, int* info); -/* DSYGST - reduce a real symmetric-definite generalized */ -/* eigenproblem to standard form */ -La_extern void -F77_NAME(dsygst)(const int* itype, const char* uplo, - const int* n, double* a, const int* lda, - const double* b, const int* ldb, int* info); -/* DSYGV - compute all the eigenvalues, and optionally, the */ -/* eigenvectors of a real generalized symmetric-definite */ -/* eigenproblem, of the form A*x=(lambda);*B*x, A*Bx=(lambda);*x, */ -/* or B*A*x=(lambda);*x */ -La_extern void -F77_NAME(dsygv)(const int* itype, const char* jobz, - const char* uplo, const int* n, - double* a, const int* lda, - double* b, const int* ldb, - double* w, double* work, const int* lwork, - int* info); -/* DSYRFS - improve the computed solution to a system of linear */ -/* equations when the coefficient matrix is symmetric indefinite, */ -/* and provides error bounds and backward error estimates for the */ -/* solution */ -La_extern void -F77_NAME(dsyrfs)(const char* uplo, const int* n, - const int* nrhs, - const double* a, const int* lda, - const double* af, const int* ldaf, - const int* ipiv, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); - -/* DSYSV - compute the solution to a real system of linear */ -/* equations A * X = B, */ -La_extern void -F77_NAME(dsysv)(const char* uplo, const int* n, - const int* nrhs, - double* a, const int* lda, int* ipiv, - double* b, const int* ldb, - double* work, const int* lwork, int* info); - -/* DSYSVX - use the diagonal pivoting factorization to compute */ -/* the solution to a real system of linear equations A * X = B, */ -La_extern void -F77_NAME(dsysvx)(const int* fact, const char* uplo, - const int* n, const int* nrhs, - const double* a, const int* lda, - double* af, const int* ldaf, int* ipiv, - const double* b, const int* ldb, - double* x, const int* ldx, double* rcond, - double* ferr, double* berr, - double* work, const int* lwork, - int* iwork, int* info); - -/* DSYTD2 - reduce a real symmetric matrix A to symmetric */ -/* tridiagonal form T by an orthogonal similarity transformation */ -La_extern void -F77_NAME(dsytd2)(const char* uplo, const int* n, - double* a, const int* lda, - double* d, double* e, double* tau, - int* info); - -/* DSYTF2 - compute the factorization of a real symmetric matrix */ -/* A using the Bunch-Kaufman diagonal pivoting method */ -La_extern void -F77_NAME(dsytf2)(const char* uplo, const int* n, - double* a, const int* lda, - int* ipiv, int* info); - -/* DSYTRD - reduce a real symmetric matrix A to real symmetric */ -/* tridiagonal form T by an orthogonal similarity transformation */ -La_extern void -F77_NAME(dsytrd)(const char* uplo, const int* n, - double* a, const int* lda, - double* d, double* e, double* tau, - double* work, const int* lwork, int* info); - -/* DSYTRF - compute the factorization of a real symmetric matrix */ -/* A using the Bunch-Kaufman diagonal pivoting method */ -La_extern void -F77_NAME(dsytrf)(const char* uplo, const int* n, - double* a, const int* lda, int* ipiv, - double* work, const int* lwork, int* info); - -/* DSYTRI - compute the inverse of a real symmetric indefinite */ -/* matrix A using the factorization A = U*D*U**T or A = L*D*L**T */ -/* computed by DSYTRF */ -La_extern void -F77_NAME(dsytri)(const char* uplo, const int* n, - double* a, const int* lda, const int* ipiv, - double* work, int* info); - -/* DSYTRS - solve a system of linear equations A*X = B with a */ -/* real symmetric matrix A using the factorization A = U*D*U**T or */ -/* A = L*D*L**T computed by DSYTRF */ -La_extern void -F77_NAME(dsytrs)(const char* uplo, const int* n, - const int* nrhs, - const double* a, const int* lda, - const int* ipiv, - double* b, const int* ldb, int* info); - -/* Double precision Triangular Band matrices */ - -/* DTBCON - estimate the reciprocal of the condition number of a */ -/* triangular band matrix A, in either the 1-norm or the */ -/* infinity-norm */ -La_extern void -F77_NAME(dtbcon)(const char* norm, const char* uplo, - const char* diag, const int* n, const int* kd, - const double* ab, const int* ldab, - double* rcond, double* work, - int* iwork, int* info); -/* DTBRFS - provide error bounds and backward error estimates for */ -/* the solution to a system of linear equations with a triangular */ -/* band coefficient matrix */ -La_extern void -F77_NAME(dtbrfs)(const char* uplo, const char* trans, - const char* diag, const int* n, const int* kd, - const int* nrhs, - const double* ab, const int* ldab, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); -/* DTBTRS - solve a triangular system of the form A * X = B or */ -/* A**T * X = B, */ -La_extern void -F77_NAME(dtbtrs)(const char* uplo, const char* trans, - const char* diag, const int* n, - const int* kd, const int* nrhs, - const double* ab, const int* ldab, - double* b, const int* ldb, int* info); - -/* Double precision Triangular matrices Generalized problems */ - -/* DTGEVC - compute some or all of the right and/or left */ -/* generalized eigenvectors of a pair of real upper triangular */ -/* matrices (A,B); */ -La_extern void -F77_NAME(dtgevc)(const char* side, const char* howmny, - const int* select, const int* n, - const double* a, const int* lda, - const double* b, const int* ldb, - double* vl, const int* ldvl, - double* vr, const int* ldvr, - const int* mm, int* m, double* work, int* info); - -/* DTGSJA - compute the generalized singular value decomposition */ -/* (GSVD); of two real upper triangular (or trapezoidal); matrices */ -/* A and B */ -La_extern void -F77_NAME(dtgsja)(const char* jobu, const char* jobv, const char* jobq, - const int* m, const int* p, const int* n, - const int* k, const int* l, - double* a, const int* lda, - double* b, const int* ldb, - const double* tola, const double* tolb, - double* alpha, double* beta, - double* u, const int* ldu, - double* v, const int* ldv, - double* q, const int* ldq, - double* work, int* ncycle, int* info); - -/* Double precision Triangular matrices Packed storage */ - -/* DTPCON - estimate the reciprocal of the condition number of a */ -/* packed triangular matrix A, in either the 1-norm or the */ -/* infinity-norm */ -La_extern void -F77_NAME(dtpcon)(const char* norm, const char* uplo, - const char* diag, const int* n, - const double* ap, double* rcond, - double* work, int* iwork, int* info); - -/* DTPRFS - provide error bounds and backward error estimates for */ -/* the solution to a system of linear equations with a triangular */ -/* packed coefficient matrix */ -La_extern void -F77_NAME(dtprfs)(const char* uplo, const char* trans, - const char* diag, const int* n, - const int* nrhs, const double* ap, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); - -/* Double precision TRiangular matrices */ - -/* DTPTRI - compute the inverse of a real upper or lower */ -/* triangular matrix A stored in packed format */ -La_extern void -F77_NAME(dtptri)(const char* uplo, const char* diag, - const int* n, double* ap, int* info); - -/* DTPTRS - solve a triangular system of the form A * X = B or */ -/* A**T * X = B, */ -La_extern void -F77_NAME(dtptrs)(const char* uplo, const char* trans, - const char* diag, const int* n, - const int* nrhs, const double* ap, - double* b, const int* ldb, int* info); - -/* DTRCON - estimate the reciprocal of the condition number of a */ -/* triangular matrix A, in either the 1-norm or the infinity-norm */ -La_extern void -F77_NAME(dtrcon)(const char* norm, const char* uplo, - const char* diag, const int* n, - const double* a, const int* lda, - double* rcond, double* work, - int* iwork, int* info); - -/* DTREVC - compute some or all of the right and/or left */ -/* eigenvectors of a real upper quasi-triangular matrix T */ -La_extern void -F77_NAME(dtrevc)(const char* side, const char* howmny, - const int* select, const int* n, - const double* t, const int* ldt, - double* vl, const int* ldvl, - double* vr, const int* ldvr, - const int* mm, int* m, double* work, int* info); - -/* DTREXC - reorder the real Schur factorization of a real matrix */ -/* A = Q*T*Q**T, so that the diagonal block of T with row index */ -/* IFST is moved to row ILST */ -La_extern void -F77_NAME(dtrexc)(const char* compq, const int* n, - double* t, const int* ldt, - double* q, const int* ldq, - int* ifst, int* ILST, - double* work, int* info); - -/* DTRRFS - provide error bounds and backward error estimates for */ -/* the solution to a system of linear equations with a triangular */ -/* coefficient matrix */ -La_extern void -F77_NAME(dtrrfs)(const char* uplo, const char* trans, - const char* diag, const int* n, const int* nrhs, - const double* a, const int* lda, - const double* b, const int* ldb, - double* x, const int* ldx, - double* ferr, double* berr, - double* work, int* iwork, int* info); - -/* DTRSEN - reorder the real Schur factorization of a real matrix */ -/* A = Q*T*Q**T, so that a selected cluster of eigenvalues appears */ -/* in the leading diagonal blocks of the upper quasi-triangular */ -/* matrix T, */ -La_extern void -F77_NAME(dtrsen)(const char* job, const char* compq, - const int* select, const int* n, - double* t, const int* ldt, - double* q, const int* ldq, - double* wr, double* wi, - int* m, double* s, double* sep, - double* work, const int* lwork, - int* iwork, const int* liwork, int* info); - -/* DTRSNA - estimate reciprocal condition numbers for specified */ -/* eigenvalues and/or right eigenvectors of a real upper */ -/* quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q */ -/* orthogonal); */ -La_extern void -F77_NAME(dtrsna)(const char* job, const char* howmny, - const int* select, const int* n, - const double* t, const int* ldt, - const double* vl, const int* ldvl, - const double* vr, const int* ldvr, - double* s, double* sep, const int* mm, - int* m, double* work, const int* lwork, - int* iwork, int* info); - -/* DTRSYL - solve the real Sylvester matrix equation */ -La_extern void -F77_NAME(dtrsyl)(const char* trana, const char* tranb, - const int* isgn, const int* m, const int* n, - const double* a, const int* lda, - const double* b, const int* ldb, - double* c, const int* ldc, - double* scale, int* info); - -/* DTRTI2 - compute the inverse of a real upper or lower */ -/* triangular matrix */ -La_extern void -F77_NAME(dtrti2)(const char* uplo, const char* diag, - const int* n, double* a, const int* lda, - int* info); - -/* DTRTRI - compute the inverse of a real upper or lower */ -/* triangular matrix A */ -La_extern void -F77_NAME(dtrtri)(const char* uplo, const char* diag, - const int* n, double* a, const int* lda, - int* info); - -/* DTRTRS - solve a triangular system of the form A * X = B or */ -/* A**T * X = B */ -La_extern void -F77_NAME(dtrtrs)(const char* uplo, const char* trans, - const char* diag, const int* n, const int* nrhs, - const double* a, const int* lda, - double* b, const int* ldb, int* info); - -/* DTZRQF - reduce the M-by-N ( M<=N ); real upper trapezoidal */ -/* matrix A to upper triangular form by means of orthogonal */ -/* transformations */ -La_extern void -F77_NAME(dtzrqf)(const int* m, const int* n, - double* a, const int* lda, - double* tau, int* info); - - - -/* 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 */ -La_extern void -F77_NAME(dhgeqz)(const char* job, const char* compq, const char* compz, - const int* n, const int *ILO, const int* IHI, - double* a, const int* lda, - double* b, const int* ldb, - double* alphar, double* alphai, const double* beta, - double* q, const int* ldq, - double* z, const int* ldz, - double* work, const int* lwork, int* info); -/* DHSEIN - use inverse iteration to find specified right and/or */ -/* left eigenvectors of a real upper Hessenberg matrix H */ -La_extern void -F77_NAME(dhsein)(const char* side, const char* eigsrc, - const char* initv, int* select, - const int* n, double* h, const int* ldh, - double* wr, double* wi, - double* vl, const int* ldvl, - double* vr, const int* ldvr, - const int* mm, int* m, double* work, - int* ifaill, int* ifailr, int* info); -/* DHSEQR - compute the eigenvalues of a real upper Hessenberg */ -/* matrix H and, optionally, the matrices T and Z from the Schur */ -/* decomposition H = Z T Z**T, where T is an upper */ -/* quasi-triangular matrix (the Schur form);, and Z is the */ -/* orthogonal matrix of Schur vectors */ -La_extern void -F77_NAME(dhseqr)(const char* job, const char* compz, const int* n, - const int* ilo, const int* ihi, - double* h, const int* ldh, - double* wr, double* wi, - double* z, const int* ldz, - double* work, const int* lwork, int* info); -/* DLABAD - take as input the values computed by SLAMCH for */ -/* underflow and overflow, and returns the square root of each of */ -/* these values if the log of LARGE is sufficiently large */ -La_extern void -F77_NAME(dlabad)(double* small, double* large); -/* DLABRD - reduce the first NB rows and columns of a real */ -/* general m by n matrix A to upper or lower bidiagonal form by an */ -/* orthogonal transformation Q' * A * P, and returns the matrices */ -/* X and Y which are needed to apply the transformation to the */ -/* unreduced part of A */ -La_extern void -F77_NAME(dlabrd)(const int* m, const int* n, const int* nb, - double* a, const int* lda, double* d, double* e, - double* tauq, double* taup, - double* x, const int* ldx, double* y, const int* ldy); -/* DLACON - estimate the 1-norm of a square, real matrix A */ -La_extern void -F77_NAME(dlacon)(const int* n, double* v, double* x, - int* isgn, double* est, int* kase); -/* DLACPY - copy all or part of a two-dimensional matrix A to */ -/* another matrix B */ -La_extern void -F77_NAME(dlacpy)(const char* uplo, const int* m, const int* n, - const double* a, const int* lda, - double* b, const int* ldb); -/* DLADIV - perform complex division in real arithmetic */ -La_extern void -F77_NAME(dladiv)(const double* a, const double* b, - const double* c, const double* d, - double* p, double* q); -/* DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] */ -/* [ B C ] */ -La_extern void -F77_NAME(dlae2)(const double* a, const double* b, const double* c, - double* rt1, double* rt2); -/* DLAEBZ - contain the iteration loops which compute and use the */ -/* function N(w);, which is the count of eigenvalues of a */ -/* symmetric tridiagonal matrix T less than or equal to its */ -/* argument w */ -La_extern void -F77_NAME(dlaebz)(const int* ijob, const int* nitmax, const int* n, - const int* mmax, const int* minp, const int* nbmin, - const double* abstol, const double* reltol, - const double* pivmin, double* d, double* e, - double* e2, int* nval, double* ab, double* c, - int* mout, int* nab, double* work, int* iwork, - int* info); -/* DLAED0 - compute all eigenvalues and corresponding */ -/* eigenvectors of a symmetric tridiagonal matrix using the divide */ -/* and conquer method */ -La_extern void -F77_NAME(dlaed0)(const int* icompq, const int* qsiz, const int* n, - double* d, double* e, double* q, const int* ldq, - double* qstore, const int* ldqs, - double* work, int* iwork, int* info); -/* DLAED1 - compute the updated eigensystem of a diagonal matrix */ -/* after modification by a rank-one symmetric matrix */ -La_extern void -F77_NAME(dlaed1)(const int* n, double* d, double* q, const int* ldq, - int* indxq, const double* rho, const int* cutpnt, - double* work, int* iwork, int* info); -/* DLAED2 - merge the two sets of eigenvalues together into a */ -/* single sorted set */ -La_extern void -F77_NAME(dlaed2)(const int* k, const int* n, double* d, - double* q, const int* ldq, int* indxq, - double* rho, 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 */ -La_extern 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 */ -La_extern void -F77_NAME(dlaed4)(const int* n, const int* i, const double* d, - const double* z, const double* delta, - const double* rho, double* dlam, int* info); -/* DLAED5 - subroutine computes the I-th eigenvalue of a */ -/* symmetric rank-one modification of a 2-by-2 diagonal matrix */ -/* diag( D ); + RHO The diagonal elements in the array D are */ -/* assumed to satisfy D(i); < D(j); for i < j */ -La_extern void -F77_NAME(dlaed5)(const int* i, const double* d, const double* z, - double* delta, const double* rho, double* dlam); -/* DLAED6 - compute the positive or negative root (closest to the */ -/* origin); of z(1); z(2); z(3); f(x); = rho + --------- + */ -/* ---------- + --------- d(1);-x d(2);-x d(3);-x It is assumed */ -/* that if ORGATI = .true */ -La_extern void -F77_NAME(dlaed6)(const int* kniter, const int* orgati, - const double* rho, const double* d, - const double* z, const double* finit, - double* tau, int* info); -/* DLAED7 - compute the updated eigensystem of a diagonal matrix */ -/* after modification by a rank-one symmetric matrix */ -La_extern void -F77_NAME(dlaed7)(const int* icompq, const int* n, - const int* qsiz, const int* tlvls, - const int* curlvl, const int* curpbm, - double* d, double* q, const int* ldq, - int* indxq, const double* rho, const int* cutpnt, - double* qstore, double* qptr, const int* prmptr, - const int* perm, const int* givptr, - const int* givcol, const double* givnum, - double* work, int* iwork, int* info); -/* DLAED8 - merge the two sets of eigenvalues together into a */ -/* single sorted set */ -La_extern void -F77_NAME(dlaed8)(const int* icompq, const int* k, - const int* n, const int* qsiz, - double* d, double* q, const int* ldq, - const int* indxq, double* rho, - const int* cutpnt, const double* z, - double* dlamda, double* q2, const int* ldq2, - double* w, int* perm, int* givptr, - int* givcol, double* givnum, int* indxp, - int* indx, int* info); -/* DLAED9 - find the roots of the secular equation, as defined by */ -/* the values in double* d, Z, and RHO, between KSTART and KSTOP */ -La_extern void -F77_NAME(dlaed9)(const int* k, const int* kstart, const int* kstop, - const int* n, double* d, double* q, const int* ldq, - const double* rho, const double* dlamda, - const double* w, double* s, const int* lds, int* info); -/* DLAEDA - compute the Z vector corresponding to the merge step */ -/* in the CURLVLth step of the merge process with TLVLS steps for */ -/* the CURPBMth problem */ -La_extern void -F77_NAME(dlaeda)(const int* n, const int* tlvls, const int* curlvl, - const int* curpbm, const int* prmptr, const int* perm, - const int* givptr, const int* givcol, - const double* givnum, const double* q, - const int* qptr, double* z, double* ztemp, int* info); -/* DLAEIN - use inverse iteration to find a right or left */ -/* eigenvector corresponding to the eigenvalue (WR,WI); of a real */ -/* upper Hessenberg matrix H */ -La_extern void -F77_NAME(dlaein)(const int* rightv, const int* noinit, const int* n, - const double* h, const int* ldh, - const double* wr, const double* wi, - double* vr, double* vi, - double* b, const int* ldb, double* work, - const double* eps3, const double* smlnum, - const double* bignum, int* info); -/* DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric */ -/* matrix [ A B ] [ B C ] */ -La_extern void -F77_NAME(dlaev2)(const double* a, const double* b, const double* c, - double* rt1, double* rt2, double* cs1, double *sn1); -/* DLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 */ -/* or 2 in an upper quasi-triangular matrix T by an orthogonal */ -/* similarity transformation */ -La_extern void -F77_NAME(dlaexc)(const int* wantq, const int* n, double* t, const int* ldt, - double* q, const int* ldq, const int* j1, - const int* n1, const int* n2, double* work, int* info); -/* DLAG2 - compute the eigenvalues of a 2 x 2 generalized */ -/* eigenvalue problem A - w B, with scaling as necessary to aextern void */ -/* over-/underflow */ -La_extern void -F77_NAME(dlag2)(const double* a, const int* lda, const double* b, - const int* ldb, const double* safmin, - double* scale1, double* scale2, - double* wr1, double* wr2, double* wi); -/* DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such */ -/* that if ( UPPER ); then U'*A*Q = U'*( A1 A2 );*Q = ( x 0 ); */ -/* ( 0 A3 ); ( x x ); and V'*B*Q = V'*( B1 B2 );*Q = ( x 0 ); ( */ -/* 0 B3 ); ( x x ); or if ( .NOT.UPPER ); then U'*A*Q = U'*( A1 */ -/* 0 );*Q = ( x x ); ( A2 A3 ); ( 0 x ); and V'*B*Q = V'*( B1 0 */ -/* );*Q = ( x x ); ( B2 B3 ); ( 0 x ); The rows of the */ -/* transformed A and B are parallel, where U = ( CSU SNU );, V = */ -/* ( CSV SNV );, Q = ( CSQ SNQ ); ( -SNU CSU ); ( -SNV CSV ); ( */ -/* -SNQ CSQ ); Z' denotes the transpose of Z */ -La_extern void -F77_NAME(dlags2)(const int* upper, - const double* a1, const double* a2, const double* a3, - const double* b1, const double* b2, const double* b3, - double* csu, double* snu, - double* csv, double* snv, double *csq, double *snq); -/* DLAGTF - factorize the matrix (T - lambda*I);, where T is an n */ -/* by n tridiagonal matrix and lambda is a scalar, as T - */ -/* lambda*I = PLU, */ -La_extern void -F77_NAME(dlagtf)(const int* n, double* a, const double* lambda, - double* b, double* c, const double *tol, - double* d, int* in, int* info); -/* DLAGTM - perform a matrix-vector product of the form B := */ -/* alpha * A * X + beta * B where A is a tridiagonal matrix of */ -/* order N, B and X are N by NRHS matrices, and alpha and beta are */ -/* real scalars, each of which may be 0., 1., or -1 */ -La_extern void -F77_NAME(dlagtm)(const char* trans, const int* n, const int* nrhs, - const double* alpha, const double* dl, - const double* d, const double* du, - const double* x, const int* ldx, const double* beta, - double* b, const int* ldb); -/* DLAGTS - may be used to solve one of the systems of equations */ -/* (T - lambda*I);*x = y or (T - lambda*I);'*x = y, */ -La_extern void -F77_NAME(dlagts)(const int* job, const int* n, - const double* a, const double* b, - const double* c, const double* d, - const int* in, double* y, double* tol, int* info); -/* DLAHQR - an auxiliary routine called by DHSEQR to update the */ -/* eigenvalues and Schur decomposition already computed by DHSEQR, */ -/* by dealing with the Hessenberg submatrix in rows and columns */ -/* ILO to IHI */ -La_extern void -F77_NAME(dlahqr)(const int* wantt, const int* wantz, const int* n, - const int* ilo, const int* ihi, - double* H, const int* ldh, double* wr, double* wi, - const int* iloz, const int* ihiz, - double* z, const int* ldz, int* info); -/* DLAHRD - reduce the first NB columns of a real general */ -/* n-by-(n-k+1); matrix A so that elements below the k-th */ -/* subdiagonal are zero */ -La_extern void -F77_NAME(dlahrd)(const int* n, const int* k, const int* nb, - double* a, const int* lda, - double* tau, double* t, const int* ldt, - double* y, const int* ldy); -/* DLAIC1 - apply one step of incremental condition estimation in */ -/* its simplest version */ -La_extern void -F77_NAME(dlaic1)(const int* job, const int* j, const double* x, - const double* sest, const double* w, - const double* gamma, double* sestpr, - double* s, double* c); -/* DLALN2 - solve a system of the form (ca A - w D ); X = s B or */ -/* (ca A' - w D); X = s B with possible scaling ("s"); and */ -/* perturbation of A */ -La_extern void -F77_NAME(dlaln2)(const int* ltrans, const int* na, const int* nw, - const double* smin, const double* ca, - const double* a, const int* lda, - const double* d1, const double* d2, - const double* b, const int* ldb, - const double* wr, const double* wi, - double* x, const int* ldx, double* scale, - double* xnorm, int* info); -/* DLAMCH - determine double precision machine parameters */ -La_extern double -F77_NAME(dlamch)(const char* cmach); -/* DLAMRG - will create a permutation list which will merge the */ -/* elements of A (which is composed of two independently sorted */ -/* sets); into a single set which is sorted in ascending order */ -La_extern void -F77_NAME(dlamrg)(const int* n1, const int* n2, const double* a, - const int* dtrd1, const int* dtrd2, int* index); -/* DLANGB - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of an n by n band matrix A, with kl sub-diagonals and ku */ -/* super-diagonals */ -La_extern double -F77_NAME(dlangb)(const char* norm, const int* n, - const int* kl, const int* ku, const double* ab, - const int* ldab, double* work); -/* DLANGE - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a real matrix A */ -La_extern double -F77_NAME(dlange)(const char* norm, const int* m, const int* n, - const double* a, const int* lda, double* work); -/* DLANGT - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a real tridiagonal matrix A */ -La_extern double -F77_NAME(dlangt)(const char* norm, const int* n, - const double* dl, const double* d, - const double* du); -/* DLANHS - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a Hessenberg matrix A */ -La_extern double -F77_NAME(dlanhs)(const char* norm, const int* n, - const double* a, const int* lda, double* work); -/* DLANSB - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of an n by n symmetric band matrix A, with k */ -/* super-diagonals */ -La_extern double -F77_NAME(dlansb)(const char* norm, const char* uplo, - const int* n, const int* k, - const double* ab, const int* ldab, double* work); -/* DLANSP - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a real symmetric matrix A, supplied in packed form */ -La_extern double -F77_NAME(dlansp)(const char* norm, const char* uplo, - const int* n, const double* ap, double* work); -/* DLANST - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a real symmetric tridiagonal matrix A */ -La_extern double -F77_NAME(dlanst)(const char* norm, const int* n, - const double* d, const double* e); -/* DLANSY - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a real symmetric matrix A */ -La_extern double -F77_NAME(dlansy)(const char* norm, const char* uplo, const int* n, - const double* a, const int* lda, double* work); -/* DLANTB - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of an n by n triangular band matrix A, with ( k + 1 ) diagonals */ -La_extern double -F77_NAME(dlantb)(const char* norm, const char* uplo, - const char* diag, const int* n, const int* k, - const double* ab, const int* ldab, double* work); -/* DLANTP - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a triangular matrix A, supplied in packed form */ -La_extern double -F77_NAME(dlantp)(const char* norm, const char* uplo, const char* diag, - const int* n, const double* ap, double* work); -/* DLANTR - return the value of the one norm, or the Frobenius */ -/* norm, or the infinity norm, or the element of largest absolute */ -/* value of a trapezoidal or triangular matrix A */ -La_extern double -F77_NAME(dlantr)(const char* norm, const char* uplo, - const char* diag, const int* m, const int* n, - const double* a, const int* lda, double* work); -/* DLANV2 - compute the Schur factorization of a real 2-by-2 */ -/* nonsymmetric matrix in standard form */ -La_extern void -F77_NAME(dlanv2)(double* a, double* b, double* c, double* d, - double* rt1r, double* rt1i, double* rt2r, double* rt2i, - double* cs, double *sn); -/* DLAPLL - two column vectors X and Y, let A = ( X Y ); */ -La_extern void -F77_NAME(dlapll)(const int* n, double* x, const int* incx, - double* y, const int* incy, double* ssmin); -/* DLAPMT - rearrange the columns of the M by N matrix X as */ -/* specified by the permutation K(1);,K(2);,...,K(N); of the */ -/* integers 1,...,N */ -La_extern void -F77_NAME(dlapmt)(const int* forwrd, const int* m, const int* n, - double* x, const int* ldx, const int* k); -/* DLAPY2 - return sqrt(x**2+y**2);, taking care not to cause */ -/* unnecessary overflow */ -La_extern double -F77_NAME(dlapy2)(const double* x, const double* y); -/* DLAPY3 - return sqrt(x**2+y**2+z**2);, taking care not to */ -/* cause unnecessary overflow */ -La_extern double -F77_NAME(dlapy3)(const double* x, const double* y, const double* z); -/* DLAQGB - equilibrate a general M by N band matrix A with KL */ -/* subdiagonals and KU superdiagonals using the row and scaling */ -/* factors in the vectors R and C */ -La_extern void -F77_NAME(dlaqgb)(const int* m, const int* n, - const int* kl, const int* ku, - double* ab, const int* ldab, - double* r, double* c, - double* rowcnd, double* colcnd, - const double* amax, char* equed); -/* DLAQGE - equilibrate a general M by N matrix A using the row */ -/* and scaling factors in the vectors R and C */ -La_extern void -F77_NAME(dlaqge)(const int* m, const int* n, - double* a, const int* lda, - double* r, double* c, - double* rowcnd, double* colcnd, - const double* amax, char* equed); -/* DLAQSB - equilibrate a symmetric band matrix A using the */ -/* scaling factors in the vector S */ -La_extern void -F77_NAME(dlaqsb)(const char* uplo, const int* n, const int* kd, - double* ab, const int* ldab, const double* s, - const double* scond, const double* amax, char* equed); -/* DLAQSP - equilibrate a symmetric matrix A using the scaling */ -/* factors in the vector S */ -La_extern void -F77_NAME(dlaqsp)(const char* uplo, const int* n, - double* ap, const double* s, const double* scond, - const double* amax, int* equed); -/* DLAQSY - equilibrate a symmetric matrix A using the scaling */ -/* factors in the vector S */ -La_extern void -F77_NAME(dlaqsy)(const char* uplo, const int* n, - double* a, const int* lda, - const double* s, const double* scond, - const double* amax, int* equed); -/* DLAQTR - solve the real quasi-triangular system */ -/* op(T) * p = scale*c */ -La_extern void -F77_NAME(dlaqtr)(const int* ltran, const int* lreal, const int* n, - const double* t, const int* ldt, - const double* b, const double* w, - double* scale, double* x, double* work, int* info); -/* DLAR2V - apply a vector of real plane rotations from both */ -/* sides to a sequence of 2-by-2 real symmetric matrices, defined */ -/* by the elements of the vectors x, y and z */ -La_extern void -F77_NAME(dlar2v)(const int* n, double* x, double* y, - double* z, const int* incx, - const double* c, const double* s, - const int* incc); -/* DLARF - apply a real elementary reflector H to a real m by n */ -/* matrix C, from either the left or the right */ -La_extern void -F77_NAME(dlarf)(const char* side, const int* m, const int* n, - const double* v, const int* incv, const double* tau, - double* c, const int* ldc, double* work); -/* DLARFB - apply a real block reflector H or its transpose H' */ -/* to a real m by n matrix C, from either the left or the right */ -La_extern void -F77_NAME(dlarfb)(const char* side, const char* trans, - const char* direct, const char* storev, - const int* m, const int* n, const int* k, - const double* v, const int* ldv, - const double* t, const int* ldt, - double* c, const int* ldc, - double* work, const int* lwork); -/* DLARFG - generate a real elementary reflector H of order n, */ -/* such that H * ( alpha ) = ( beta ), H' * H = I */ -La_extern void -F77_NAME(dlarfg)(const int* n, const double* alpha, - double* x, const int* incx, double* tau); -/* DLARFT - form the triangular factor T of a real block */ -/* reflector H of order n, which is defined as a product of k */ -/* elementary reflectors */ -La_extern void -F77_NAME(dlarft)(const char* direct, const char* storev, - const int* n, const int* k, double* v, const int* ldv, - const double* tau, double* t, const int* ldt); -/* DLARFX - apply a real elementary reflector H to a real m by n */ -/* matrix C, from either the left or the right */ -La_extern void -F77_NAME(dlarfx)(const char* side, const int* m, const int* n, - const double* v, const double* tau, - double* c, const int* ldc, double* work); -/* DLARGV - generate a vector of real plane rotations, determined */ -/* by elements of the real vectors x and y */ -La_extern void -F77_NAME(dlargv)(const int* n, double* x, const int* incx, - double* y, const int* incy, double* c, const int* incc); -/* DLARNV - return a vector of n random real numbers from a */ -/* uniform or normal distribution */ -La_extern void -F77_NAME(dlarnv)(const int* idist, int* iseed, const int* n, double* x); -/* DLARTG - generate a plane rotation so that [ CS SN ] */ -La_extern void -F77_NAME(dlartg)(const double* f, const double* g, double* cs, - double* sn, double *r); -/* DLARTV - apply a vector of real plane rotations to elements of */ -/* the real vectors x and y */ -La_extern void -F77_NAME(dlartv)(const int* n, double* x, const int* incx, - double* y, const int* incy, - const double* c, const double* s, - const int* incc); -/* DLARUV - return a vector of n random real numbers from a */ -/* uniform (0,1); */ -La_extern void -F77_NAME(dlaruv)(int* iseed, const int* n, double* x); - -/* DLAS2 - compute the singular values of the 2-by-2 matrix */ -/* [ F G ] [ 0 H ] */ -La_extern void -F77_NAME(dlas2)(const double* f, const double* g, const double* h, - double* ssmin, double* ssmax); - -/* DLASCL - multiply the M by N real matrix A by the real scalar */ -/* CTO/CFROM */ -La_extern void -F77_NAME(dlascl)(const char* type, - const int* kl,const int* ku, - double* cfrom, double* cto, - const int* m, const int* n, - double* a, const int* lda, int* info); - -/* DLASET - initialize an m-by-n matrix A to BETA on the diagonal */ -/* and ALPHA on the offdiagonals */ -La_extern void -F77_NAME(dlaset)(const char* uplo, const int* m, const int* n, - const double* alpha, const double* beta, - double* a, const int* lda); -/* DLASQ1 - DLASQ1 computes the singular values of a real N-by-N */ -/* bidiagonal matrix with diagonal D and off-diagonal E */ -La_extern void -F77_NAME(dlasq1)(const int* n, double* d, double* e, - double* work, int* info); -/* DLASQ2 - DLASQ2 computes the singular values of a real N-by-N */ -/* unreduced bidiagonal matrix with squared diagonal elements in */ -/* Q and squared off-diagonal elements in E */ -La_extern void -F77_NAME(dlasq2)(const int* m, double* q, double* e, - double* qq, double* ee, const double* eps, - const double* tol2, const double* small2, - double* sup, int* kend, int* info); -/* DLASQ3 - DLASQ3 is the workhorse of the whole bidiagonal SVD */ -/* algorithm */ -La_extern void -F77_NAME(dlasq3)(int* n, double* q, double* e, double* qq, - double* ee, double* sup, double *sigma, - int* kend, int* off, int* iphase, - const int* iconv, const double* eps, - const double* tol2, const double* small2); -/* DLASQ4 - DLASQ4 estimates TAU, the smallest eigenvalue of a */ -/* matrix */ -La_extern void -F77_NAME(dlasq4)(const int* n, const double* q, const double* e, - double* tau, double* sup); -/* DLASR - perform the transformation A := P*A, when SIDE = 'L' */ -/* or 'l' ( Left-hand side ); A := A*P', when SIDE = 'R' or 'r' */ -/* ( Right-hand side ); where A is an m by n real matrix and P is */ -/* an orthogonal matrix, */ -La_extern void -F77_NAME(dlasr)(const char* side, const char* pivot, - const char* direct, const int* m, const int* n, - const double* c, const double* s, - double* a, const int* lda); -/* DLASRT - the numbers in D in increasing order (if ID = 'I'); */ -/* or in decreasing order (if ID = 'D' ); */ -La_extern void -F77_NAME(dlasrt)(const char* id, const int* n, double* d, int* info); -/* DLASSQ - return the values scl and smsq such that ( scl**2 */ -/* );*smsq = x( 1 );**2 +...+ x( n );**2 + ( scale**2 );*sumsq, */ -La_extern void -F77_NAME(dlassq)(const int* n, const double* x, const int* incx, - double* scale, double* sumsq); -/* DLASV2 - compute the singular value decomposition of a 2-by-2 */ -/* triangular matrix [ F G ] [ 0 H ] */ -La_extern void -F77_NAME(dlasv2)(const double* f, const double* g, const double* h, - double* ssmin, double* ssmax, double* snr, double* csr, - double* snl, double* csl); -/* DLASWP - perform a series of row interchanges on the matrix A */ -La_extern void -F77_NAME(dlaswp)(const int* n, double* a, const int* lda, - const int* k1, const int* k2, - const int* ipiv, const int* incx); -/* DLASY2 - solve for the N1 by N2 matrix double* x, 1 <= N1,N2 <= 2, in */ -/* op(TL);*X + ISGN*X*op(TR); = SCALE*B, */ -La_extern void -F77_NAME(dlasy2)(const int* ltranl, const int* ltranr, - const int* isgn, const int* n1, const int* n2, - const double* tl, const int* ldtl, - const double* tr, const int* ldtr, - const double* b, const int* ldb, - double* scale, double* x, const int* ldx, - double* xnorm, int* info); -/* DLASYF - compute a partial factorization of a real symmetric */ -/* matrix A using the Bunch-Kaufman diagonal pivoting method */ -La_extern void -F77_NAME(dlasyf)(const char* uplo, const int* n, - const int* nb, const int* kb, - double* a, const int* lda, int* ipiv, - double* w, const int* ldw, int* info); -/* DLATBS - solve one of the triangular systems A *x = s*b or */ -/* A'*x = s*b with scaling to prevent overflow, where A is an */ -/* upper or lower triangular band matrix */ -La_extern void -F77_NAME(dlatbs)(const char* uplo, const char* trans, - const char* diag, const char* normin, - const int* n, const int* kd, - const double* ab, const int* ldab, - double* x, double* scale, double* cnorm, int* info); -/* DLATPS - solve one of the triangular systems A *x = s*b or */ -/* A'*x = s*b with scaling to prevent overflow, where A is an */ -/* upper or lower triangular matrix stored in packed form */ -La_extern void -F77_NAME(dlatps)(const char* uplo, const char* trans, - const char* diag, const char* normin, - const int* n, const double* ap, - double* x, double* scale, double* cnorm, int* info); -/* DLATRD - reduce NB rows and columns of a real symmetric matrix */ -/* A to symmetric tridiagonal form by an orthogonal similarity */ -/* transformation Q' * A * Q, and returns the matrices V and W */ -/* which are needed to apply the transformation to the unreduced */ -/* part of A */ -La_extern void -F77_NAME(dlatrd)(const char* uplo, const int* n, const int* nb, - double* a, const int* lda, double* e, double* tau, - double* w, const int* ldw); -/* DLATRS - solve one of the triangular systems A *x = s*b or */ -/* A'*x = s*b with scaling to prevent overflow */ -La_extern void -F77_NAME(dlatrs)(const char* uplo, const char* trans, - const char* diag, const char* normin, - const int* n, const double* a, const int* lda, - double* x, double* scale, double* cnorm, int* info); -/* DLATZM - apply a Householder matrix generated by DTZRQF to a */ -/* matrix */ -La_extern void -F77_NAME(dlatzm)(const char* side, const int* m, const int* n, - const double* v, const int* incv, - const double* tau, double* c1, double* c2, - const int* ldc, double* work); -/* DLAUU2 - compute the product U * U' or L' * const int* l, where the */ -/* triangular factor U or L is stored in the upper or lower */ -/* triangular part of the array A */ -La_extern void -F77_NAME(dlauu2)(const char* uplo, const int* n, - double* a, const int* lda, int* info); -/* DLAUUM - compute the product U * U' or L' * L, where the */ -/* triangular factor U or L is stored in the upper or lower */ -/* triangular part of the array A */ -La_extern void -F77_NAME(dlauum)(const char* uplo, const int* n, - double* a, const int* lda, int* info); - - -/* ======================================================================== */ - -/* Selected Double Complex Lapack Routines - ======== - */ - -/* IZMAX1 finds the index of the element whose real part has maximum - * absolute value. */ -La_extern int -F77_NAME(izmax1)(const int *n, Rcomplex *cx, const int *incx); - - -/* ZGECON estimates the reciprocal of the condition number of a general - * complex matrix A, in either the 1-norm or the infinity-norm, using - * the LU factorization computed by ZGETRF. - */ -La_extern void -F77_NAME(zgecon)(const char *norm, const int *n, - const Rcomplex *a, const int *lda, - const double *anorm, double *rcond, - Rcomplex *work, double *rwork, int *info); - -/* ZGESV computes the solution to a complex system of linear equations */ -La_extern void -F77_NAME(zgesv)(const int *n, const int *nrhs, Rcomplex *a, - const int *lda, int *ipiv, Rcomplex *b, - const int *ldb, int *info); - -/* ZGEQP3 computes a QR factorization with column pivoting */ -La_extern void -F77_NAME(zgeqp3)(const int *m, const int *n, - Rcomplex *a, const int *lda, - int *jpvt, Rcomplex *tau, - Rcomplex *work, const int *lwork, - double *rwork, int *info); - -/* ZUNMQR applies Q or Q**H from the Left or Right */ -La_extern void -F77_NAME(zunmqr)(const char *side, const char *trans, - const int *m, const int *n, const int *k, - Rcomplex *a, const int *lda, - Rcomplex *tau, - Rcomplex *c, const int *ldc, - Rcomplex *work, const int *lwork, int *info); - -/* ZTRTRS solves triangular systems */ -La_extern void -F77_NAME(ztrtrs)(const char *uplo, const char *trans, const char *diag, - const int *n, const int *nrhs, - Rcomplex *a, const int *lda, - Rcomplex *b, const int *ldb, int *info); -/* ZGESVD - compute the singular value decomposition (SVD); of a */ -/* real M-by-N matrix A, optionally computing the left and/or */ -/* right singular vectors */ -La_extern void -F77_NAME(zgesvd)(const char *jobu, const char *jobvt, - const int *m, const int *n, - Rcomplex *a, const int *lda, double *s, - Rcomplex *u, const int *ldu, - Rcomplex *vt, const int *ldvt, - Rcomplex *work, const int *lwork, double *rwork, - int *info); - -/* ZGHEEV - compute all eigenvalues and, optionally, eigenvectors */ -/* of a Hermitian matrix A */ -La_extern void -F77_NAME(zheev)(const char *jobz, const char *uplo, - const int *n, Rcomplex *a, const int *lda, - double *w, Rcomplex *work, const int *lwork, - double *rwork, int *info); - -/* ZGGEEV - compute all eigenvalues and, optionally, eigenvectors */ -/* of a complex non-symmetric matrix A */ -La_extern void -F77_NAME(zgeev)(const char *jobvl, const char *jobvr, - const int *n, Rcomplex *a, const int *lda, - Rcomplex *wr, Rcomplex *vl, const int *ldvl, - Rcomplex *vr, const int *ldvr, - Rcomplex *work, const int *lwork, - double *rwork, int *info); - - -/* NOTE: The following entry points were traditionally in this file, - but are not provided by R's libRlapack */ - -/* DZSUM1 - take the sum of the absolute values of a complex */ -/* vector and returns a double precision result */ -La_extern double -F77_NAME(dzsum1)(const int *n, Rcomplex *CX, const int *incx); - -/* ZLACN2 estimates the 1-norm of a square, complex matrix A. - * Reverse communication is used for evaluating matrix-vector products. -*/ -La_extern void -F77_NAME(zlacn2)(const int *n, Rcomplex *v, Rcomplex *x, - double *est, int *kase, int *isave); - -/* ZLANTR - return the value of the one norm, or the Frobenius norm, */ -/* or the infinity norm, or the element of largest absolute value of */ -/* a trapezoidal or triangular matrix A */ -La_extern double -F77_NAME(zlantr)(const char *norm, const char *uplo, const char *diag, - const int *m, const int *n, Rcomplex *a, - const int *lda, double *work); - -/* ======================================================================== */ - -/* Other double precision and double complex Lapack routines - provided by libRlapack. - - These are extracted from the CLAPACK headers. -*/ - -La_extern void -F77_NAME(dbdsdc)(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); - -La_extern void -F77_NAME(dgegs)(char *jobvsl, char *jobvsr, int *n, - double *a, int *lda, double *b, int *ldb, double * - alphar, double *alphai, double *beta, double *vsl, - int *ldvsl, double *vsr, int *ldvsr, double *work, - int *lwork, int *info); - -La_extern void -F77_NAME(dgelsd)(int *m, int *n, int *nrhs, - double *a, int *lda, double *b, int *ldb, double * - s, double *rcond, int *rank, double *work, int *lwork, - int *iwork, int *info); - -La_extern void -F77_NAME(dgelsx)(int *m, int *n, int *nrhs, - double *a, int *lda, double *b, int *ldb, int * - jpvt, double *rcond, int *rank, double *work, int * - info); - -La_extern void -F77_NAME(dgesc2)(int *n, double *a, int *lda, - double *rhs, int *ipiv, int *jpiv, double *scale); - -/* DGESDD - compute the singular value decomposition (SVD); of a */ -/* real M-by-N matrix A, optionally computing the left and/or */ -/* right singular vectors. If singular vectors are desired, it uses a */ -/* divide-and-conquer algorithm. */ -La_extern void -F77_NAME(dgesdd)(const char *jobz, - const int *m, const int *n, - double *a, const int *lda, double *s, - double *u, const int *ldu, - double *vt, const int *ldvt, - double *work, const int *lwork, int *iwork, int *info); - -La_extern void -F77_NAME(dgetc2)(int *n, double *a, int *lda, int - *ipiv, int *jpiv, int *info); - -typedef int (*L_fp)(); -La_extern void -F77_NAME(dggesx)(char *jobvsl, char *jobvsr, char *sort, L_fp - delctg, char *sense, int *n, double *a, int *lda, - double *b, int *ldb, int *sdim, double *alphar, - double *alphai, double *beta, double *vsl, int *ldvsl, - double *vsr, int *ldvsr, double *rconde, double * - rcondv, double *work, int *lwork, int *iwork, int * - liwork, int *bwork, int *info); - -La_extern void -F77_NAME(dggev)(char *jobvl, char *jobvr, int *n, double * - a, int *lda, double *b, int *ldb, double *alphar, - double *alphai, double *beta, double *vl, int *ldvl, - double *vr, int *ldvr, double *work, int *lwork, - int *info); - -La_extern void -F77_NAME(dggevx)(char *balanc, char *jobvl, char *jobvr, char * - sense, int *n, double *a, int *lda, double *b, - int *ldb, double *alphar, double *alphai, double * - beta, double *vl, int *ldvl, double *vr, int *ldvr, - int *ilo, int *ihi, double *lscale, double *rscale, - double *abnrm, double *bbnrm, double *rconde, double * - rcondv, double *work, int *lwork, int *iwork, int * - bwork, int *info); - -La_extern void -F77_NAME(dggsvp)(char *jobu, char *jobv, char *jobq, int *m, - int *p, int *n, double *a, int *lda, double *b, - int *ldb, double *tola, double *tolb, int *k, int - *l, double *u, int *ldu, double *v, int *ldv, - double *q, int *ldq, int *iwork, double *tau, - double *work, int *info); - -La_extern void -F77_NAME(dgtts2)(int *itrans, int *n, int *nrhs, - double *dl, double *d, double *du, double *du2, - int *ipiv, double *b, int *ldb); -La_extern void -F77_NAME(dlagv2)(double *a, int *lda, double *b, int *ldb, double *alphar, - double *alphai, double * beta, double *csl, double *snl, - double *csr, double * snr); - -La_extern void -F77_NAME(dlals0)(int *icompq, int *nl, int *nr, - int *sqre, int *nrhs, double *b, int *ldb, double - *bx, int *ldbx, int *perm, int *givptr, int *givcol, - int *ldgcol, double *givnum, int *ldgnum, double * - poles, double *difl, double *difr, double *z, int * - k, double *c, double *s, double *work, int *info); - -La_extern void -F77_NAME(dlalsa)(int *icompq, int *smlsiz, int *n, - int *nrhs, double *b, int *ldb, double *bx, int * - ldbx, double *u, int *ldu, double *vt, int *k, - double *difl, double *difr, double *z, double * - poles, int *givptr, int *givcol, int *ldgcol, int * - perm, double *givnum, double *c, double *s, double * - work, int *iwork, int *info); - -La_extern void -F77_NAME(dlalsd)(char *uplo, int *smlsiz, int *n, int - *nrhs, double *d, double *e, double *b, int *ldb, - double *rcond, int *rank, double *work, int *iwork, - int *info); - -La_extern void -F77_NAME(dlamc1)(int *beta, int *t, int *rnd, int - *ieee1); - -La_extern void -F77_NAME(dlamc2)(int *beta, int *t, int *rnd, - double *eps, int *emin, double *rmin, int *emax, - double *rmax); - -La_extern double -F77_NAME(dlamc3)(double *a, double *b); - -La_extern void -F77_NAME(dlamc4)(int *emin, double *start, int *base); - -La_extern void -F77_NAME(dlamc5)(int *beta, int *p, int *emin, - int *ieee, int *emax, double *rmax); - -La_extern void -F77_NAME(dlaqp2)(int *m, int *n, int *offset, - double *a, int *lda, int *jpvt, double *tau, - double *vn1, double *vn2, double *work); - -La_extern void -F77_NAME(dlaqps)(int *m, int *n, int *offset, int - *nb, int *kb, double *a, int *lda, int *jpvt, - double *tau, double *vn1, double *vn2, double *auxv, - double *f, int *ldf); - -La_extern void -F77_NAME(dlar1v)(int *n, int *b1, int *bn, double - *sigma, double *d, double *l, double *ld, double * - lld, double *gersch, double *z, double *ztz, double - *mingma, int *r, int *isuppz, double *work); - -La_extern void -F77_NAME(dlarrb)(int *n, double *d, double *l, - double *ld, double *lld, int *ifirst, int *ilast, - double *sigma, double *reltol, double *w, double * - wgap, double *werr, double *work, int *iwork, int * - info); - -La_extern void -F77_NAME(dlarre)(int *n, double *d, double *e, - double *tol, int *nsplit, int *isplit, int *m, - double *w, double *woff, double *gersch, double *work, - int *info); - -La_extern void -F77_NAME(dlarrf)(int *n, double *d, double *l, - double *ld, double *lld, int *ifirst, int *ilast, - double *w, double *dplus, double *lplus, double *work, - int *iwork, int *info); - -La_extern void -F77_NAME(dlarrv)(int *n, double *d, double *l, - int *isplit, int *m, double *w, int *iblock, - double *gersch, double *tol, double *z, int *ldz, - int *isuppz, double *work, int *iwork, int *info); - -La_extern void -F77_NAME(dlarz)(char *side, int *m, int *n, int *l, - double *v, int *incv, double *tau, double *c, - int *ldc, double *work); - -La_extern void -F77_NAME(dlarzb)(char *side, char *trans, char *direct, char * - storev, int *m, int *n, int *k, int *l, double *v, - int *ldv, double *t, int *ldt, double *c, int * - ldc, double *work, int *ldwork); - -La_extern void -F77_NAME(dlarzt)(char *direct, char *storev, int *n, int * - k, double *v, int *ldv, double *tau, double *t, - int *ldt); - -La_extern void -F77_NAME(dlasd0)(int *n, int *sqre, double *d, - double *e, double *u, int *ldu, double *vt, int * - ldvt, int *smlsiz, int *iwork, double *work, int * - info); - -La_extern void -F77_NAME(dlasd1)(int *nl, int *nr, int *sqre, - double *d, double *alpha, double *beta, double *u, - int *ldu, double *vt, int *ldvt, int *idxq, int * - iwork, double *work, int *info); - -La_extern void -F77_NAME(dlasd2)(int *nl, int *nr, int *sqre, int - *k, double *d, double *z, double *alpha, double * - beta, double *u, int *ldu, double *vt, int *ldvt, - double *dsigma, double *u2, int *ldu2, double *vt2, - int *ldvt2, int *idxp, int *idx, int *idxc, int * - idxq, int *coltyp, int *info); - -La_extern void -F77_NAME(dlasd3)(int *nl, int *nr, int *sqre, int - *k, double *d, double *q, int *ldq, double *dsigma, - double *u, int *ldu, double *u2, int *ldu2, - double *vt, int *ldvt, double *vt2, int *ldvt2, - int *idxc, int *ctot, double *z, int *info); - -La_extern void -F77_NAME(dlasd4)(int *n, int *i, double *d, - double *z, double *delta, double *rho, double * - sigma, double *work, int *info); - -La_extern void -F77_NAME(dlasd5)(int *i, double *d, double *z, - double *delta, double *rho, double *dsigma, double * - work); - -La_extern void -F77_NAME(dlasd6)(int *icompq, int *nl, int *nr, - int *sqre, double *d, double *vf, double *vl, - double *alpha, double *beta, int *idxq, int *perm, - int *givptr, int *givcol, int *ldgcol, double *givnum, - int *ldgnum, double *poles, double *difl, double * - difr, double *z, int *k, double *c, double *s, - double *work, int *iwork, int *info); - -La_extern void -F77_NAME(dlasd7)(int *icompq, int *nl, int *nr, - int *sqre, int *k, double *d, double *z, - double *zw, double *vf, double *vfw, double *vl, - double *vlw, double *alpha, double *beta, double * - dsigma, int *idx, int *idxp, int *idxq, int *perm, - int *givptr, int *givcol, int *ldgcol, double *givnum, - int *ldgnum, double *c, double *s, int *info); - -La_extern void -F77_NAME(dlasd8)(int *icompq, int *k, double *d, - double *z, double *vf, double *vl, double *difl, - double *difr, int *lddifr, double *dsigma, double * - work, int *info); - -La_extern void -F77_NAME(dlasd9)(int *icompq, int *ldu, int *k, - double *d, double *z, double *vf, double *vl, - double *difl, double *difr, double *dsigma, double * - work, int *info); - -La_extern void -F77_NAME(dlasda)(int *icompq, int *smlsiz, int *n, - int *sqre, double *d, double *e, double *u, int - *ldu, double *vt, int *k, double *difl, double *difr, - double *z, double *poles, int *givptr, int *givcol, - int *ldgcol, int *perm, double *givnum, double *c, - double *s, double *work, int *iwork, int *info); - -La_extern void -F77_NAME(dlasdq)(char *uplo, int *sqre, int *n, int * - ncvt, int *nru, int *ncc, double *d, double *e, - double *vt, int *ldvt, double *u, int *ldu, - double *c, int *ldc, double *work, int *info); - -La_extern void -F77_NAME(dlasdt)(int *n, int *lvl, int *nd, int * - inode, int *ndiml, int *ndimr, int *msub); - -La_extern void -F77_NAME(dlasq5)(int *i0, int *n0, double *z, - int *pp, double *tau, double *dmin, double *dmin1, - double *dmin2, double *dn, double *dnm1, double *dnm2, - int *ieee); - -La_extern void -F77_NAME(dlasq6)(int *i0, int *n0, double *z, - int *pp, double *dmin, double *dmin1, double *dmin2, - double *dn, double *dnm1, double *dnm2); - -La_extern void -F77_NAME(dlatdf)(int *ijob, int *n, double *z, - int *ldz, double *rhs, double *rdsum, double *rdscal, - int *ipiv, int *jpiv); - -La_extern void -F77_NAME(dlatrz)(int *m, int *n, int *l, double * - a, int *lda, double *tau, double *work); - -La_extern void -F77_NAME(dormr3)(char *side, char *trans, int *m, int *n, - int *k, int *l, double *a, int *lda, double *tau, - double *c, int *ldc, double *work, int *info); - -La_extern void -F77_NAME(dormrz)(char *side, char *trans, int *m, int *n, - int *k, int *l, double *a, int *lda, double *tau, - double *c, int *ldc, double *work, int *lwork, - int *info); - -La_extern void -F77_NAME(dptts2)(int *n, int *nrhs, double *d, - double *e, double *b, int *ldb); - -La_extern void -F77_NAME(dsbgvd)(char *jobz, char *uplo, int *n, int *ka, - int *kb, double *ab, int *ldab, double *bb, int * - ldbb, double *w, double *z, int *ldz, double *work, - int *lwork, int *iwork, int *liwork, int *info); - -La_extern void -F77_NAME(dsbgvx)(char *jobz, char *range, char *uplo, int *n, - int *ka, int *kb, double *ab, int *ldab, double * - bb, int *ldbb, double *q, int *ldq, double *vl, - double *vu, int *il, int *iu, double *abstol, int - *m, double *w, double *z, int *ldz, double *work, - int *iwork, int *ifail, int *info); - -La_extern void -F77_NAME(dspgvd)(int *itype, char *jobz, char *uplo, int * - n, double *ap, double *bp, double *w, double *z, - int *ldz, double *work, int *lwork, int *iwork, - int *liwork, int *info); - -La_extern void -F77_NAME(dspgvx)(int *itype, char *jobz, char *range, char * - uplo, int *n, double *ap, double *bp, double *vl, - double *vu, int *il, int *iu, double *abstol, int - *m, double *w, double *z, int *ldz, double *work, - int *iwork, int *ifail, int *info); - -La_extern void -F77_NAME(dstegr)(char *jobz, char *range, int *n, double * - d, double *e, double *vl, double *vu, int *il, - int *iu, double *abstol, int *m, double *w, - double *z, int *ldz, int *isuppz, double *work, - int *lwork, int *iwork, int *liwork, int *info); - -La_extern void -F77_NAME(dstevr)(char *jobz, char *range, int *n, double * - d, double *e, double *vl, double *vu, int *il, - int *iu, double *abstol, int *m, double *w, - double *z, int *ldz, int *isuppz, double *work, - int *lwork, int *iwork, int *liwork, int *info); - -La_extern void -F77_NAME(dsygvd)(int *itype, char *jobz, char *uplo, int * - n, double *a, int *lda, double *b, int *ldb, - double *w, double *work, int *lwork, int *iwork, - int *liwork, int *info); - -La_extern void -F77_NAME(dsygvx)(int *itype, char *jobz, char *range, char * - uplo, int *n, double *a, int *lda, double *b, int - *ldb, double *vl, double *vu, int *il, int *iu, - double *abstol, int *m, double *w, double *z, - int *ldz, double *work, int *lwork, int *iwork, - int *ifail, int *info); - -La_extern void -F77_NAME(dtgex2)(int *wantq, int *wantz, int *n, - double *a, int *lda, double *b, int *ldb, double * - q, int *ldq, double *z, int *ldz, int *j1, int * - n1, int *n2, double *work, int *lwork, int *info); - -La_extern void -F77_NAME(dtgexc)(int *wantq, int *wantz, int *n, - double *a, int *lda, double *b, int *ldb, double * - q, int *ldq, double *z, int *ldz, int *ifst, - int *ilst, double *work, int *lwork, int *info); - -La_extern void -F77_NAME(dtgsen)(int *ijob, int *wantq, int *wantz, - int *select, int *n, double *a, int *lda, double * - b, int *ldb, double *alphar, double *alphai, double * - beta, double *q, int *ldq, double *z, int *ldz, - int *m, double *pl, double *pr, double *dif, - double *work, int *lwork, int *iwork, int *liwork, - int *info); - -La_extern void -F77_NAME(dtgsna)(char *job, char *howmny, int *select, - int *n, double *a, int *lda, double *b, int *ldb, - double *vl, int *ldvl, double *vr, int *ldvr, - double *s, double *dif, int *mm, int *m, double * - work, int *lwork, int *iwork, int *info); - -La_extern void -F77_NAME(dtgsy2)(char *trans, int *ijob, int *m, int * - n, double *a, int *lda, double *b, int *ldb, - double *c, int *ldc, double *d, int *ldd, - double *e, int *lde, double *f, int *ldf, double * - scale, double *rdsum, double *rdscal, int *iwork, int - *pq, int *info); - -La_extern void -F77_NAME(dtgsyl)(char *trans, int *ijob, int *m, int * - n, double *a, int *lda, double *b, int *ldb, - double *c, int *ldc, double *d, int *ldd, - double *e, int *lde, double *f, int *ldf, double * - scale, double *dif, double *work, int *lwork, int * - iwork, int *info); - -La_extern void -F77_NAME(dtzrzf)(int *m, int *n, double *a, int * - lda, double *tau, double *work, int *lwork, int *info); - -La_extern void -F77_NAME(dpstrf)(const char* uplo, const int* n, - double* a, const int* lda, int* piv, int* rank, - double* tol, double *work, int* info); - - -La_extern int -F77_NAME(lsame)(char *ca, char *cb); - -La_extern 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); - -La_extern void -F77_NAME(zdrot)(int *n, Rcomplex *cx, int *incx, - Rcomplex *cy, int *incy, double *c, double *s); - -La_extern void -F77_NAME(zgebak)(char *job, char *side, int *n, int *ilo, - int *ihi, double *scale, int *m, Rcomplex *v, - int *ldv, int *info); - -La_extern void -F77_NAME(zgebal)(char *job, int *n, Rcomplex *a, int - *lda, int *ilo, int *ihi, double *scale, int *info); - -La_extern void -F77_NAME(zgebd2)(int *m, int *n, Rcomplex *a, - int *lda, double *d, double *e, Rcomplex *tauq, - Rcomplex *taup, Rcomplex *work, int *info); - -La_extern void -F77_NAME(zgebrd)(int *m, int *n, Rcomplex *a, - int *lda, double *d, double *e, Rcomplex *tauq, - Rcomplex *taup, Rcomplex *work, int *lwork, int * - info); -La_extern void -F77_NAME(zgehd2)(int *n, int *ilo, int *ihi, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *info); - -La_extern void -F77_NAME(zgehrd)(int *n, int *ilo, int *ihi, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zgelq2)(int *m, int *n, Rcomplex *a, - int *lda, Rcomplex *tau, Rcomplex *work, int *info); - -La_extern void -F77_NAME(zgelqf)(int *m, int *n, Rcomplex *a, - int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, - int *info); - -La_extern void -F77_NAME(zgeqr2)(int *m, int *n, Rcomplex *a, - int *lda, Rcomplex *tau, Rcomplex *work, int *info); - -La_extern void -F77_NAME(zgeqrf)(int *m, int *n, Rcomplex *a, - int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, - int *info); - -La_extern void -F77_NAME(zgetf2)(int *m, int *n, Rcomplex *a, - int *lda, int *ipiv, int *info); - -La_extern void -F77_NAME(zgetrf)(int *m, int *n, Rcomplex *a, - int *lda, int *ipiv, int *info); - -La_extern void -F77_NAME(zgetrs)(char *trans, int *n, int *nrhs, - Rcomplex *a, int *lda, int *ipiv, Rcomplex *b, - int *ldb, int *info); - - -La_extern void -F77_NAME(zhetd2)(char *uplo, int *n, Rcomplex *a, int *lda, double *d, - double *e, Rcomplex *tau, int *info); - -La_extern void -F77_NAME(zhetrd)(char *uplo, int *n, Rcomplex *a, - int *lda, double *d, double *e, Rcomplex *tau, - Rcomplex *work, int *lwork, int *info); - -La_extern void -F77_NAME(zhseqr)(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); - -La_extern void -F77_NAME(zlabrd)(int *m, int *n, int *nb, - Rcomplex *a, int *lda, double *d, double *e, - Rcomplex *tauq, Rcomplex *taup, Rcomplex *x, int * - ldx, Rcomplex *y, int *ldy); - -La_extern void -F77_NAME(zlacgv)(int *n, Rcomplex *x, int *incx); - -La_extern void -F77_NAME(zlacpy)(char *uplo, int *m, int *n, - Rcomplex *a, int *lda, Rcomplex *b, int *ldb); - -La_extern void -F77_NAME(zlahqr)(int *wantt, int *wantz, int *n, - int *ilo, int *ihi, Rcomplex *h, int *ldh, - Rcomplex *w, int *iloz, int *ihiz, Rcomplex *z, - int *ldz, int *info); - -La_extern void -F77_NAME(zlahrd)(int *n, int *k, int *nb, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex *t, - int *ldt, Rcomplex *y, int *ldy); - -La_extern double -F77_NAME(zlange)(char *norm, int *m, int *n, Rcomplex *a, int *lda, - double *work); - -La_extern double -F77_NAME(zlanhe)(char *norm, char *uplo, int *n, Rcomplex *a, - int *lda, double *work); - -La_extern double -F77_NAME(zlanhs)(char *norm, int *n, Rcomplex *a, int *lda, double *work); - - -La_extern void -F77_NAME(zlaqp2)(int *m, int *n, int *offset, - Rcomplex *a, int *lda, int *jpvt, Rcomplex *tau, - double *vn1, double *vn2, Rcomplex *work); - -La_extern void -F77_NAME(zlaqps)(int *m, int *n, int *offset, int - *nb, int *kb, Rcomplex *a, int *lda, int *jpvt, - Rcomplex *tau, double *vn1, double *vn2, Rcomplex * - auxv, Rcomplex *f, int *ldf); - -La_extern void -F77_NAME(zlarf)(char *side, int *m, int *n, Rcomplex - *v, int *incv, Rcomplex *tau, Rcomplex *c, int * - ldc, Rcomplex *work); - -La_extern 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); - -La_extern void -F77_NAME(zlarfg)(int *n, Rcomplex *alpha, Rcomplex * - x, int *incx, Rcomplex *tau); - -La_extern void -F77_NAME(zlarft)(char *direct, char *storev, int *n, int * - k, Rcomplex *v, int *ldv, Rcomplex *tau, Rcomplex * - t, int *ldt); - -La_extern void -F77_NAME(zlarfx)(char *side, int *m, int *n, - Rcomplex *v, Rcomplex *tau, Rcomplex *c, int * - ldc, Rcomplex *work); - -La_extern void -F77_NAME(zlascl)(char *type, int *kl, int *ku, - double *cfrom, double *cto, int *m, int *n, - Rcomplex *a, int *lda, int *info); - -La_extern void -F77_NAME(zlaset)(char *uplo, int *m, int *n, - Rcomplex *alpha, Rcomplex *beta, Rcomplex *a, int * - lda); - -La_extern void -F77_NAME(zlasr)(char *side, char *pivot, char *direct, int *m, - int *n, double *c, double *s, Rcomplex *a, - int *lda); - -La_extern void -F77_NAME(zlassq)(int *n, Rcomplex *x, int *incx, - double *scale, double *sumsq); - -La_extern void -F77_NAME(zlaswp)(int *n, Rcomplex *a, int *lda, - int *k1, int *k2, int *ipiv, int *incx); - -La_extern void -F77_NAME(zlatrd)(char *uplo, int *n, int *nb, - Rcomplex *a, int *lda, double *e, Rcomplex *tau, - Rcomplex *w, int *ldw); - -La_extern 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); - -La_extern void -F77_NAME(zsteqr)(char *compz, int *n, double *d, - double *e, Rcomplex *z, int *ldz, double *work, - int *info); - -/* ZTRCON estimates the reciprocal of the condition number of a - * triangular matrix A, in either the 1-norm or the infinity-norm. - */ -La_extern void -F77_NAME(ztrcon)(const char *norm, const char *uplo, const char *diag, - const int *n, const Rcomplex *a, const int *lda, - double *rcond, Rcomplex *work, double *rwork, int *info); - -La_extern void -F77_NAME(ztrevc)(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); - -La_extern void -F77_NAME(zung2l)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *info); - -La_extern void -F77_NAME(zung2r)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *info); - -La_extern void -F77_NAME(zungbr)(char *vect, int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zunghr)(int *n, int *ilo, int *ihi, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zungl2)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *info); - -La_extern void -F77_NAME(zunglq)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zungql)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zungqr)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zungr2)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *info); - -La_extern void -F77_NAME(zungrq)(int *m, int *n, int *k, - Rcomplex *a, int *lda, Rcomplex *tau, Rcomplex * - work, int *lwork, int *info); - -La_extern void -F77_NAME(zungtr)(char *uplo, int *n, Rcomplex *a, - int *lda, Rcomplex *tau, Rcomplex *work, int *lwork, - int *info); - -La_extern 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); - -La_extern 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); - -La_extern 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); - -La_extern 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 */ |