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29932 ripley 1 
/*
2 
 *  R : A Computer Language for Statistical Data Analysis
85049 ripley 3 
 *  Copyright (C) 2003-2023 The R Core Team.
29932 ripley 4 
 *
71657 plummer 5 
 *  This header file is free software; you can redistribute it and/or modify
29932 ripley 6 
 *  it under the terms of the GNU Lesser General Public License as published by
7 
 *  the Free Software Foundation; either version 2.1 of the License, or
8 
 *  (at your option) any later version.
9 
 *
71657 plummer 10 
 *  This file is part of R. R is distributed under the terms of the
11 
 *  GNU General Public License, either Version 2, June 1991 or Version 3,
12 
 *  June 2007. See doc/COPYRIGHTS for details of the copyright status of R.
13 
 *
29932 ripley 14 
 *  This program is distributed in the hope that it will be useful,
15 
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
16 
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
17 
 *  GNU Lesser General Public License for more details.
18 
 *
19 
 *  You should have received a copy of the GNU Lesser General Public License
42308 ripley 20 
 *  along with this program; if not, a copy is available at
68949 ripley 21 
 *  https://www.R-project.org/Licenses/
29932 ripley 22 
 */
23 
 
60961 ripley 24 
/*
25 
   C declarations of BLAS Fortran subroutines always available in R.
26 
 
27 
   Part of the API.
28 
 
71463 ripley 29 
   R packages that use these should have PKG_LIBS in src/Makevars include
60961 ripley 30 
   $(BLAS_LIBS) $(FLIBS)
31 
 */
32 
 
23063 bates 33 
#ifndef R_BLAS_H
34 
#define R_BLAS_H
35 
 
36 
#include <R_ext/RS.h>		/* for F77_... */
37 
 
76600 ripley 38 
#ifdef FC_LEN_T
76585 ripley 39 
# include <stddef.h> // for size_t if needed
40 
# define FCLEN ,FC_LEN_T
41 
# define FCONE ,(FC_LEN_T)1
42 
#else
43 
# define FCLEN
44 
# define FCONE
45 
#endif
46 
 
85054 ripley 47 
/* Allow for future 64-bit nrow, ncol and increments. by using int64_t .
48 
   configure checked that Fortran INTEGER is 32-bit and the same as C int.
49 
   Only LSAME (not included here) has LOGICAL in its declaration.
50 
   It is unclear what i[dz]amaz should return: the reference code has INTEGER,
51 
   but CBLAS has size_t. Apple Accelerate has __LAPACK_int, so int or long
52 
   for ILP64.
53 
*/
85049 ripley 54 
#ifndef ILP64
55 
# define BLAS_INT int
56 
#endif
57 
 
85053 ripley 58 
#ifndef BLAS_complex
59 
# include <R_ext/Complex.h>
60 
# define BLAS_complex Rcomplex
61 
#endif
62 
 
23063 bates 63 
#ifdef  __cplusplus
64 
extern "C" {
65 
#endif
66 
 
60961 ripley 67 
// never defined in R itself.
44687 maechler 68 
#ifndef BLAS_extern
69 
#define BLAS_extern extern
70 
#endif
71 
 
23063 bates 72 
/* Double Precision Level 1 BLAS */
73 
 
44687 maechler 74 
BLAS_extern double /* DASUM - sum of absolute values of a one-dimensional array */
85049 ripley 75 
F77_NAME(dasum)(const BLAS_INT *n, const double *dx, const BLAS_INT *incx);
76573 ripley 76 
BLAS_extern void   /* DAXPY - replace y by da*x + y */
85049 ripley 77 
F77_NAME(daxpy)(const BLAS_INT *n, const double *da,
78 
		const double *dx, const BLAS_INT *incx,
79 
		double *dy, const BLAS_INT *incy);
44687 maechler 80 
BLAS_extern void   /* DCOPY - copy x to y */
85049 ripley 81 
F77_NAME(dcopy)(const BLAS_INT *n, const double *dx, const BLAS_INT *incx,
82 
		double *dy, const BLAS_INT *incy);
44687 maechler 83 
BLAS_extern double /* DDOT - inner product of x and y */
85049 ripley 84 
F77_NAME(ddot)(const BLAS_INT *n, const double *dx, const BLAS_INT *incx,
85 
	       const double *dy, const BLAS_INT *incy);
44687 maechler 86 
BLAS_extern double /* DNRM2 - 2-norm of a vector */
85049 ripley 87 
F77_NAME(dnrm2)(const BLAS_INT *n, const double *dx, const BLAS_INT *incx);
88 
BLAS_extern void   /* DROT - apply a Givens rotation */
89 
F77_NAME(drot)(const BLAS_INT *n, double *dx, const BLAS_INT *incx,
90 
	       double *dy, const BLAS_INT *incy, const double *c, const double *s);
91 
BLAS_extern void   /* DROTG - generate a Givens rotation */
23063 bates 92 
F77_NAME(drotg)(const double *a, const double *b, double *c, double *s);
85049 ripley 93 
BLAS_extern void   /* DROTM - apply a modified Givens rotation */
94 
F77_NAME(drotm)(const BLAS_INT *n, double *dx, const BLAS_INT *incx,
95 
		double *dy, const BLAS_INT *incy, const double *dparam);
96 
BLAS_extern void   /* DROTMG - generate a modified Givens rotation */
36367 ripley 97 
F77_NAME(drotmg)(const double *dd1, const double *dd2, const double *dx1,
36352 ripley 98 
		 const double *dy1, double *param);
44687 maechler 99 
BLAS_extern void   /* DSCAL - scale a one-dimensional array */
85049 ripley 100 
F77_NAME(dscal)(const BLAS_INT *n, const double *alpha, double *dx, const BLAS_INT *incx);
44687 maechler 101 
BLAS_extern void   /* DSWAP - interchange one-dimensional arrays */
85049 ripley 102 
F77_NAME(dswap)(const BLAS_INT *n, double *dx, const BLAS_INT *incx,
103 
		double *dy, const BLAS_INT *incy);
104 
BLAS_extern BLAS_INT    /* IDAMAX - return the index of the element with max abs value */
105 
F77_NAME(idamax)(const BLAS_INT *n, const double *dx, const BLAS_INT *incx);
23063 bates 106 
 
107 
/* Double Precision Level 2 BLAS */
108 
 
109 
/* DGBMV - perform one of the matrix-vector operations */
110 
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, */
44687 maechler 111 
BLAS_extern void
85049 ripley 112 
F77_NAME(dgbmv)(const char *trans, const BLAS_INT *m, const BLAS_INT *n,
113 
		const BLAS_INT *kl,const BLAS_INT *ku,
114 
		const double *alpha, const double *a, const BLAS_INT *lda,
115 
		const double *x, const BLAS_INT *incx,
116 
		const double *beta, double *y, const BLAS_INT *incy FCLEN);
23063 bates 117 
/* DGEMV - perform one of the matrix-vector operations */
118 
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,  */
44687 maechler 119 
BLAS_extern void
85049 ripley 120 
F77_NAME(dgemv)(const char *trans, const BLAS_INT *m, const BLAS_INT *n,
121 
		const double *alpha, const double *a, const BLAS_INT *lda,
122 
		const double *x, const BLAS_INT *incx, const double *beta,
123 
		double *y, const BLAS_INT *incy FCLEN);
23063 bates 124 
/* DSBMV - perform the matrix-vector operation */
125 
/* y := alpha*A*x + beta*y, */
44687 maechler 126 
BLAS_extern void
85049 ripley 127 
F77_NAME(dsbmv)(const char *uplo, const BLAS_INT *n, const BLAS_INT *k,
128 
		const double *alpha, const double *a, const BLAS_INT *lda,
129 
		const double *x, const BLAS_INT *incx,
130 
		const double *beta, double *y, const BLAS_INT *incy FCLEN);
23063 bates 131 
/* DSPMV - perform the matrix-vector operation */
132 
/* y := alpha*A*x + beta*y, */
44687 maechler 133 
BLAS_extern void
85049 ripley 134 
F77_NAME(dspmv)(const char *uplo, const BLAS_INT *n,
23063 bates 135 
		const double *alpha, const double *ap,
85049 ripley 136 
		const double *x, const BLAS_INT *incx,
137 
		const double *beta, double *y, const BLAS_INT *incy FCLEN);
23063 bates 138 
 
139 
/* DSYMV - perform the matrix-vector operation */
140 
/*  y := alpha*A*x + beta*y, */
44687 maechler 141 
BLAS_extern void
85049 ripley 142 
F77_NAME(dsymv)(const char *uplo, const BLAS_INT *n, const double *alpha,
143 
		const double *a, const BLAS_INT *lda,
144 
		const double *x, const BLAS_INT *incx,
145 
		const double *beta, double *y, const BLAS_INT *incy FCLEN);
23063 bates 146 
/* DTBMV - perform one of the matrix-vector operations */
147 
/* x := A*x, or x := A'*x, */
44687 maechler 148 
BLAS_extern void
23063 bates 149 
F77_NAME(dtbmv)(const char *uplo, const char *trans,
85049 ripley 150 
		const char *diag, const BLAS_INT *n, const BLAS_INT *k,
151 
		const double *a, const BLAS_INT *lda,
152 
		double *x, const BLAS_INT *incx FCLEN FCLEN FCLEN);
23063 bates 153 
/* DTPMV - perform one of the matrix-vector operations */
154 
/* x := A*x, or x := A'*x, */
44687 maechler 155 
BLAS_extern void
23063 bates 156 
F77_NAME(dtpmv)(const char *uplo, const char *trans, const char *diag,
85049 ripley 157 
		const BLAS_INT *n, const double *ap,
158 
		double *x, const BLAS_INT *incx FCLEN FCLEN FCLEN);
23063 bates 159 
/* DTRMV - perform one of the matrix-vector operations  */
160 
/* x := A*x, or x := A'*x, */
44687 maechler 161 
BLAS_extern void
23063 bates 162 
F77_NAME(dtrmv)(const char *uplo, const char *trans, const char *diag,
85049 ripley 163 
		const BLAS_INT *n, const double *a, const BLAS_INT *lda,
164 
		double *x, const BLAS_INT *incx FCLEN FCLEN FCLEN);
23063 bates 165 
/* DTBSV - solve one of the systems of equations */
166 
/* A*x = b, or A'*x = b, */
44687 maechler 167 
BLAS_extern void
23063 bates 168 
F77_NAME(dtbsv)(const char *uplo, const char *trans,
85049 ripley 169 
		const char *diag, const BLAS_INT *n, const BLAS_INT *k,
170 
		const double *a, const BLAS_INT *lda,
171 
		double *x, const BLAS_INT *incx FCLEN FCLEN FCLEN);
23063 bates 172 
/* DTPSV - solve one of the systems of equations */
173 
/* A*x = b, or A'*x = b, */
44687 maechler 174 
BLAS_extern void
23063 bates 175 
F77_NAME(dtpsv)(const char *uplo, const char *trans,
85049 ripley 176 
		const char *diag, const BLAS_INT *n,
177 
		const double *ap, double *x, const BLAS_INT *incx
76585 ripley 178 
		FCLEN FCLEN FCLEN);
23063 bates 179 
/* DTRSV - solve one of the systems of equations */
180 
/* A*x = b, or A'*x = b, */
44687 maechler 181 
BLAS_extern void
23063 bates 182 
F77_NAME(dtrsv)(const char *uplo, const char *trans,
85049 ripley 183 
		const char *diag, const BLAS_INT *n,
184 
		const double *a, const BLAS_INT *lda,
185 
		double *x, const BLAS_INT *incx FCLEN FCLEN FCLEN);
23063 bates 186 
/* DGER - perform the rank 1 operation   A := alpha*x*y' + A */
44687 maechler 187 
BLAS_extern void
85049 ripley 188 
F77_NAME(dger)(const BLAS_INT *m, const BLAS_INT *n, const double *alpha,
189 
	       const double *x, const BLAS_INT *incx,
190 
	       const double *y, const BLAS_INT *incy,
191 
	       double *a, const BLAS_INT *lda);
23063 bates 192 
/* DSYR - perform the symmetric rank 1 operation A := alpha*x*x' + A */
44687 maechler 193 
BLAS_extern void
85049 ripley 194 
F77_NAME(dsyr)(const char *uplo, const BLAS_INT *n, const double *alpha,
195 
	       const double *x, const BLAS_INT *incx,
196 
	       double *a, const BLAS_INT *lda FCLEN);
23063 bates 197 
/* DSPR - perform the symmetric rank 1 operation A := alpha*x*x' + A */
44687 maechler 198 
BLAS_extern void
85049 ripley 199 
F77_NAME(dspr)(const char *uplo, const BLAS_INT *n, const double *alpha,
200 
	       const double *x, const BLAS_INT *incx, double *ap FCLEN);
23063 bates 201 
/* DSYR2 - perform the symmetric rank 2 operation */
202 
/* A := alpha*x*y' + alpha*y*x' + A, */
44687 maechler 203 
BLAS_extern void
85049 ripley 204 
F77_NAME(dsyr2)(const char *uplo, const BLAS_INT *n, const double *alpha,
205 
		const double *x, const BLAS_INT *incx,
206 
		const double *y, const BLAS_INT *incy,
207 
		double *a, const BLAS_INT *lda FCLEN);
23063 bates 208 
/* DSPR2 - perform the symmetric rank 2 operation */
209 
/* A := alpha*x*y' + alpha*y*x' + A,  */
44687 maechler 210 
BLAS_extern void
85049 ripley 211 
F77_NAME(dspr2)(const char *uplo, const BLAS_INT *n, const double *alpha,
212 
		const double *x, const BLAS_INT *incx,
213 
		const double *y, const BLAS_INT *incy, double *ap FCLEN);
23063 bates 214 
 
215 
/* Double Precision Level 3 BLAS */
216 
 
217 
/* DGEMM - perform one of the matrix-matrix operations    */
218 
/* C := alpha*op( A )*op( B ) + beta*C */
44687 maechler 219 
BLAS_extern void
85049 ripley 220 
F77_NAME(dgemm)(const char *transa, const char *transb, const BLAS_INT *m,
221 
		const BLAS_INT *n, const BLAS_INT *k, const double *alpha,
222 
		const double *a, const BLAS_INT *lda,
223 
		const double *b, const BLAS_INT *ldb,
224 
		const double *beta, double *c, const BLAS_INT *ldc
76585 ripley 225 
		FCLEN FCLEN);
23063 bates 226 
/* DTRSM - solve one of the matrix equations  */
227 
/* op(A)*X = alpha*B, or  X*op(A) = alpha*B  */
44687 maechler 228 
BLAS_extern void
23063 bates 229 
F77_NAME(dtrsm)(const char *side, const char *uplo,
230 
		const char *transa, const char *diag,
85049 ripley 231 
		const BLAS_INT *m, const BLAS_INT *n, const double *alpha,
232 
		const double *a, const BLAS_INT *lda,
233 
		double *b, const BLAS_INT *ldb
76585 ripley 234 
		FCLEN FCLEN FCLEN FCLEN);
23063 bates 235 
/* DTRMM - perform one of the matrix-matrix operations */
236 
/* B := alpha*op( A )*B, or B := alpha*B*op( A ) */
44687 maechler 237 
BLAS_extern void
23063 bates 238 
F77_NAME(dtrmm)(const char *side, const char *uplo, const char *transa,
85049 ripley 239 
		const char *diag, const BLAS_INT *m, const BLAS_INT *n,
240 
		const double *alpha, const double *a, const BLAS_INT *lda,
241 
		double *b, const BLAS_INT *ldb
76585 ripley 242 
		FCLEN FCLEN FCLEN FCLEN);
23063 bates 243 
/* DSYMM - perform one of the matrix-matrix operations   */
244 
/*  C := alpha*A*B + beta*C, */
44687 maechler 245 
BLAS_extern void
85049 ripley 246 
F77_NAME(dsymm)(const char *side, const char *uplo, const BLAS_INT *m,
247 
		const BLAS_INT *n, const double *alpha,
248 
		const double *a, const BLAS_INT *lda,
249 
		const double *b, const BLAS_INT *ldb,
250 
		const double *beta, double *c, const BLAS_INT *ldc
76585 ripley 251 
		FCLEN FCLEN);
23063 bates 252 
/* DSYRK - perform one of the symmetric rank k operations */
253 
/* C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C */
44687 maechler 254 
BLAS_extern void
23063 bates 255 
F77_NAME(dsyrk)(const char *uplo, const char *trans,
85049 ripley 256 
		const BLAS_INT *n, const BLAS_INT *k,
257 
		const double *alpha, const double *a, const BLAS_INT *lda,
258 
		const double *beta, double *c, const BLAS_INT *ldc
76585 ripley 259 
		FCLEN FCLEN);
23063 bates 260 
/* DSYR2K - perform one of the symmetric rank 2k operations */
261 
/* C := alpha*A*B' + alpha*B*A' + beta*C or */
262 
/* C := alpha*A'*B + alpha*B'*A + beta*C */
44687 maechler 263 
BLAS_extern void
23063 bates 264 
F77_NAME(dsyr2k)(const char *uplo, const char *trans,
85049 ripley 265 
		 const BLAS_INT *n, const BLAS_INT *k,
266 
		 const double *alpha, const double *a, const BLAS_INT *lda,
267 
		 const double *b, const BLAS_INT *ldb,
268 
		 const double *beta, double *c, const BLAS_INT *ldc
76585 ripley 269 
		 FCLEN FCLEN);
36352 ripley 270 
/*
85073 ripley 271 
  LSAME is declared in Lapack.h.
272 
  (https://netlib.org/lapack/explore-html/dc/d9c/_i_n_s_t_a_l_l_2lsame_8f_ada799b40a93f1fd2c6d1a86a95f21631.html
273 
  calls it a 'LAPACK auxiliary routine'.)
274 
 
275 
  It is used in the code of other BLAS routines and hence included in
276 
  src/extra/blas/blas.f.  However, it is not included by
277 
   Apple's Accelerate (nor cblas: it is in lapacke).
36352 ripley 278 
*/
35002 ripley 279 
 
36367 ripley 280 
/* Double complex BLAS routines added for 2.3.0 */
44669 maechler 281 
/* #ifdef HAVE_FORTRAN_DOUBLE_COMPLEX */
44687 maechler 282 
    BLAS_extern double
85053 ripley 283 
    F77_NAME(dcabs1)(const BLAS_complex *z);
44687 maechler 284 
    BLAS_extern double
85053 ripley 285 
    F77_NAME(dzasum)(const BLAS_INT *n, const BLAS_complex *zx, const BLAS_INT *incx);
44687 maechler 286 
    BLAS_extern double
85053 ripley 287 
    F77_NAME(dznrm2)(const BLAS_INT *n, const BLAS_complex *x, const BLAS_INT *incx);
85049 ripley 288 
    BLAS_extern BLAS_INT
85053 ripley 289 
    F77_NAME(izamax)(const BLAS_INT *n, const BLAS_complex *zx, const BLAS_INT *incx);
44687 maechler 290 
    BLAS_extern void
85053 ripley 291 
    F77_NAME(zaxpy)(const BLAS_INT *n, const BLAS_complex *za, const BLAS_complex *zx,
292 
		    const BLAS_INT *incx, const BLAS_complex *zy, const BLAS_INT *incy);
44687 maechler 293 
    BLAS_extern void
85053 ripley 294 
    F77_NAME(zcopy)(const BLAS_INT *n, const BLAS_complex *zx, const BLAS_INT *incx,
295 
		    const BLAS_complex *zy, const BLAS_INT *incy);
58613 ripley 296 
 
297 
    /* WARNING!  The next two return a value that may not be
298 
       compatible between C and Fortran, and even if it is, this might
299 
       not be the right translation to C.  Only use after
300 
       configure-testing with your compilers.
301 
     */
85053 ripley 302 
    BLAS_extern BLAS_complex
85049 ripley 303 
    F77_NAME(zdotc)(const BLAS_INT *n,
85053 ripley 304 
		    const BLAS_complex *zx, const BLAS_INT *incx,
305 
		    const BLAS_complex *zy, const BLAS_INT *incy);
306 
    BLAS_extern BLAS_complex
85049 ripley 307 
    F77_NAME(zdotu)(const BLAS_INT *n,
85053 ripley 308 
		    const BLAS_complex *zx, const BLAS_INT *incx,
309 
		    const BLAS_complex *zy, const BLAS_INT *incy);
58613 ripley 310 
 
44687 maechler 311 
    BLAS_extern void
85049 ripley 312 
    F77_NAME(zdrot)(const BLAS_INT *n,
85053 ripley 313 
		    const BLAS_complex *zx, const BLAS_INT *incx,
314 
		    BLAS_complex *zy, const BLAS_INT *incy,
71463 ripley 315 
		    const double *c, const double *s);
44687 maechler 316 
    BLAS_extern void
85049 ripley 317 
    F77_NAME(zdscal)(const BLAS_INT *n, const double *da,
85053 ripley 318 
		     BLAS_complex *zx, const BLAS_INT *incx);
44687 maechler 319 
    BLAS_extern void
85049 ripley 320 
    F77_NAME(zgbmv)(const char *trans, BLAS_INT *m, BLAS_INT *n, BLAS_INT *kl,
85053 ripley 321 
		    BLAS_INT *ku, BLAS_complex *alpha, BLAS_complex *a, BLAS_INT *lda,
322 
		    BLAS_complex *x, BLAS_INT *incx, BLAS_complex *beta, BLAS_complex *y,
85049 ripley 323 
		    BLAS_INT *incy FCLEN);
44687 maechler 324 
    BLAS_extern void
85049 ripley 325 
    F77_NAME(zgemm)(const char *transa, const char *transb, const BLAS_INT *m,
85053 ripley 326 
		    const BLAS_INT *n, const BLAS_INT *k, const BLAS_complex *alpha,
327 
		    const BLAS_complex *a, const BLAS_INT *lda,
328 
		    const BLAS_complex *b, const BLAS_INT *ldb,
329 
		    const BLAS_complex *beta, BLAS_complex *c, const BLAS_INT *ldc
76585 ripley 330 
		    FCLEN FCLEN);
44687 maechler 331 
    BLAS_extern void
85049 ripley 332 
    F77_NAME(zgemv)(const char *trans, const BLAS_INT *m, const BLAS_INT *n,
85053 ripley 333 
		    const BLAS_complex *alpha, const BLAS_complex *a, const BLAS_INT *lda,
334 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *beta,
335 
		    BLAS_complex *y, const BLAS_INT *incy FCLEN);
44687 maechler 336 
    BLAS_extern void
85053 ripley 337 
    F77_NAME(zgerc)(const BLAS_INT *m, const BLAS_INT *n, const BLAS_complex *alpha,
338 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *y,
339 
		    const BLAS_INT *incy, BLAS_complex *a, const BLAS_INT *lda);
44687 maechler 340 
    BLAS_extern void
85053 ripley 341 
    F77_NAME(zgeru)(const BLAS_INT *m, const BLAS_INT *n, const BLAS_complex *alpha,
342 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *y,
343 
		    const BLAS_INT *incy, BLAS_complex *a, const BLAS_INT *lda);
44687 maechler 344 
    BLAS_extern void
85049 ripley 345 
    F77_NAME(zhbmv)(const char *uplo, const BLAS_INT *n, const BLAS_INT *k,
85053 ripley 346 
		    const BLAS_complex *alpha, const BLAS_complex *a, const BLAS_INT *lda,
347 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *beta,
348 
		    BLAS_complex *y, const BLAS_INT *incy FCLEN);
44687 maechler 349 
    BLAS_extern void
85049 ripley 350 
    F77_NAME(zhemm)(const char *side, const char *uplo, const BLAS_INT *m,
85053 ripley 351 
		    const BLAS_INT *n, const BLAS_complex *alpha, const BLAS_complex *a,
352 
		    const BLAS_INT *lda, const BLAS_complex *b, const BLAS_INT *ldb,
353 
		    const BLAS_complex *beta, BLAS_complex *c, const BLAS_INT *ldc
76585 ripley 354 
		    FCLEN FCLEN);
44687 maechler 355 
    BLAS_extern void
85053 ripley 356 
    F77_NAME(zhemv)(const char *uplo, const BLAS_INT *n, const BLAS_complex *alpha,
357 
		    const BLAS_complex *a, const BLAS_INT *lda, const BLAS_complex *x,
358 
		    const BLAS_INT *incx, const BLAS_complex *beta,
359 
		    BLAS_complex *y, const BLAS_INT *incy FCLEN);
44687 maechler 360 
    BLAS_extern void
85049 ripley 361 
    F77_NAME(zher)(const char *uplo, const BLAS_INT *n, const double *alpha,
85053 ripley 362 
		   const BLAS_complex *x, const BLAS_INT *incx, BLAS_complex *a,
85049 ripley 363 
		   const BLAS_INT *lda FCLEN);
44687 maechler 364 
    BLAS_extern void
85053 ripley 365 
    F77_NAME(zher2)(const char *uplo, const BLAS_INT *n, const BLAS_complex *alpha,
366 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *y,
367 
		    const BLAS_INT *incy, BLAS_complex *a, const BLAS_INT *lda FCLEN);
44687 maechler 368 
    BLAS_extern void
85049 ripley 369 
    F77_NAME(zher2k)(const char *uplo, const char *trans, const BLAS_INT *n,
85053 ripley 370 
		     const BLAS_INT *k, const BLAS_complex *alpha, const BLAS_complex *a,
371 
		     const BLAS_INT *lda, const BLAS_complex *b, const  BLAS_INT *ldb,
372 
		     const double *beta, BLAS_complex *c, const BLAS_INT *ldc
76585 ripley 373 
		     FCLEN FCLEN);
44687 maechler 374 
    BLAS_extern void
85049 ripley 375 
    F77_NAME(zherk)(const char *uplo, const char *trans, const BLAS_INT *n,
85053 ripley 376 
		    const BLAS_INT *k, const double *alpha, const BLAS_complex *a,
377 
		    const BLAS_INT *lda, const double *beta, BLAS_complex *c,
85049 ripley 378 
		    const BLAS_INT *ldc FCLEN FCLEN);
44687 maechler 379 
    BLAS_extern void
85053 ripley 380 
    F77_NAME(zhpmv)(const char *uplo, const BLAS_INT *n, const BLAS_complex *alpha,
381 
		    const BLAS_complex *ap, const BLAS_complex *x, const BLAS_INT *incx,
382 
		    const BLAS_complex * beta, BLAS_complex *y, const BLAS_INT *incy
76585 ripley 383 
		    FCLEN);
44687 maechler 384 
    BLAS_extern void
85049 ripley 385 
    F77_NAME(zhpr)(const char *uplo, const BLAS_INT *n, const double *alpha,
85053 ripley 386 
		   const BLAS_complex *x, const BLAS_INT *incx, BLAS_complex *ap
76585 ripley 387 
		   FCLEN);
44687 maechler 388 
    BLAS_extern void
85053 ripley 389 
    F77_NAME(zhpr2)(const char *uplo, const BLAS_INT *n, const BLAS_complex *alpha,
390 
		    const BLAS_complex *x, const BLAS_INT *incx, const BLAS_complex *y,
391 
		    const BLAS_INT *incy, BLAS_complex *ap FCLEN);
44687 maechler 392 
    BLAS_extern void
85053 ripley 393 
    F77_NAME(zrotg)(const BLAS_complex *ca, const BLAS_complex *cb,
394 
		    double *c, BLAS_complex *s);
44687 maechler 395 
    BLAS_extern void
85053 ripley 396 
    F77_NAME(zscal)(const BLAS_INT *n, const BLAS_complex *za, BLAS_complex *zx,
85049 ripley 397 
		    const BLAS_INT *incx);
44687 maechler 398 
    BLAS_extern void
85053 ripley 399 
    F77_NAME(zswap)(const BLAS_INT *n, BLAS_complex *zx, const BLAS_INT *incx,
400 
		    BLAS_complex *zy, const BLAS_INT *incy);
44687 maechler 401 
    BLAS_extern void
85049 ripley 402 
    F77_NAME(zsymm)(const char *side, const char *uplo, const BLAS_INT *m,
85053 ripley 403 
		    const BLAS_INT *n, const BLAS_complex *alpha, const BLAS_complex *a,
404 
		    const BLAS_INT *lda, const BLAS_complex *b, const BLAS_INT *ldb,
405 
		    const BLAS_complex *beta, BLAS_complex *c, const BLAS_INT *ldc
76585 ripley 406 
		    FCLEN FCLEN);
44687 maechler 407 
    BLAS_extern void
85049 ripley 408 
    F77_NAME(zsyr2k)(const char *uplo, const char *trans, BLAS_INT *n, BLAS_INT *k,
85053 ripley 409 
		     BLAS_complex *alpha, BLAS_complex *a, BLAS_INT *lda, BLAS_complex *b,
410 
		     BLAS_INT *ldb, BLAS_complex *beta, BLAS_complex *c, BLAS_INT *ldc
76585 ripley 411 
		     FCLEN FCLEN);
44687 maechler 412 
    BLAS_extern void
85049 ripley 413 
    F77_NAME(zsyrk)(const char *uplo, const char *trans, const  BLAS_INT *n,
85053 ripley 414 
		    const BLAS_INT *k, const BLAS_complex *alpha, const BLAS_complex *a,
415 
		    const BLAS_INT *lda, const BLAS_complex *beta, BLAS_complex *c,
85049 ripley 416 
		    const BLAS_INT *ldc FCLEN FCLEN);
44687 maechler 417 
    BLAS_extern void
71463 ripley 418 
    F77_NAME(ztbmv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 419 
		    const BLAS_INT *n, const BLAS_INT *k, const BLAS_complex *a,
420 
		    const BLAS_INT *lda, BLAS_complex *x, const BLAS_INT *incx
76585 ripley 421 
		    FCLEN FCLEN FCLEN);
44687 maechler 422 
    BLAS_extern void
71463 ripley 423 
    F77_NAME(ztbsv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 424 
		    const BLAS_INT *n, const BLAS_INT *k, const BLAS_complex *a,
425 
		    const BLAS_INT *lda, BLAS_complex *x, const BLAS_INT *incx
76585 ripley 426 
		    FCLEN FCLEN FCLEN);
44687 maechler 427 
    BLAS_extern void
71463 ripley 428 
    F77_NAME(ztpmv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 429 
		    const BLAS_INT *n, const BLAS_complex *ap, BLAS_complex *x,
85049 ripley 430 
		    const BLAS_INT *incx FCLEN FCLEN FCLEN);
44687 maechler 431 
    BLAS_extern void
71463 ripley 432 
    F77_NAME(ztpsv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 433 
		    const BLAS_INT *n, const BLAS_complex *ap, BLAS_complex *x,
85049 ripley 434 
		    const BLAS_INT *incx FCLEN FCLEN FCLEN);
44687 maechler 435 
    BLAS_extern void
71463 ripley 436 
    F77_NAME(ztrmm)(const char *side, const char *uplo, const char *transa,
85049 ripley 437 
		    const char *diag, const BLAS_INT *m, const BLAS_INT *n,
85053 ripley 438 
		    const BLAS_complex *alpha, const BLAS_complex *a,
439 
		    const BLAS_INT *lda, BLAS_complex *b, const BLAS_INT *ldb
76585 ripley 440 
		    FCLEN FCLEN FCLEN FCLEN);
44687 maechler 441 
    BLAS_extern void
71463 ripley 442 
    F77_NAME(ztrmv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 443 
		    const BLAS_INT *n, const BLAS_complex *a, const BLAS_INT *lda,
444 
		    BLAS_complex *x, const BLAS_INT *incx
76585 ripley 445 
		    FCLEN FCLEN FCLEN);
44687 maechler 446 
    BLAS_extern void
71463 ripley 447 
    F77_NAME(ztrsm)(const char *side, const char *uplo, const char *transa,
85053 ripley 448 
		    const char *diag, BLAS_INT *m, BLAS_INT *n, BLAS_complex *alpha,
449 
		    BLAS_complex *a, BLAS_INT *lda, BLAS_complex *b, BLAS_INT *ldb
76585 ripley 450 
		    FCLEN FCLEN FCLEN FCLEN);
44687 maechler 451 
    BLAS_extern void
71463 ripley 452 
    F77_NAME(ztrsv)(const char *uplo, const char *trans, const char *diag,
85053 ripley 453 
		    const BLAS_INT *n, const BLAS_complex *a, const BLAS_INT *lda,
454 
		    BLAS_complex *x, const BLAS_INT *incx
76585 ripley 455 
		    FCLEN FCLEN FCLEN);
44669 maechler 456 
/* #endif */
36367 ripley 457 
 
86265 maechler 458 
/* ZSPMV  performs the matrix-vector operation
459 
 *
460 
 *     y := alpha*A*x + beta*y,
461 
 *
462 
 * where alpha and beta are scalars, x and y are n element vectors
463 
 * and A is an n by n symmetric matrix, supplied in packed form.
464 
 * Added in R 4.4.0
465 
 */
466 
BLAS_extern void
467 
F77_NAME(zspmv)(const char *uplo, const BLAS_INT *n,
468 
		 const BLAS_complex *alpha, const BLAS_complex *ap,
469 
		 const BLAS_complex *x, const BLAS_INT *incx,
470 
		 const BLAS_complex *beta, BLAS_complex *y, const BLAS_INT *incy FCLEN);
471 
 
23063 bates 472 
#ifdef  __cplusplus
473 
}
474 
#endif
475 
 
476 
#endif /* R_BLAS_H */