Jovan Ivković / Mbed 2 deprecated Linpack

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Dependencies:   mbed

main.cpp@4:557ad9613c6e, 2017-01-03 (annotated)

Committer:
JovanEps
Date:
Tue Jan 03 14:24:52 2017 +0000
Revision:
4:557ad9613c6e
Parent:
3:da1132c65314
Child:
5:2b929fbd5c69
Must be lower to N2 -3

Who changed what in which revision?

UserRevisionLine numberNew contents of line
JovanEps 0:43b96e9650ef 1 //********************************************************
JovanEps 3:da1132c65314 2 //** BETA---------------
JovanEps 2:273153e44338 3 //** Nucleo-144 Stm32F746 and Stm32F767 benchmark ******
JovanEps 2:273153e44338 4 //** Limpack -port form Arduino IDE *****
JovanEps 0:43b96e9650ef 5 //** Jovan Ivkovic - 2016 ******
JovanEps 0:43b96e9650ef 6 //********************************************************
JovanEps 0:43b96e9650ef 7 #include "mbed.h"
JovanEps 2:273153e44338 8
JovanEps 2:273153e44338 9 /* the following is optional depending on the timing function used */
JovanEps 2:273153e44338 10 # include <stdlib.h>
JovanEps 2:273153e44338 11 # include <stdio.h>
JovanEps 2:273153e44338 12 # include <math.h>
JovanEps 2:273153e44338 13
JovanEps 0:43b96e9650ef 14 DigitalOut myled(LED1);
JovanEps 0:43b96e9650ef 15 Serial pc(USBTX, USBRX);
JovanEps 0:43b96e9650ef 16 Timer timer;
JovanEps 0:43b96e9650ef 17
JovanEps 2:273153e44338 18 int do_benchmark( void );
JovanEps 4:557ad9613c6e 19 //double cpu_time( void );
JovanEps 2:273153e44338 20 void daxpy( int n, double da, double dx[], int incx, double dy[], int incy );
JovanEps 2:273153e44338 21 double ddot( int n, double dx[], int incx, double dy[], int incy );
JovanEps 2:273153e44338 22 int dgefa( double a[], int lda, int n, int ipvt[] );
JovanEps 2:273153e44338 23 void dgesl( double a[], int lda, int n, int ipvt[], double b[], int job );
JovanEps 2:273153e44338 24 void dscal( int n, double sa, double x[], int incx );
JovanEps 2:273153e44338 25 int idamax( int n, double dx[], int incx );
JovanEps 2:273153e44338 26 double r8_abs( double x );
JovanEps 2:273153e44338 27 double r8_epsilon( void );
JovanEps 2:273153e44338 28 double r8_max( double x, double y );
JovanEps 2:273153e44338 29 double r8_random(int iseed[4] );
JovanEps 2:273153e44338 30 double *r8mat_gen ( int lda, int n );
JovanEps 0:43b96e9650ef 31
JovanEps 2:273153e44338 32 //static FILE uartout = {0} ;
JovanEps 0:43b96e9650ef 33
JovanEps 2:273153e44338 34 //static int uart_putchar (char c, FILE *stream)
JovanEps 2:273153e44338 35 //{
JovanEps 2:273153e44338 36 // Serial.write(c) ;
JovanEps 2:273153e44338 37 // return 0 ;
JovanEps 2:273153e44338 38 //}
JovanEps 0:43b96e9650ef 39
JovanEps 2:273153e44338 40 //void setup() {
JovanEps 2:273153e44338 41 // Serial.begin(9600);
JovanEps 2:273153e44338 42 // fdev_setup_stream (&uartout, uart_putchar, NULL, _FDEV_SETUP_WRITE);
JovanEps 2:273153e44338 43 // stdout = &uartout ;
JovanEps 2:273153e44338 44 //}
JovanEps 0:43b96e9650ef 45
JovanEps 2:273153e44338 46 int main()
JovanEps 0:43b96e9650ef 47 {
JovanEps 4:557ad9613c6e 48 pc.baud(115200);
JovanEps 4:557ad9613c6e 49 //pc.baud(9600);
JovanEps 2:273153e44338 50
JovanEps 2:273153e44338 51 while(1) {
JovanEps 2:273153e44338 52
JovanEps 2:273153e44338 53 pc.printf("Starting benchmark...\n");
JovanEps 2:273153e44338 54
JovanEps 2:273153e44338 55 do_benchmark();
JovanEps 4:557ad9613c6e 56
JovanEps 2:273153e44338 57 pc.printf(" kraj \n\n");
JovanEps 2:273153e44338 58 }
JovanEps 2:273153e44338 59 }
JovanEps 2:273153e44338 60
JovanEps 2:273153e44338 61 /******************************************************************************/
JovanEps 0:43b96e9650ef 62
JovanEps 2:273153e44338 63 int do_benchmark ( void )
JovanEps 0:43b96e9650ef 64
JovanEps 2:273153e44338 65 /******************************************************************************/
JovanEps 2:273153e44338 66 /*
JovanEps 2:273153e44338 67 Purpose:
JovanEps 2:273153e44338 68
JovanEps 2:273153e44338 69 MAIN is the main program for LINPACK_BENCH.
JovanEps 0:43b96e9650ef 70
JovanEps 2:273153e44338 71 Discussion:
JovanEps 2:273153e44338 72
JovanEps 2:273153e44338 73 LINPACK_BENCH drives the double precision LINPACK benchmark program.
JovanEps 2:273153e44338 74
JovanEps 2:273153e44338 75 Modified:
JovanEps 2:273153e44338 76
JovanEps 2:273153e44338 77 25 July 2008
JovanEps 2:273153e44338 78
JovanEps 2:273153e44338 79 Parameters:
JovanEps 0:43b96e9650ef 80
JovanEps 2:273153e44338 81 N is the problem size.
JovanEps 0:43b96e9650ef 82 */
JovanEps 2:273153e44338 83 {
JovanEps 4:557ad9613c6e 84 # define N 2
JovanEps 2:273153e44338 85 # define LDA ( N + 1 )
JovanEps 2:273153e44338 86
JovanEps 3:da1132c65314 87 //static double a[90];
JovanEps 2:273153e44338 88 static double *a;
JovanEps 2:273153e44338 89 static double a_max;
JovanEps 3:da1132c65314 90 //static double b[9];
JovanEps 2:273153e44338 91 static double *b;
JovanEps 2:273153e44338 92 static double b_max;
JovanEps 2:273153e44338 93 const double cray = 0.056;
JovanEps 2:273153e44338 94 static double eps;
JovanEps 2:273153e44338 95 int i;
JovanEps 2:273153e44338 96 int info;
JovanEps 3:da1132c65314 97 static int *ipvt;
JovanEps 2:273153e44338 98 int j;
JovanEps 2:273153e44338 99 int job;
JovanEps 2:273153e44338 100 double ops;
JovanEps 3:da1132c65314 101 static double *resid;
JovanEps 2:273153e44338 102 double resid_max;
JovanEps 2:273153e44338 103 double residn;
JovanEps 3:da1132c65314 104 static double *rhs;
JovanEps 3:da1132c65314 105 double t1 = 0.0;
JovanEps 3:da1132c65314 106 double t2 = 0.0;
JovanEps 2:273153e44338 107 static double time[6];
JovanEps 2:273153e44338 108 double total;
JovanEps 3:da1132c65314 109 double *x;
JovanEps 2:273153e44338 110
JovanEps 0:43b96e9650ef 111
JovanEps 2:273153e44338 112 pc.printf ( "\n" );
JovanEps 2:273153e44338 113 pc.printf ( "LINPACK_BENCH\n" );
JovanEps 2:273153e44338 114 pc.printf ( " C version\n" );
JovanEps 2:273153e44338 115 pc.printf ( "\n" );
JovanEps 2:273153e44338 116 pc.printf ( " The LINPACK benchmark.\n" );
JovanEps 2:273153e44338 117 pc.printf ( " Language: C\n" );
JovanEps 2:273153e44338 118 pc.printf ( " Datatype: Double precision real\n" );
JovanEps 2:273153e44338 119 pc.printf ( " Matrix order N = %d\n", N );
JovanEps 2:273153e44338 120 pc.printf ( " Leading matrix dimension LDA = %d\n", LDA );
JovanEps 2:273153e44338 121
JovanEps 4:557ad9613c6e 122 ops = ( double ) ( 2L * N * N * N ) / 3 + 2 * ( N * N );
JovanEps 2:273153e44338 123
JovanEps 2:273153e44338 124 /*
JovanEps 2:273153e44338 125 Allocate space for arrays.
JovanEps 2:273153e44338 126 */
JovanEps 2:273153e44338 127 a = r8mat_gen ( LDA, N );
JovanEps 3:da1132c65314 128 //r8mat_gen ( LDA, N, a);
JovanEps 0:43b96e9650ef 129
JovanEps 2:273153e44338 130 a_max = 0.0;
JovanEps 2:273153e44338 131 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 132 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 133 a_max = r8_max ( a_max, a[i+j*LDA] );
JovanEps 2:273153e44338 134 }
JovanEps 0:43b96e9650ef 135 }
JovanEps 0:43b96e9650ef 136
JovanEps 2:273153e44338 137 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 138 x[i] = 1.0;
JovanEps 2:273153e44338 139 }
JovanEps 0:43b96e9650ef 140
JovanEps 2:273153e44338 141 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 142 b[i] = 0.0;
JovanEps 2:273153e44338 143 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 144 b[i] = b[i] + a[i+j*LDA] * x[j];
JovanEps 2:273153e44338 145 }
JovanEps 0:43b96e9650ef 146 }
JovanEps 0:43b96e9650ef 147
JovanEps 2:273153e44338 148 timer.start();
JovanEps 4:557ad9613c6e 149
JovanEps 2:273153e44338 150 //*****************
JovanEps 3:da1132c65314 151 t1 = ( double ) timer.read_us() / 1000000.0;
JovanEps 4:557ad9613c6e 152
JovanEps 2:273153e44338 153 info = dgefa ( a, LDA, N, ipvt );
JovanEps 0:43b96e9650ef 154
JovanEps 3:da1132c65314 155 t2 = ( double ) timer.read_us() / 1000000.0;
JovanEps 4:557ad9613c6e 156
JovanEps 2:273153e44338 157 if ( info != 0 ) {
JovanEps 2:273153e44338 158 pc.printf ( "\n" );
JovanEps 2:273153e44338 159 pc.printf ( "LINPACK_BENCH - Fatal error!\n" );
JovanEps 2:273153e44338 160 pc.printf ( " The matrix A is apparently singular.\n" );
JovanEps 2:273153e44338 161 pc.printf ( " Abnormal end of execution.\n" );
JovanEps 2:273153e44338 162 return 1;
JovanEps 1:be78b18b8347 163 }
JovanEps 3:da1132c65314 164 time[0] = ( double ) t2 - t1;
JovanEps 4:557ad9613c6e 165
JovanEps 4:557ad9613c6e 166
JovanEps 3:da1132c65314 167 timer.reset();
JovanEps 2:273153e44338 168
JovanEps 2:273153e44338 169 //*********
JovanEps 4:557ad9613c6e 170
JovanEps 3:da1132c65314 171 t1 = ( double ) timer.read_us() / 1000000.0;
JovanEps 2:273153e44338 172
JovanEps 2:273153e44338 173 job = 0;
JovanEps 2:273153e44338 174 dgesl ( a, LDA, N, ipvt, b, job );
JovanEps 2:273153e44338 175
JovanEps 3:da1132c65314 176 t2 = ( double ) timer.read_us() / 1000000.0;
JovanEps 3:da1132c65314 177 time[1] = ( double ) t2 - t1;
JovanEps 2:273153e44338 178
JovanEps 2:273153e44338 179 total = time[0] + time[1];
JovanEps 0:43b96e9650ef 180
JovanEps 4:557ad9613c6e 181 timer.stop();
JovanEps 4:557ad9613c6e 182
JovanEps 2:273153e44338 183 //*********
JovanEps 2:273153e44338 184
JovanEps 2:273153e44338 185 /*
JovanEps 2:273153e44338 186 Compute a residual to verify results.
JovanEps 2:273153e44338 187 */
JovanEps 2:273153e44338 188 a = r8mat_gen ( LDA, N );
JovanEps 3:da1132c65314 189 //r8mat_gen ( LDA, N, a);
JovanEps 2:273153e44338 190
JovanEps 2:273153e44338 191 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 192 x[i] = 1.0;
JovanEps 2:273153e44338 193 }
JovanEps 0:43b96e9650ef 194
JovanEps 2:273153e44338 195 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 196 rhs[i] = 0.0;
JovanEps 2:273153e44338 197 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 198 rhs[i] = rhs[i] + a[i+j*LDA] * x[j];
JovanEps 2:273153e44338 199 }
JovanEps 2:273153e44338 200 }
JovanEps 0:43b96e9650ef 201
JovanEps 2:273153e44338 202 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 203 resid[i] = -rhs[i];
JovanEps 2:273153e44338 204 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 205 resid[i] = resid[i] + a[i+j*LDA] * b[j];
JovanEps 2:273153e44338 206 }
JovanEps 2:273153e44338 207 }
JovanEps 2:273153e44338 208
JovanEps 2:273153e44338 209 resid_max = 0.0;
JovanEps 2:273153e44338 210 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 211 resid_max = r8_max ( resid_max, r8_abs ( resid[i] ) );
JovanEps 2:273153e44338 212 }
JovanEps 2:273153e44338 213
JovanEps 2:273153e44338 214 b_max = 0.0;
JovanEps 2:273153e44338 215 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 216 b_max = r8_max ( b_max, r8_abs ( b[i] ) );
JovanEps 0:43b96e9650ef 217 }
JovanEps 0:43b96e9650ef 218
JovanEps 2:273153e44338 219 eps = r8_epsilon ( );
JovanEps 2:273153e44338 220
JovanEps 2:273153e44338 221 residn = resid_max / ( double ) N / a_max / b_max / eps;
JovanEps 2:273153e44338 222
JovanEps 2:273153e44338 223 time[2] = total;
JovanEps 2:273153e44338 224
JovanEps 4:557ad9613c6e 225 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 226 /*
JovanEps 3:da1132c65314 227 if ( 0.0 < total)
JovanEps 2:273153e44338 228 {
JovanEps 3:da1132c65314 229 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 230 }
JovanEps 4:557ad9613c6e 231 else
JovanEps 2:273153e44338 232 {
JovanEps 2:273153e44338 233 time[3] = -1.0;
JovanEps 2:273153e44338 234 }
JovanEps 4:557ad9613c6e 235 */
JovanEps 4:557ad9613c6e 236
JovanEps 2:273153e44338 237 time[4] = 2.0 / time[3];
JovanEps 2:273153e44338 238 time[5] = total / cray;
JovanEps 2:273153e44338 239
JovanEps 4:557ad9613c6e 240 //pc.printf( " \n\n ");
JovanEps 4:557ad9613c6e 241 //pc.printf( "\n Norm. Resid Resid MACHEP X[1] X[N]\n" );
JovanEps 4:557ad9613c6e 242 pc.printf( "\n MACHEP X[1] X[N]\n" );
JovanEps 3:da1132c65314 243 //pc.printf(" %14f", residn);
JovanEps 3:da1132c65314 244 //pc.printf(" %14f", resid_max);
JovanEps 4:557ad9613c6e 245 pc.printf(" %14e", eps);
JovanEps 4:557ad9613c6e 246 pc.printf(" %14f", b[0]);
JovanEps 4:557ad9613c6e 247 pc.printf(" %14f ",b[N-1]);
JovanEps 4:557ad9613c6e 248 pc.printf("\n\n");
JovanEps 4:557ad9613c6e 249 //pc.printf( " %14f %14f %14e %14f %14f \n", residn, resid_max, eps, b[0], b[N-1] );
JovanEps 0:43b96e9650ef 250
JovanEps 2:273153e44338 251 pc.printf( " \n\n ");
JovanEps 4:557ad9613c6e 252 pc.printf( " Factor Solve Total MFLOPS Unit Cray-Ratio \n\n" );
JovanEps 4:557ad9613c6e 253
JovanEps 2:273153e44338 254 for(int ii=0; ii<6; ii++) {
JovanEps 4:557ad9613c6e 255 pc.printf(" %9f", time[ii]);
JovanEps 2:273153e44338 256 }
JovanEps 4:557ad9613c6e 257
JovanEps 4:557ad9613c6e 258 //pc.printf( " %9f %9f %9f %9f %9f %9f\n", time[0], time[1], time[2], time[3], time[4], time[5] );
JovanEps 2:273153e44338 259
JovanEps 2:273153e44338 260 /*
JovanEps 2:273153e44338 261 Terminate.
JovanEps 2:273153e44338 262 */
JovanEps 2:273153e44338 263 pc.printf( "\n" );
JovanEps 2:273153e44338 264 pc.printf( "LINPACK_BENCH\n" );
JovanEps 2:273153e44338 265 pc.printf( " Normal end of execution.\n" );
JovanEps 2:273153e44338 266
JovanEps 2:273153e44338 267 pc.printf( "\n" );
JovanEps 2:273153e44338 268
JovanEps 2:273153e44338 269 return 0;
JovanEps 2:273153e44338 270 # undef LDA
JovanEps 2:273153e44338 271 # undef N
JovanEps 2:273153e44338 272 }
JovanEps 4:557ad9613c6e 273
JovanEps 2:273153e44338 274 /******************************************************************************/
JovanEps 2:273153e44338 275
JovanEps 4:557ad9613c6e 276 //double cpu_time ( void )
JovanEps 2:273153e44338 277
JovanEps 2:273153e44338 278 /******************************************************************************/
JovanEps 0:43b96e9650ef 279 /*
JovanEps 2:273153e44338 280 Purpose:
JovanEps 2:273153e44338 281
JovanEps 2:273153e44338 282 CPU_TIME returns the current reading on the CPU clock.
JovanEps 2:273153e44338 283
JovanEps 2:273153e44338 284 Discussion:
JovanEps 0:43b96e9650ef 285
JovanEps 2:273153e44338 286 The CPU time measurements available through this routine are often
JovanEps 2:273153e44338 287 not very accurate. In some cases, the accuracy is no better than
JovanEps 2:273153e44338 288 a hundredth of a second.
JovanEps 2:273153e44338 289
JovanEps 2:273153e44338 290 koristi mbed.Timer
JovanEps 2:273153e44338 291
JovanEps 2:273153e44338 292 */
JovanEps 4:557ad9613c6e 293 //{
JovanEps 4:557ad9613c6e 294 // double vreme;
JovanEps 4:557ad9613c6e 295
JovanEps 4:557ad9613c6e 296 // vreme = timer.read_ms() / 1000;
JovanEps 2:273153e44338 297
JovanEps 4:557ad9613c6e 298 // return vreme;
JovanEps 4:557ad9613c6e 299 //}
JovanEps 4:557ad9613c6e 300 /******************************************************************************/
JovanEps 2:273153e44338 301
JovanEps 2:273153e44338 302
JovanEps 2:273153e44338 303 void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy )
JovanEps 2:273153e44338 304
JovanEps 2:273153e44338 305 /******************************************************************************/
JovanEps 2:273153e44338 306 /*
JovanEps 2:273153e44338 307 Purpose:
JovanEps 2:273153e44338 308
JovanEps 2:273153e44338 309 DAXPY computes constant times a vector plus a vector.
JovanEps 2:273153e44338 310
JovanEps 2:273153e44338 311 Discussion:
JovanEps 2:273153e44338 312
JovanEps 2:273153e44338 313 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 314
JovanEps 2:273153e44338 315 Modified:
JovanEps 2:273153e44338 316
JovanEps 2:273153e44338 317 30 March 2007
JovanEps 2:273153e44338 318
JovanEps 2:273153e44338 319 Author:
JovanEps 0:43b96e9650ef 320
JovanEps 2:273153e44338 321 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 322 C version by John Burkardt
JovanEps 2:273153e44338 323
JovanEps 2:273153e44338 324 Reference:
JovanEps 2:273153e44338 325
JovanEps 2:273153e44338 326 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 327 LINPACK User's Guide,
JovanEps 2:273153e44338 328 SIAM, 1979.
JovanEps 2:273153e44338 329
JovanEps 2:273153e44338 330 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 331 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 332 Algorithm 539,
JovanEps 2:273153e44338 333 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 334 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 335
JovanEps 2:273153e44338 336 Parameters:
JovanEps 2:273153e44338 337
JovanEps 2:273153e44338 338 Input, int N, the number of elements in DX and DY.
JovanEps 2:273153e44338 339
JovanEps 2:273153e44338 340 Input, double DA, the multiplier of DX.
JovanEps 2:273153e44338 341
JovanEps 2:273153e44338 342 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 343
JovanEps 2:273153e44338 344 Input, int INCX, the increment between successive entries of DX.
JovanEps 2:273153e44338 345
JovanEps 2:273153e44338 346 Input/output, double DY[*], the second vector.
JovanEps 2:273153e44338 347 On output, DY[*] has been replaced by DY[*] + DA * DX[*].
JovanEps 2:273153e44338 348
JovanEps 2:273153e44338 349 Input, int INCY, the increment between successive entries of DY.
JovanEps 2:273153e44338 350 */
JovanEps 2:273153e44338 351 {
JovanEps 2:273153e44338 352 int i;
JovanEps 2:273153e44338 353 int ix;
JovanEps 2:273153e44338 354 int iy;
JovanEps 2:273153e44338 355 int m;
JovanEps 2:273153e44338 356
JovanEps 2:273153e44338 357 if ( n <= 0 ) {
JovanEps 2:273153e44338 358 return;
JovanEps 0:43b96e9650ef 359 }
JovanEps 0:43b96e9650ef 360
JovanEps 2:273153e44338 361 if ( da == 0.0 ) {
JovanEps 2:273153e44338 362 return;
JovanEps 2:273153e44338 363 }
JovanEps 2:273153e44338 364 /*
JovanEps 2:273153e44338 365 Code for unequal increments or equal increments
JovanEps 2:273153e44338 366 not equal to 1.
JovanEps 2:273153e44338 367 */
JovanEps 2:273153e44338 368 if ( incx != 1 || incy != 1 ) {
JovanEps 2:273153e44338 369 if ( 0 <= incx ) {
JovanEps 2:273153e44338 370 ix = 0;
JovanEps 2:273153e44338 371 } else {
JovanEps 2:273153e44338 372 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 373 }
JovanEps 2:273153e44338 374
JovanEps 2:273153e44338 375 if ( 0 <= incy ) {
JovanEps 2:273153e44338 376 iy = 0;
JovanEps 2:273153e44338 377 } else {
JovanEps 2:273153e44338 378 iy = ( - n + 1 ) * incy;
JovanEps 2:273153e44338 379 }
JovanEps 0:43b96e9650ef 380
JovanEps 2:273153e44338 381 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 382 dy[iy] = dy[iy] + da * dx[ix];
JovanEps 2:273153e44338 383 ix = ix + incx;
JovanEps 2:273153e44338 384 iy = iy + incy;
JovanEps 2:273153e44338 385 }
JovanEps 2:273153e44338 386 }
JovanEps 2:273153e44338 387 /*
JovanEps 2:273153e44338 388 Code for both increments equal to 1.
JovanEps 2:273153e44338 389 */
JovanEps 2:273153e44338 390 else {
JovanEps 2:273153e44338 391 m = n % 4;
JovanEps 2:273153e44338 392
JovanEps 2:273153e44338 393 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 394 dy[i] = dy[i] + da * dx[i];
JovanEps 2:273153e44338 395 }
JovanEps 2:273153e44338 396
JovanEps 2:273153e44338 397 for ( i = m; i < n; i = i + 4 ) {
JovanEps 2:273153e44338 398 dy[i ] = dy[i ] + da * dx[i ];
JovanEps 2:273153e44338 399 dy[i+1] = dy[i+1] + da * dx[i+1];
JovanEps 2:273153e44338 400 dy[i+2] = dy[i+2] + da * dx[i+2];
JovanEps 2:273153e44338 401 dy[i+3] = dy[i+3] + da * dx[i+3];
JovanEps 2:273153e44338 402 }
JovanEps 2:273153e44338 403 }
JovanEps 2:273153e44338 404 return;
JovanEps 2:273153e44338 405 }
JovanEps 2:273153e44338 406 /******************************************************************************/
JovanEps 2:273153e44338 407
JovanEps 2:273153e44338 408 double ddot ( int n, double dx[], int incx, double dy[], int incy )
JovanEps 2:273153e44338 409
JovanEps 2:273153e44338 410 /******************************************************************************/
JovanEps 0:43b96e9650ef 411 /*
JovanEps 2:273153e44338 412 Purpose:
JovanEps 2:273153e44338 413
JovanEps 2:273153e44338 414 DDOT forms the dot product of two vectors.
JovanEps 2:273153e44338 415
JovanEps 2:273153e44338 416 Discussion:
JovanEps 2:273153e44338 417
JovanEps 2:273153e44338 418 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 419
JovanEps 2:273153e44338 420 Modified:
JovanEps 2:273153e44338 421
JovanEps 2:273153e44338 422 30 March 2007
JovanEps 2:273153e44338 423
JovanEps 2:273153e44338 424 Author:
JovanEps 2:273153e44338 425
JovanEps 2:273153e44338 426 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 427 C version by John Burkardt
JovanEps 2:273153e44338 428
JovanEps 2:273153e44338 429 Reference:
JovanEps 2:273153e44338 430
JovanEps 2:273153e44338 431 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 432 LINPACK User's Guide,
JovanEps 2:273153e44338 433 SIAM, 1979.
JovanEps 2:273153e44338 434
JovanEps 2:273153e44338 435 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 436 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 437 Algorithm 539,
JovanEps 2:273153e44338 438 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 439 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 440
JovanEps 2:273153e44338 441 Parameters:
JovanEps 2:273153e44338 442
JovanEps 2:273153e44338 443 Input, int N, the number of entries in the vectors.
JovanEps 2:273153e44338 444
JovanEps 2:273153e44338 445 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 446
JovanEps 2:273153e44338 447 Input, int INCX, the increment between successive entries in DX.
JovanEps 2:273153e44338 448
JovanEps 2:273153e44338 449 Input, double DY[*], the second vector.
JovanEps 2:273153e44338 450
JovanEps 2:273153e44338 451 Input, int INCY, the increment between successive entries in DY.
JovanEps 2:273153e44338 452
JovanEps 2:273153e44338 453 Output, double DDOT, the sum of the product of the corresponding
JovanEps 2:273153e44338 454 entries of DX and DY.
JovanEps 0:43b96e9650ef 455 */
JovanEps 2:273153e44338 456 {
JovanEps 2:273153e44338 457 double dtemp;
JovanEps 2:273153e44338 458 int i;
JovanEps 2:273153e44338 459 int ix;
JovanEps 2:273153e44338 460 int iy;
JovanEps 2:273153e44338 461 int m;
JovanEps 2:273153e44338 462
JovanEps 2:273153e44338 463 dtemp = 0.0;
JovanEps 2:273153e44338 464
JovanEps 2:273153e44338 465 if ( n <= 0 ) {
JovanEps 2:273153e44338 466 return dtemp;
JovanEps 2:273153e44338 467 }
JovanEps 2:273153e44338 468 /*
JovanEps 2:273153e44338 469 Code for unequal increments or equal increments
JovanEps 2:273153e44338 470 not equal to 1.
JovanEps 2:273153e44338 471 */
JovanEps 2:273153e44338 472 if ( incx != 1 || incy != 1 ) {
JovanEps 2:273153e44338 473 if ( 0 <= incx ) {
JovanEps 2:273153e44338 474 ix = 0;
JovanEps 2:273153e44338 475 } else {
JovanEps 2:273153e44338 476 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 477 }
JovanEps 2:273153e44338 478
JovanEps 2:273153e44338 479 if ( 0 <= incy ) {
JovanEps 2:273153e44338 480 iy = 0;
JovanEps 2:273153e44338 481 } else {
JovanEps 2:273153e44338 482 iy = ( - n + 1 ) * incy;
JovanEps 2:273153e44338 483 }
JovanEps 2:273153e44338 484
JovanEps 2:273153e44338 485 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 486 dtemp = dtemp + dx[ix] * dy[iy];
JovanEps 2:273153e44338 487 ix = ix + incx;
JovanEps 2:273153e44338 488 iy = iy + incy;
JovanEps 2:273153e44338 489 }
JovanEps 2:273153e44338 490 }
JovanEps 2:273153e44338 491 /*
JovanEps 2:273153e44338 492 Code for both increments equal to 1.
JovanEps 2:273153e44338 493 */
JovanEps 2:273153e44338 494 else {
JovanEps 2:273153e44338 495 m = n % 5;
JovanEps 2:273153e44338 496
JovanEps 2:273153e44338 497 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 498 dtemp = dtemp + dx[i] * dy[i];
JovanEps 2:273153e44338 499 }
JovanEps 2:273153e44338 500
JovanEps 2:273153e44338 501 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 502 dtemp = dtemp + dx[i ] * dy[i ]
JovanEps 2:273153e44338 503 + dx[i+1] * dy[i+1]
JovanEps 2:273153e44338 504 + dx[i+2] * dy[i+2]
JovanEps 2:273153e44338 505 + dx[i+3] * dy[i+3]
JovanEps 2:273153e44338 506 + dx[i+4] * dy[i+4];
JovanEps 2:273153e44338 507 }
JovanEps 2:273153e44338 508 }
JovanEps 2:273153e44338 509 return dtemp;
JovanEps 2:273153e44338 510 }
JovanEps 2:273153e44338 511 /******************************************************************************/
JovanEps 2:273153e44338 512
JovanEps 2:273153e44338 513 int dgefa ( double a[], int lda, int n, int ipvt[] )
JovanEps 2:273153e44338 514
JovanEps 2:273153e44338 515 /******************************************************************************/
JovanEps 2:273153e44338 516 /*
JovanEps 2:273153e44338 517 Purpose:
JovanEps 2:273153e44338 518
JovanEps 2:273153e44338 519 DGEFA factors a real general matrix.
JovanEps 2:273153e44338 520
JovanEps 2:273153e44338 521 Modified:
JovanEps 2:273153e44338 522
JovanEps 2:273153e44338 523 16 May 2005
JovanEps 2:273153e44338 524
JovanEps 2:273153e44338 525 Author:
JovanEps 2:273153e44338 526
JovanEps 2:273153e44338 527 C version by John Burkardt.
JovanEps 2:273153e44338 528
JovanEps 2:273153e44338 529 Reference:
JovanEps 0:43b96e9650ef 530
JovanEps 2:273153e44338 531 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 2:273153e44338 532 LINPACK User's Guide,
JovanEps 2:273153e44338 533 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 2:273153e44338 534 3600 University City Science Center,
JovanEps 2:273153e44338 535 Philadelphia, PA, 19104-2688.
JovanEps 2:273153e44338 536 ISBN 0-89871-172-X
JovanEps 2:273153e44338 537
JovanEps 2:273153e44338 538 Parameters:
JovanEps 2:273153e44338 539
JovanEps 2:273153e44338 540 Input/output, double A[LDA*N].
JovanEps 2:273153e44338 541 On intput, the matrix to be factored.
JovanEps 2:273153e44338 542 On output, an upper triangular matrix and the multipliers used to obtain
JovanEps 2:273153e44338 543 it. The factorization can be written A=L*U, where L is a product of
JovanEps 2:273153e44338 544 permutation and unit lower triangular matrices, and U is upper triangular.
JovanEps 2:273153e44338 545
JovanEps 2:273153e44338 546 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 547
JovanEps 2:273153e44338 548 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 549
JovanEps 2:273153e44338 550 Output, int IPVT[N], the pivot indices.
JovanEps 2:273153e44338 551
JovanEps 2:273153e44338 552 Output, int DGEFA, singularity indicator.
JovanEps 2:273153e44338 553 0, normal value.
JovanEps 2:273153e44338 554 K, if U(K,K) == 0. This is not an error condition for this subroutine,
JovanEps 2:273153e44338 555 but it does indicate that DGESL or DGEDI will divide by zero if called.
JovanEps 2:273153e44338 556 Use RCOND in DGECO for a reliable indication of singularity.
JovanEps 2:273153e44338 557 */
JovanEps 2:273153e44338 558 {
JovanEps 2:273153e44338 559 int info;
JovanEps 2:273153e44338 560 int j;
JovanEps 2:273153e44338 561 int k;
JovanEps 2:273153e44338 562 int l;
JovanEps 2:273153e44338 563 double t;
JovanEps 2:273153e44338 564 /*
JovanEps 2:273153e44338 565 Gaussian elimination with partial pivoting.
JovanEps 2:273153e44338 566 */
JovanEps 2:273153e44338 567 info = 0;
JovanEps 2:273153e44338 568
JovanEps 2:273153e44338 569 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 570 /*
JovanEps 2:273153e44338 571 Find L = pivot index.
JovanEps 2:273153e44338 572 */
JovanEps 2:273153e44338 573 l = idamax ( n-k+1, a+(k-1)+(k-1)*lda, 1 ) + k - 1;
JovanEps 2:273153e44338 574 ipvt[k-1] = l;
JovanEps 2:273153e44338 575 /*
JovanEps 2:273153e44338 576 Zero pivot implies this column already triangularized.
JovanEps 2:273153e44338 577 */
JovanEps 2:273153e44338 578 if ( a[l-1+(k-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 579 info = k;
JovanEps 2:273153e44338 580 continue;
JovanEps 2:273153e44338 581 }
JovanEps 2:273153e44338 582 /*
JovanEps 2:273153e44338 583 Interchange if necessary.
JovanEps 2:273153e44338 584 */
JovanEps 2:273153e44338 585 if ( l != k ) {
JovanEps 2:273153e44338 586 t = a[l-1+(k-1)*lda];
JovanEps 2:273153e44338 587 a[l-1+(k-1)*lda] = a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 588 a[k-1+(k-1)*lda] = t;
JovanEps 2:273153e44338 589 }
JovanEps 2:273153e44338 590 /*
JovanEps 2:273153e44338 591 Compute multipliers.
JovanEps 2:273153e44338 592 */
JovanEps 2:273153e44338 593 t = -1.0 / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 594
JovanEps 2:273153e44338 595 dscal ( n-k, t, a+k+(k-1)*lda, 1 );
JovanEps 2:273153e44338 596 /*
JovanEps 2:273153e44338 597 Row elimination with column indexing.
JovanEps 2:273153e44338 598 */
JovanEps 2:273153e44338 599 for ( j = k+1; j <= n; j++ ) {
JovanEps 2:273153e44338 600 t = a[l-1+(j-1)*lda];
JovanEps 2:273153e44338 601 if ( l != k ) {
JovanEps 2:273153e44338 602 a[l-1+(j-1)*lda] = a[k-1+(j-1)*lda];
JovanEps 2:273153e44338 603 a[k-1+(j-1)*lda] = t;
JovanEps 2:273153e44338 604 }
JovanEps 2:273153e44338 605 daxpy ( n-k, t, a+k+(k-1)*lda, 1, a+k+(j-1)*lda, 1 );
JovanEps 2:273153e44338 606 }
JovanEps 2:273153e44338 607
JovanEps 0:43b96e9650ef 608 }
JovanEps 0:43b96e9650ef 609
JovanEps 2:273153e44338 610 ipvt[n-1] = n;
JovanEps 0:43b96e9650ef 611
JovanEps 2:273153e44338 612 if ( a[n-1+(n-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 613 info = n;
JovanEps 0:43b96e9650ef 614 }
JovanEps 0:43b96e9650ef 615
JovanEps 2:273153e44338 616 return info;
JovanEps 2:273153e44338 617 }
JovanEps 2:273153e44338 618 /******************************************************************************/
JovanEps 0:43b96e9650ef 619
JovanEps 2:273153e44338 620 void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job )
JovanEps 2:273153e44338 621
JovanEps 2:273153e44338 622 /******************************************************************************/
JovanEps 0:43b96e9650ef 623 /*
JovanEps 2:273153e44338 624 Purpose:
JovanEps 2:273153e44338 625
JovanEps 2:273153e44338 626 DGESL solves a real general linear system A * X = B.
JovanEps 2:273153e44338 627
JovanEps 2:273153e44338 628 Discussion:
JovanEps 2:273153e44338 629
JovanEps 2:273153e44338 630 DGESL can solve either of the systems A * X = B or A' * X = B.
JovanEps 2:273153e44338 631
JovanEps 2:273153e44338 632 The system matrix must have been factored by DGECO or DGEFA.
JovanEps 2:273153e44338 633
JovanEps 2:273153e44338 634 A division by zero will occur if the input factor contains a
JovanEps 2:273153e44338 635 zero on the diagonal. Technically this indicates singularity
JovanEps 2:273153e44338 636 but it is often caused by improper arguments or improper
JovanEps 2:273153e44338 637 setting of LDA. It will not occur if the subroutines are
JovanEps 2:273153e44338 638 called correctly and if DGECO has set 0.0 < RCOND
JovanEps 2:273153e44338 639 or DGEFA has set INFO == 0.
JovanEps 2:273153e44338 640
JovanEps 2:273153e44338 641 Modified:
JovanEps 2:273153e44338 642
JovanEps 2:273153e44338 643 16 May 2005
JovanEps 2:273153e44338 644
JovanEps 2:273153e44338 645 Author:
JovanEps 2:273153e44338 646
JovanEps 2:273153e44338 647 C version by John Burkardt.
JovanEps 2:273153e44338 648
JovanEps 2:273153e44338 649 Reference:
JovanEps 2:273153e44338 650
JovanEps 2:273153e44338 651 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 2:273153e44338 652 LINPACK User's Guide,
JovanEps 2:273153e44338 653 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 2:273153e44338 654 3600 University City Science Center,
JovanEps 2:273153e44338 655 Philadelphia, PA, 19104-2688.
JovanEps 2:273153e44338 656 ISBN 0-89871-172-X
JovanEps 2:273153e44338 657
JovanEps 2:273153e44338 658 Parameters:
JovanEps 2:273153e44338 659
JovanEps 2:273153e44338 660 Input, double A[LDA*N], the output from DGECO or DGEFA.
JovanEps 2:273153e44338 661
JovanEps 2:273153e44338 662 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 663
JovanEps 2:273153e44338 664 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 665
JovanEps 2:273153e44338 666 Input, int IPVT[N], the pivot vector from DGECO or DGEFA.
JovanEps 2:273153e44338 667
JovanEps 2:273153e44338 668 Input/output, double B[N].
JovanEps 2:273153e44338 669 On input, the right hand side vector.
JovanEps 2:273153e44338 670 On output, the solution vector.
JovanEps 0:43b96e9650ef 671
JovanEps 2:273153e44338 672 Input, int JOB.
JovanEps 2:273153e44338 673 0, solve A * X = B;
JovanEps 2:273153e44338 674 nonzero, solve A' * X = B.
JovanEps 2:273153e44338 675 */
JovanEps 2:273153e44338 676 {
JovanEps 2:273153e44338 677 int k;
JovanEps 2:273153e44338 678 int l;
JovanEps 2:273153e44338 679 double t;
JovanEps 2:273153e44338 680 /*
JovanEps 2:273153e44338 681 Solve A * X = B.
JovanEps 2:273153e44338 682 */
JovanEps 2:273153e44338 683 if ( job == 0 ) {
JovanEps 2:273153e44338 684 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 685 l = ipvt[k-1];
JovanEps 2:273153e44338 686 t = b[l-1];
JovanEps 2:273153e44338 687
JovanEps 2:273153e44338 688 if ( l != k ) {
JovanEps 2:273153e44338 689 b[l-1] = b[k-1];
JovanEps 2:273153e44338 690 b[k-1] = t;
JovanEps 2:273153e44338 691 }
JovanEps 2:273153e44338 692
JovanEps 2:273153e44338 693 daxpy ( n-k, t, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 694
JovanEps 2:273153e44338 695 }
JovanEps 0:43b96e9650ef 696
JovanEps 2:273153e44338 697 for ( k = n; 1 <= k; k-- ) {
JovanEps 2:273153e44338 698 b[k-1] = b[k-1] / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 699 t = -b[k-1];
JovanEps 2:273153e44338 700 daxpy ( k-1, t, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 701 }
JovanEps 2:273153e44338 702 }
JovanEps 2:273153e44338 703 /*
JovanEps 2:273153e44338 704 Solve A' * X = B.
JovanEps 2:273153e44338 705 */
JovanEps 2:273153e44338 706 else {
JovanEps 2:273153e44338 707 for ( k = 1; k <= n; k++ ) {
JovanEps 2:273153e44338 708 t = ddot ( k-1, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 709 b[k-1] = ( b[k-1] - t ) / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 710 }
JovanEps 0:43b96e9650ef 711
JovanEps 2:273153e44338 712 for ( k = n-1; 1 <= k; k-- ) {
JovanEps 2:273153e44338 713 b[k-1] = b[k-1] + ddot ( n-k, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 714 l = ipvt[k-1];
JovanEps 2:273153e44338 715
JovanEps 2:273153e44338 716 if ( l != k ) {
JovanEps 2:273153e44338 717 t = b[l-1];
JovanEps 2:273153e44338 718 b[l-1] = b[k-1];
JovanEps 2:273153e44338 719 b[k-1] = t;
JovanEps 2:273153e44338 720 }
JovanEps 2:273153e44338 721 }
JovanEps 2:273153e44338 722 }
JovanEps 2:273153e44338 723 return;
JovanEps 2:273153e44338 724 }
JovanEps 2:273153e44338 725 /******************************************************************************/
JovanEps 2:273153e44338 726
JovanEps 2:273153e44338 727 void dscal ( int n, double sa, double x[], int incx )
JovanEps 2:273153e44338 728
JovanEps 2:273153e44338 729 /******************************************************************************/
JovanEps 0:43b96e9650ef 730 /*
JovanEps 2:273153e44338 731 Purpose:
JovanEps 2:273153e44338 732
JovanEps 2:273153e44338 733 DSCAL scales a vector by a constant.
JovanEps 2:273153e44338 734
JovanEps 2:273153e44338 735 Modified:
JovanEps 2:273153e44338 736
JovanEps 2:273153e44338 737 30 March 2007
JovanEps 2:273153e44338 738
JovanEps 2:273153e44338 739 Author:
JovanEps 2:273153e44338 740
JovanEps 2:273153e44338 741 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 742 C version by John Burkardt
JovanEps 2:273153e44338 743
JovanEps 2:273153e44338 744 Reference:
JovanEps 2:273153e44338 745
JovanEps 2:273153e44338 746 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 747 LINPACK User's Guide,
JovanEps 2:273153e44338 748 SIAM, 1979.
JovanEps 2:273153e44338 749
JovanEps 2:273153e44338 750 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 751 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 752 Algorithm 539,
JovanEps 2:273153e44338 753 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 754 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 755
JovanEps 2:273153e44338 756 Parameters:
JovanEps 2:273153e44338 757
JovanEps 2:273153e44338 758 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 759
JovanEps 2:273153e44338 760 Input, double SA, the multiplier.
JovanEps 2:273153e44338 761
JovanEps 2:273153e44338 762 Input/output, double X[*], the vector to be scaled.
JovanEps 2:273153e44338 763
JovanEps 2:273153e44338 764 Input, int INCX, the increment between successive entries of X.
JovanEps 0:43b96e9650ef 765 */
JovanEps 2:273153e44338 766 {
JovanEps 2:273153e44338 767 int i;
JovanEps 2:273153e44338 768 int ix;
JovanEps 2:273153e44338 769 int m;
JovanEps 2:273153e44338 770
JovanEps 2:273153e44338 771 if ( n <= 0 ) {
JovanEps 2:273153e44338 772 } else if ( incx == 1 ) {
JovanEps 2:273153e44338 773 m = n % 5;
JovanEps 2:273153e44338 774
JovanEps 2:273153e44338 775 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 776 x[i] = sa * x[i];
JovanEps 2:273153e44338 777 }
JovanEps 0:43b96e9650ef 778
JovanEps 2:273153e44338 779 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 780 x[i] = sa * x[i];
JovanEps 2:273153e44338 781 x[i+1] = sa * x[i+1];
JovanEps 2:273153e44338 782 x[i+2] = sa * x[i+2];
JovanEps 2:273153e44338 783 x[i+3] = sa * x[i+3];
JovanEps 2:273153e44338 784 x[i+4] = sa * x[i+4];
JovanEps 2:273153e44338 785 }
JovanEps 2:273153e44338 786 } else {
JovanEps 2:273153e44338 787 if ( 0 <= incx ) {
JovanEps 2:273153e44338 788 ix = 0;
JovanEps 2:273153e44338 789 } else {
JovanEps 2:273153e44338 790 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 791 }
JovanEps 2:273153e44338 792
JovanEps 2:273153e44338 793 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 794 x[ix] = sa * x[ix];
JovanEps 2:273153e44338 795 ix = ix + incx;
JovanEps 2:273153e44338 796 }
JovanEps 2:273153e44338 797 }
JovanEps 2:273153e44338 798 return;
JovanEps 2:273153e44338 799 }
JovanEps 2:273153e44338 800 /******************************************************************************/
JovanEps 2:273153e44338 801
JovanEps 2:273153e44338 802 int idamax ( int n, double dx[], int incx )
JovanEps 2:273153e44338 803
JovanEps 2:273153e44338 804 /******************************************************************************/
JovanEps 0:43b96e9650ef 805 /*
JovanEps 2:273153e44338 806 Purpose:
JovanEps 2:273153e44338 807
JovanEps 2:273153e44338 808 IDAMAX finds the index of the vector element of maximum absolute value.
JovanEps 2:273153e44338 809
JovanEps 2:273153e44338 810 Discussion:
JovanEps 2:273153e44338 811
JovanEps 2:273153e44338 812 WARNING: This index is a 1-based index, not a 0-based index!
JovanEps 2:273153e44338 813
JovanEps 2:273153e44338 814 Modified:
JovanEps 2:273153e44338 815
JovanEps 2:273153e44338 816 30 March 2007
JovanEps 2:273153e44338 817
JovanEps 2:273153e44338 818 Author:
JovanEps 2:273153e44338 819
JovanEps 2:273153e44338 820 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 821 C version by John Burkardt
JovanEps 2:273153e44338 822
JovanEps 2:273153e44338 823 Reference:
JovanEps 2:273153e44338 824
JovanEps 2:273153e44338 825 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 826 LINPACK User's Guide,
JovanEps 2:273153e44338 827 SIAM, 1979.
JovanEps 2:273153e44338 828
JovanEps 2:273153e44338 829 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 830 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 831 Algorithm 539,
JovanEps 2:273153e44338 832 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 833 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 834
JovanEps 2:273153e44338 835 Parameters:
JovanEps 2:273153e44338 836
JovanEps 2:273153e44338 837 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 838
JovanEps 2:273153e44338 839 Input, double X[*], the vector to be examined.
JovanEps 2:273153e44338 840
JovanEps 2:273153e44338 841 Input, int INCX, the increment between successive entries of SX.
JovanEps 2:273153e44338 842
JovanEps 2:273153e44338 843 Output, int IDAMAX, the index of the element of maximum
JovanEps 2:273153e44338 844 absolute value.
JovanEps 0:43b96e9650ef 845 */
JovanEps 2:273153e44338 846 {
JovanEps 2:273153e44338 847 double dmax;
JovanEps 2:273153e44338 848 int i;
JovanEps 2:273153e44338 849 int ix;
JovanEps 2:273153e44338 850 int value;
JovanEps 2:273153e44338 851
JovanEps 2:273153e44338 852 value = 0;
JovanEps 0:43b96e9650ef 853
JovanEps 2:273153e44338 854 if ( n < 1 || incx <= 0 ) {
JovanEps 2:273153e44338 855 return value;
JovanEps 2:273153e44338 856 }
JovanEps 2:273153e44338 857
JovanEps 2:273153e44338 858 value = 1;
JovanEps 2:273153e44338 859
JovanEps 2:273153e44338 860 if ( n == 1 ) {
JovanEps 2:273153e44338 861 return value;
JovanEps 2:273153e44338 862 }
JovanEps 0:43b96e9650ef 863
JovanEps 2:273153e44338 864 if ( incx == 1 ) {
JovanEps 2:273153e44338 865 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 866
JovanEps 2:273153e44338 867 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 868 if ( dmax < r8_abs ( dx[i] ) ) {
JovanEps 2:273153e44338 869 value = i + 1;
JovanEps 2:273153e44338 870 dmax = r8_abs ( dx[i] );
JovanEps 2:273153e44338 871 }
JovanEps 2:273153e44338 872 }
JovanEps 2:273153e44338 873 } else {
JovanEps 2:273153e44338 874 ix = 0;
JovanEps 2:273153e44338 875 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 876 ix = ix + incx;
JovanEps 2:273153e44338 877
JovanEps 2:273153e44338 878 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 879 if ( dmax < r8_abs ( dx[ix] ) ) {
JovanEps 2:273153e44338 880 value = i + 1;
JovanEps 2:273153e44338 881 dmax = r8_abs ( dx[ix] );
JovanEps 2:273153e44338 882 }
JovanEps 2:273153e44338 883 ix = ix + incx;
JovanEps 2:273153e44338 884 }
JovanEps 2:273153e44338 885 }
JovanEps 0:43b96e9650ef 886
JovanEps 2:273153e44338 887 return value;
JovanEps 2:273153e44338 888 }
JovanEps 2:273153e44338 889 /******************************************************************************/
JovanEps 2:273153e44338 890
JovanEps 2:273153e44338 891 double r8_abs ( double x )
JovanEps 2:273153e44338 892
JovanEps 2:273153e44338 893 /******************************************************************************/
JovanEps 2:273153e44338 894 /*
JovanEps 2:273153e44338 895 Purpose:
JovanEps 2:273153e44338 896
JovanEps 2:273153e44338 897 R8_ABS returns the absolute value of a R8.
JovanEps 0:43b96e9650ef 898
JovanEps 2:273153e44338 899 Modified:
JovanEps 2:273153e44338 900
JovanEps 2:273153e44338 901 02 April 2005
JovanEps 2:273153e44338 902
JovanEps 2:273153e44338 903 Author:
JovanEps 0:43b96e9650ef 904
JovanEps 2:273153e44338 905 John Burkardt
JovanEps 2:273153e44338 906
JovanEps 2:273153e44338 907 Parameters:
JovanEps 2:273153e44338 908
JovanEps 2:273153e44338 909 Input, double X, the quantity whose absolute value is desired.
JovanEps 2:273153e44338 910
JovanEps 2:273153e44338 911 Output, double R8_ABS, the absolute value of X.
JovanEps 2:273153e44338 912 */
JovanEps 0:43b96e9650ef 913 {
JovanEps 2:273153e44338 914 double value;
JovanEps 2:273153e44338 915
JovanEps 2:273153e44338 916 if ( 0.0 <= x ) {
JovanEps 2:273153e44338 917 value = x;
JovanEps 2:273153e44338 918 } else {
JovanEps 2:273153e44338 919 value = -x;
JovanEps 2:273153e44338 920 }
JovanEps 2:273153e44338 921 return value;
JovanEps 2:273153e44338 922 }
JovanEps 2:273153e44338 923 /******************************************************************************/
JovanEps 2:273153e44338 924
JovanEps 2:273153e44338 925 double r8_epsilon ( void )
JovanEps 0:43b96e9650ef 926
JovanEps 2:273153e44338 927 /******************************************************************************/
JovanEps 2:273153e44338 928 /*
JovanEps 2:273153e44338 929 Purpose:
JovanEps 2:273153e44338 930
JovanEps 2:273153e44338 931 R8_EPSILON returns the R8 round off unit.
JovanEps 2:273153e44338 932
JovanEps 2:273153e44338 933 Discussion:
JovanEps 2:273153e44338 934
JovanEps 2:273153e44338 935 R8_EPSILON is a number R which is a power of 2 with the property that,
JovanEps 2:273153e44338 936 to the precision of the computer's arithmetic,
JovanEps 2:273153e44338 937 1 < 1 + R
JovanEps 2:273153e44338 938 but
JovanEps 2:273153e44338 939 1 = ( 1 + R / 2 )
JovanEps 0:43b96e9650ef 940
JovanEps 2:273153e44338 941 Licensing:
JovanEps 2:273153e44338 942
JovanEps 2:273153e44338 943 This code is distributed under the GNU LGPL license.
JovanEps 2:273153e44338 944
JovanEps 2:273153e44338 945 Modified:
JovanEps 2:273153e44338 946
JovanEps 2:273153e44338 947 08 May 2006
JovanEps 2:273153e44338 948
JovanEps 2:273153e44338 949 Author:
JovanEps 2:273153e44338 950
JovanEps 2:273153e44338 951 John Burkardt
JovanEps 2:273153e44338 952
JovanEps 2:273153e44338 953 Parameters:
JovanEps 0:43b96e9650ef 954
JovanEps 2:273153e44338 955 Output, double R8_EPSILON, the double precision round-off unit.
JovanEps 2:273153e44338 956 */
JovanEps 0:43b96e9650ef 957 {
JovanEps 2:273153e44338 958 double r;
JovanEps 2:273153e44338 959
JovanEps 2:273153e44338 960 r = 1.0;
JovanEps 2:273153e44338 961
JovanEps 2:273153e44338 962 while ( 1.0 < ( double ) ( 1.0 + r ) ) {
JovanEps 2:273153e44338 963 r = r / 2.0;
JovanEps 2:273153e44338 964 }
JovanEps 2:273153e44338 965 r = 2.0 * r;
JovanEps 2:273153e44338 966
JovanEps 2:273153e44338 967 return r;
JovanEps 0:43b96e9650ef 968 }
JovanEps 2:273153e44338 969 /******************************************************************************/
JovanEps 0:43b96e9650ef 970
JovanEps 2:273153e44338 971 double r8_max ( double x, double y )
JovanEps 2:273153e44338 972
JovanEps 2:273153e44338 973 /******************************************************************************/
JovanEps 2:273153e44338 974 /*
JovanEps 2:273153e44338 975 Purpose:
JovanEps 2:273153e44338 976
JovanEps 2:273153e44338 977 R8_MAX returns the maximum of two R8's.
JovanEps 2:273153e44338 978
JovanEps 2:273153e44338 979 Modified:
JovanEps 2:273153e44338 980
JovanEps 2:273153e44338 981 18 August 2004
JovanEps 2:273153e44338 982
JovanEps 2:273153e44338 983 Author:
JovanEps 0:43b96e9650ef 984
JovanEps 2:273153e44338 985 John Burkardt
JovanEps 2:273153e44338 986
JovanEps 2:273153e44338 987 Parameters:
JovanEps 2:273153e44338 988
JovanEps 2:273153e44338 989 Input, double X, Y, the quantities to compare.
JovanEps 0:43b96e9650ef 990
JovanEps 2:273153e44338 991 Output, double R8_MAX, the maximum of X and Y.
JovanEps 2:273153e44338 992 */
JovanEps 0:43b96e9650ef 993 {
JovanEps 2:273153e44338 994 double value;
JovanEps 2:273153e44338 995
JovanEps 2:273153e44338 996 if ( y < x ) {
JovanEps 2:273153e44338 997 value = x;
JovanEps 2:273153e44338 998 } else {
JovanEps 2:273153e44338 999 value = y;
JovanEps 2:273153e44338 1000 }
JovanEps 2:273153e44338 1001 return value;
JovanEps 0:43b96e9650ef 1002 }
JovanEps 2:273153e44338 1003 /******************************************************************************/
JovanEps 2:273153e44338 1004
JovanEps 2:273153e44338 1005 double r8_random ( int iseed[4] )
JovanEps 2:273153e44338 1006
JovanEps 2:273153e44338 1007 /******************************************************************************/
JovanEps 2:273153e44338 1008 /*
JovanEps 2:273153e44338 1009 Purpose:
JovanEps 2:273153e44338 1010
JovanEps 2:273153e44338 1011 R8_RANDOM returns a uniformly distributed random number between 0 and 1.
JovanEps 2:273153e44338 1012
JovanEps 2:273153e44338 1013 Discussion:
JovanEps 0:43b96e9650ef 1014
JovanEps 2:273153e44338 1015 This routine uses a multiplicative congruential method with modulus
JovanEps 2:273153e44338 1016 2**48 and multiplier 33952834046453 (see G.S.Fishman,
JovanEps 2:273153e44338 1017 'Multiplicative congruential random number generators with modulus
JovanEps 2:273153e44338 1018 2**b: an exhaustive analysis for b = 32 and a partial analysis for
JovanEps 2:273153e44338 1019 b = 48', Math. Comp. 189, pp 331-344, 1990).
JovanEps 2:273153e44338 1020
JovanEps 2:273153e44338 1021 48-bit integers are stored in 4 integer array elements with 12 bits
JovanEps 2:273153e44338 1022 per element. Hence the routine is portable across machines with
JovanEps 2:273153e44338 1023 integers of 32 bits or more.
JovanEps 2:273153e44338 1024
JovanEps 2:273153e44338 1025 Parameters:
JovanEps 2:273153e44338 1026
JovanEps 2:273153e44338 1027 Input/output, integer ISEED(4).
JovanEps 2:273153e44338 1028 On entry, the seed of the random number generator; the array
JovanEps 2:273153e44338 1029 elements must be between 0 and 4095, and ISEED(4) must be odd.
JovanEps 2:273153e44338 1030 On exit, the seed is updated.
JovanEps 2:273153e44338 1031
JovanEps 2:273153e44338 1032 Output, double R8_RANDOM, the next pseudorandom number.
JovanEps 2:273153e44338 1033 */
JovanEps 1:be78b18b8347 1034 {
JovanEps 2:273153e44338 1035 int ipw2 = 4096;
JovanEps 2:273153e44338 1036 int it1;
JovanEps 2:273153e44338 1037 int it2;
JovanEps 2:273153e44338 1038 int it3;
JovanEps 2:273153e44338 1039 int it4;
JovanEps 2:273153e44338 1040 int m1 = 494;
JovanEps 2:273153e44338 1041 int m2 = 322;
JovanEps 2:273153e44338 1042 int m3 = 2508;
JovanEps 2:273153e44338 1043 int m4 = 2549;
JovanEps 2:273153e44338 1044 double r = 1.0 / 4096.0;
JovanEps 2:273153e44338 1045 double value;
JovanEps 2:273153e44338 1046 /*
JovanEps 2:273153e44338 1047 Multiply the seed by the multiplier modulo 2**48.
JovanEps 2:273153e44338 1048 */
JovanEps 2:273153e44338 1049 it4 = iseed[3] * m4;
JovanEps 2:273153e44338 1050 it3 = it4 / ipw2;
JovanEps 2:273153e44338 1051 it4 = it4 - ipw2 * it3;
JovanEps 2:273153e44338 1052 it3 = it3 + iseed[2] * m4 + iseed[3] * m3;
JovanEps 2:273153e44338 1053 it2 = it3 / ipw2;
JovanEps 2:273153e44338 1054 it3 = it3 - ipw2 * it2;
JovanEps 2:273153e44338 1055 it2 = it2 + iseed[1] * m4 + iseed[2] * m3 + iseed[3] * m2;
JovanEps 2:273153e44338 1056 it1 = it2 / ipw2;
JovanEps 2:273153e44338 1057 it2 = it2 - ipw2 * it1;
JovanEps 2:273153e44338 1058 it1 = it1 + iseed[0] * m4 + iseed[1] * m3 + iseed[2] * m2 + iseed[3] * m1;
JovanEps 2:273153e44338 1059 it1 = ( it1 % ipw2 );
JovanEps 2:273153e44338 1060 /*
JovanEps 2:273153e44338 1061 Return updated seed
JovanEps 2:273153e44338 1062 */
JovanEps 2:273153e44338 1063 iseed[0] = it1;
JovanEps 2:273153e44338 1064 iseed[1] = it2;
JovanEps 2:273153e44338 1065 iseed[2] = it3;
JovanEps 2:273153e44338 1066 iseed[3] = it4;
JovanEps 2:273153e44338 1067 /*
JovanEps 2:273153e44338 1068 Convert 48-bit integer to a real number in the interval (0,1)
JovanEps 2:273153e44338 1069 */
JovanEps 2:273153e44338 1070 value =
JovanEps 2:273153e44338 1071 r * ( ( double ) ( it1 )
JovanEps 2:273153e44338 1072 + r * ( ( double ) ( it2 )
JovanEps 2:273153e44338 1073 + r * ( ( double ) ( it3 )
JovanEps 2:273153e44338 1074 + r * ( ( double ) ( it4 ) ) ) ) );
JovanEps 2:273153e44338 1075
JovanEps 2:273153e44338 1076 return value;
JovanEps 2:273153e44338 1077 }
JovanEps 2:273153e44338 1078 /******************************************************************************/
JovanEps 2:273153e44338 1079
JovanEps 2:273153e44338 1080 double *r8mat_gen ( int lda, int n )
JovanEps 2:273153e44338 1081
JovanEps 2:273153e44338 1082 /******************************************************************************/
JovanEps 2:273153e44338 1083 /*
JovanEps 2:273153e44338 1084 Purpose:
JovanEps 2:273153e44338 1085
JovanEps 2:273153e44338 1086 R8MAT_GEN generates a random R8MAT.
JovanEps 2:273153e44338 1087
JovanEps 2:273153e44338 1088 Modified:
JovanEps 2:273153e44338 1089
JovanEps 2:273153e44338 1090 06 June 2005
JovanEps 2:273153e44338 1091
JovanEps 2:273153e44338 1092 Parameters:
JovanEps 2:273153e44338 1093
JovanEps 2:273153e44338 1094 Input, integer LDA, the leading dimension of the matrix.
JovanEps 2:273153e44338 1095
JovanEps 2:273153e44338 1096 Input, integer N, the order of the matrix.
JovanEps 2:273153e44338 1097
JovanEps 2:273153e44338 1098 Output, double R8MAT_GEN[LDA*N], the N by N matrix.
JovanEps 2:273153e44338 1099 */
JovanEps 2:273153e44338 1100 {
JovanEps 3:da1132c65314 1101 double *ba;
JovanEps 2:273153e44338 1102 int i;
JovanEps 2:273153e44338 1103 int init[4] = { 1, 2, 3, 1325 };
JovanEps 2:273153e44338 1104 int j;
JovanEps 2:273153e44338 1105
JovanEps 3:da1132c65314 1106 ba = ( double * ) malloc ( lda * n * sizeof ( double ) );
JovanEps 2:273153e44338 1107
JovanEps 2:273153e44338 1108 for ( j = 1; j <= n; j++ ) {
JovanEps 2:273153e44338 1109 for ( i = 1; i <= n; i++ ) {
JovanEps 3:da1132c65314 1110 ba[i-1+(j-1)*lda] = r8_random ( init ) - 0.5;
JovanEps 2:273153e44338 1111 }
JovanEps 1:be78b18b8347 1112 }
JovanEps 2:273153e44338 1113
JovanEps 3:da1132c65314 1114 return ba;
JovanEps 0:43b96e9650ef 1115 }