Jovan Ivković / Mbed 2 deprecated Linpack

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Dependencies:   mbed

main.cpp@5:2b929fbd5c69, 2017-01-03 (annotated)

Committer:
JovanEps
Date:
Tue Jan 03 18:41:10 2017 +0000
Revision:
5:2b929fbd5c69
Parent:
4:557ad9613c6e
Child:
6:5e0f3eedaf66
RC1

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 5:2b929fbd5c69 51 while(1)
JovanEps 5:2b929fbd5c69 52 {
JovanEps 2:273153e44338 53 pc.printf("Starting benchmark...\n");
JovanEps 5:2b929fbd5c69 54
JovanEps 2:273153e44338 55 do_benchmark();
JovanEps 5:2b929fbd5c69 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 5:2b929fbd5c69 122 ops = ( double ) (( 2 * N * N * N ) / 3.0 ) + 2.0 * ( N * N )); //c++
JovanEps 5:2b929fbd5c69 123 //ops = ( double ) ( 2L * N * N * N ) / 3.0 + 2.0 * ( double ) ( (long)N * N ); // Arduiono C
JovanEps 2:273153e44338 124
JovanEps 2:273153e44338 125 /*
JovanEps 2:273153e44338 126 Allocate space for arrays.
JovanEps 2:273153e44338 127 */
JovanEps 2:273153e44338 128 a = r8mat_gen ( LDA, N );
JovanEps 3:da1132c65314 129 //r8mat_gen ( LDA, N, a);
JovanEps 0:43b96e9650ef 130
JovanEps 2:273153e44338 131 a_max = 0.0;
JovanEps 2:273153e44338 132 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 133 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 134 a_max = r8_max ( a_max, a[i+j*LDA] );
JovanEps 2:273153e44338 135 }
JovanEps 0:43b96e9650ef 136 }
JovanEps 0:43b96e9650ef 137
JovanEps 2:273153e44338 138 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 139 x[i] = 1.0;
JovanEps 2:273153e44338 140 }
JovanEps 0:43b96e9650ef 141
JovanEps 2:273153e44338 142 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 143 b[i] = 0.0;
JovanEps 2:273153e44338 144 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 145 b[i] = b[i] + a[i+j*LDA] * x[j];
JovanEps 2:273153e44338 146 }
JovanEps 0:43b96e9650ef 147 }
JovanEps 0:43b96e9650ef 148
JovanEps 2:273153e44338 149 timer.start();
JovanEps 4:557ad9613c6e 150
JovanEps 2:273153e44338 151 //*****************
JovanEps 3:da1132c65314 152 t1 = ( double ) timer.read_us() / 1000000.0;
JovanEps 4:557ad9613c6e 153
JovanEps 2:273153e44338 154 info = dgefa ( a, LDA, N, ipvt );
JovanEps 0:43b96e9650ef 155
JovanEps 3:da1132c65314 156 t2 = ( double ) timer.read_us() / 1000000.0;
JovanEps 4:557ad9613c6e 157
JovanEps 2:273153e44338 158 if ( info != 0 ) {
JovanEps 2:273153e44338 159 pc.printf ( "\n" );
JovanEps 2:273153e44338 160 pc.printf ( "LINPACK_BENCH - Fatal error!\n" );
JovanEps 2:273153e44338 161 pc.printf ( " The matrix A is apparently singular.\n" );
JovanEps 2:273153e44338 162 pc.printf ( " Abnormal end of execution.\n" );
JovanEps 2:273153e44338 163 return 1;
JovanEps 1:be78b18b8347 164 }
JovanEps 3:da1132c65314 165 time[0] = ( double ) t2 - t1;
JovanEps 4:557ad9613c6e 166
JovanEps 4:557ad9613c6e 167
JovanEps 3:da1132c65314 168 timer.reset();
JovanEps 2:273153e44338 169
JovanEps 2:273153e44338 170 //*********
JovanEps 4:557ad9613c6e 171
JovanEps 3:da1132c65314 172 t1 = ( double ) timer.read_us() / 1000000.0;
JovanEps 2:273153e44338 173
JovanEps 2:273153e44338 174 job = 0;
JovanEps 2:273153e44338 175 dgesl ( a, LDA, N, ipvt, b, job );
JovanEps 2:273153e44338 176
JovanEps 3:da1132c65314 177 t2 = ( double ) timer.read_us() / 1000000.0;
JovanEps 3:da1132c65314 178 time[1] = ( double ) t2 - t1;
JovanEps 2:273153e44338 179
JovanEps 2:273153e44338 180 total = time[0] + time[1];
JovanEps 0:43b96e9650ef 181
JovanEps 4:557ad9613c6e 182 timer.stop();
JovanEps 4:557ad9613c6e 183
JovanEps 2:273153e44338 184 //*********
JovanEps 2:273153e44338 185
JovanEps 2:273153e44338 186 /*
JovanEps 2:273153e44338 187 Compute a residual to verify results.
JovanEps 2:273153e44338 188 */
JovanEps 2:273153e44338 189 a = r8mat_gen ( LDA, N );
JovanEps 3:da1132c65314 190 //r8mat_gen ( LDA, N, a);
JovanEps 2:273153e44338 191
JovanEps 2:273153e44338 192 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 193 x[i] = 1.0;
JovanEps 2:273153e44338 194 }
JovanEps 0:43b96e9650ef 195
JovanEps 2:273153e44338 196 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 197 rhs[i] = 0.0;
JovanEps 2:273153e44338 198 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 199 rhs[i] = rhs[i] + a[i+j*LDA] * x[j];
JovanEps 2:273153e44338 200 }
JovanEps 2:273153e44338 201 }
JovanEps 0:43b96e9650ef 202
JovanEps 2:273153e44338 203 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 204 resid[i] = -rhs[i];
JovanEps 2:273153e44338 205 for ( j = 0; j < N; j++ ) {
JovanEps 2:273153e44338 206 resid[i] = resid[i] + a[i+j*LDA] * b[j];
JovanEps 2:273153e44338 207 }
JovanEps 2:273153e44338 208 }
JovanEps 2:273153e44338 209
JovanEps 2:273153e44338 210 resid_max = 0.0;
JovanEps 2:273153e44338 211 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 212 resid_max = r8_max ( resid_max, r8_abs ( resid[i] ) );
JovanEps 2:273153e44338 213 }
JovanEps 2:273153e44338 214
JovanEps 2:273153e44338 215 b_max = 0.0;
JovanEps 2:273153e44338 216 for ( i = 0; i < N; i++ ) {
JovanEps 2:273153e44338 217 b_max = r8_max ( b_max, r8_abs ( b[i] ) );
JovanEps 0:43b96e9650ef 218 }
JovanEps 0:43b96e9650ef 219
JovanEps 2:273153e44338 220 eps = r8_epsilon ( );
JovanEps 2:273153e44338 221
JovanEps 2:273153e44338 222 residn = resid_max / ( double ) N / a_max / b_max / eps;
JovanEps 5:2b929fbd5c69 223
JovanEps 2:273153e44338 224
JovanEps 2:273153e44338 225 time[2] = total;
JovanEps 2:273153e44338 226
JovanEps 4:557ad9613c6e 227 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 228 /*
JovanEps 3:da1132c65314 229 if ( 0.0 < total)
JovanEps 2:273153e44338 230 {
JovanEps 3:da1132c65314 231 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 232 }
JovanEps 4:557ad9613c6e 233 else
JovanEps 2:273153e44338 234 {
JovanEps 2:273153e44338 235 time[3] = -1.0;
JovanEps 2:273153e44338 236 }
JovanEps 4:557ad9613c6e 237 */
JovanEps 4:557ad9613c6e 238
JovanEps 2:273153e44338 239 time[4] = 2.0 / time[3];
JovanEps 2:273153e44338 240 time[5] = total / cray;
JovanEps 2:273153e44338 241
JovanEps 4:557ad9613c6e 242 //pc.printf( " \n\n ");
JovanEps 4:557ad9613c6e 243 //pc.printf( "\n Norm. Resid Resid MACHEP X[1] X[N]\n" );
JovanEps 4:557ad9613c6e 244 pc.printf( "\n MACHEP X[1] X[N]\n" );
JovanEps 3:da1132c65314 245 //pc.printf(" %14f", residn);
JovanEps 3:da1132c65314 246 //pc.printf(" %14f", resid_max);
JovanEps 4:557ad9613c6e 247 pc.printf(" %14e", eps);
JovanEps 4:557ad9613c6e 248 pc.printf(" %14f", b[0]);
JovanEps 4:557ad9613c6e 249 pc.printf(" %14f ",b[N-1]);
JovanEps 4:557ad9613c6e 250 pc.printf("\n\n");
JovanEps 4:557ad9613c6e 251 //pc.printf( " %14f %14f %14e %14f %14f \n", residn, resid_max, eps, b[0], b[N-1] );
JovanEps 0:43b96e9650ef 252
JovanEps 2:273153e44338 253 pc.printf( " \n\n ");
JovanEps 5:2b929fbd5c69 254 pc.printf( " Factor Solve Total MFLOPS Unit Cray-Ratio \n\n" );
JovanEps 4:557ad9613c6e 255
JovanEps 2:273153e44338 256 for(int ii=0; ii<6; ii++) {
JovanEps 4:557ad9613c6e 257 pc.printf(" %9f", time[ii]);
JovanEps 2:273153e44338 258 }
JovanEps 4:557ad9613c6e 259
JovanEps 4:557ad9613c6e 260 //pc.printf( " %9f %9f %9f %9f %9f %9f\n", time[0], time[1], time[2], time[3], time[4], time[5] );
JovanEps 2:273153e44338 261
JovanEps 2:273153e44338 262 /*
JovanEps 2:273153e44338 263 Terminate.
JovanEps 5:2b929fbd5c69 264 free mem
JovanEps 2:273153e44338 265 */
JovanEps 5:2b929fbd5c69 266 free ( a );
JovanEps 5:2b929fbd5c69 267 free ( b );
JovanEps 5:2b929fbd5c69 268 free ( ipvt );
JovanEps 5:2b929fbd5c69 269 free ( resid );
JovanEps 5:2b929fbd5c69 270 free ( rhs );
JovanEps 5:2b929fbd5c69 271 free ( x );
JovanEps 5:2b929fbd5c69 272
JovanEps 2:273153e44338 273 pc.printf( "\n" );
JovanEps 2:273153e44338 274 pc.printf( "LINPACK_BENCH\n" );
JovanEps 2:273153e44338 275 pc.printf( " Normal end of execution.\n" );
JovanEps 2:273153e44338 276
JovanEps 2:273153e44338 277 pc.printf( "\n" );
JovanEps 2:273153e44338 278
JovanEps 2:273153e44338 279 return 0;
JovanEps 2:273153e44338 280 # undef LDA
JovanEps 2:273153e44338 281 # undef N
JovanEps 2:273153e44338 282 }
JovanEps 4:557ad9613c6e 283
JovanEps 2:273153e44338 284 /******************************************************************************/
JovanEps 2:273153e44338 285
JovanEps 4:557ad9613c6e 286 //double cpu_time ( void )
JovanEps 2:273153e44338 287
JovanEps 2:273153e44338 288 /******************************************************************************/
JovanEps 0:43b96e9650ef 289 /*
JovanEps 2:273153e44338 290 Purpose:
JovanEps 2:273153e44338 291
JovanEps 2:273153e44338 292 CPU_TIME returns the current reading on the CPU clock.
JovanEps 2:273153e44338 293
JovanEps 2:273153e44338 294 Discussion:
JovanEps 0:43b96e9650ef 295
JovanEps 2:273153e44338 296 The CPU time measurements available through this routine are often
JovanEps 2:273153e44338 297 not very accurate. In some cases, the accuracy is no better than
JovanEps 2:273153e44338 298 a hundredth of a second.
JovanEps 2:273153e44338 299
JovanEps 2:273153e44338 300 koristi mbed.Timer
JovanEps 2:273153e44338 301
JovanEps 2:273153e44338 302 */
JovanEps 4:557ad9613c6e 303 //{
JovanEps 4:557ad9613c6e 304 // double vreme;
JovanEps 4:557ad9613c6e 305
JovanEps 4:557ad9613c6e 306 // vreme = timer.read_ms() / 1000;
JovanEps 2:273153e44338 307
JovanEps 4:557ad9613c6e 308 // return vreme;
JovanEps 4:557ad9613c6e 309 //}
JovanEps 4:557ad9613c6e 310 /******************************************************************************/
JovanEps 2:273153e44338 311
JovanEps 2:273153e44338 312
JovanEps 2:273153e44338 313 void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy )
JovanEps 2:273153e44338 314
JovanEps 2:273153e44338 315 /******************************************************************************/
JovanEps 2:273153e44338 316 /*
JovanEps 2:273153e44338 317 Purpose:
JovanEps 2:273153e44338 318
JovanEps 2:273153e44338 319 DAXPY computes constant times a vector plus a vector.
JovanEps 2:273153e44338 320
JovanEps 2:273153e44338 321 Discussion:
JovanEps 2:273153e44338 322
JovanEps 2:273153e44338 323 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 324
JovanEps 2:273153e44338 325 Modified:
JovanEps 2:273153e44338 326
JovanEps 2:273153e44338 327 30 March 2007
JovanEps 2:273153e44338 328
JovanEps 2:273153e44338 329 Author:
JovanEps 0:43b96e9650ef 330
JovanEps 2:273153e44338 331 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 332 C version by John Burkardt
JovanEps 2:273153e44338 333
JovanEps 2:273153e44338 334 Reference:
JovanEps 2:273153e44338 335
JovanEps 2:273153e44338 336 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 337 LINPACK User's Guide,
JovanEps 2:273153e44338 338 SIAM, 1979.
JovanEps 2:273153e44338 339
JovanEps 2:273153e44338 340 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 341 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 342 Algorithm 539,
JovanEps 2:273153e44338 343 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 344 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 345
JovanEps 2:273153e44338 346 Parameters:
JovanEps 2:273153e44338 347
JovanEps 2:273153e44338 348 Input, int N, the number of elements in DX and DY.
JovanEps 2:273153e44338 349
JovanEps 2:273153e44338 350 Input, double DA, the multiplier of DX.
JovanEps 2:273153e44338 351
JovanEps 2:273153e44338 352 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 353
JovanEps 2:273153e44338 354 Input, int INCX, the increment between successive entries of DX.
JovanEps 2:273153e44338 355
JovanEps 2:273153e44338 356 Input/output, double DY[*], the second vector.
JovanEps 2:273153e44338 357 On output, DY[*] has been replaced by DY[*] + DA * DX[*].
JovanEps 2:273153e44338 358
JovanEps 2:273153e44338 359 Input, int INCY, the increment between successive entries of DY.
JovanEps 2:273153e44338 360 */
JovanEps 2:273153e44338 361 {
JovanEps 2:273153e44338 362 int i;
JovanEps 2:273153e44338 363 int ix;
JovanEps 2:273153e44338 364 int iy;
JovanEps 2:273153e44338 365 int m;
JovanEps 2:273153e44338 366
JovanEps 2:273153e44338 367 if ( n <= 0 ) {
JovanEps 2:273153e44338 368 return;
JovanEps 0:43b96e9650ef 369 }
JovanEps 0:43b96e9650ef 370
JovanEps 2:273153e44338 371 if ( da == 0.0 ) {
JovanEps 2:273153e44338 372 return;
JovanEps 2:273153e44338 373 }
JovanEps 2:273153e44338 374 /*
JovanEps 2:273153e44338 375 Code for unequal increments or equal increments
JovanEps 2:273153e44338 376 not equal to 1.
JovanEps 2:273153e44338 377 */
JovanEps 2:273153e44338 378 if ( incx != 1 || incy != 1 ) {
JovanEps 2:273153e44338 379 if ( 0 <= incx ) {
JovanEps 2:273153e44338 380 ix = 0;
JovanEps 2:273153e44338 381 } else {
JovanEps 2:273153e44338 382 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 383 }
JovanEps 2:273153e44338 384
JovanEps 2:273153e44338 385 if ( 0 <= incy ) {
JovanEps 2:273153e44338 386 iy = 0;
JovanEps 2:273153e44338 387 } else {
JovanEps 2:273153e44338 388 iy = ( - n + 1 ) * incy;
JovanEps 2:273153e44338 389 }
JovanEps 0:43b96e9650ef 390
JovanEps 2:273153e44338 391 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 392 dy[iy] = dy[iy] + da * dx[ix];
JovanEps 2:273153e44338 393 ix = ix + incx;
JovanEps 2:273153e44338 394 iy = iy + incy;
JovanEps 2:273153e44338 395 }
JovanEps 2:273153e44338 396 }
JovanEps 2:273153e44338 397 /*
JovanEps 2:273153e44338 398 Code for both increments equal to 1.
JovanEps 2:273153e44338 399 */
JovanEps 2:273153e44338 400 else {
JovanEps 2:273153e44338 401 m = n % 4;
JovanEps 2:273153e44338 402
JovanEps 2:273153e44338 403 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 404 dy[i] = dy[i] + da * dx[i];
JovanEps 2:273153e44338 405 }
JovanEps 2:273153e44338 406
JovanEps 2:273153e44338 407 for ( i = m; i < n; i = i + 4 ) {
JovanEps 2:273153e44338 408 dy[i ] = dy[i ] + da * dx[i ];
JovanEps 2:273153e44338 409 dy[i+1] = dy[i+1] + da * dx[i+1];
JovanEps 2:273153e44338 410 dy[i+2] = dy[i+2] + da * dx[i+2];
JovanEps 2:273153e44338 411 dy[i+3] = dy[i+3] + da * dx[i+3];
JovanEps 2:273153e44338 412 }
JovanEps 2:273153e44338 413 }
JovanEps 2:273153e44338 414 return;
JovanEps 2:273153e44338 415 }
JovanEps 2:273153e44338 416 /******************************************************************************/
JovanEps 2:273153e44338 417
JovanEps 2:273153e44338 418 double ddot ( int n, double dx[], int incx, double dy[], int incy )
JovanEps 2:273153e44338 419
JovanEps 2:273153e44338 420 /******************************************************************************/
JovanEps 0:43b96e9650ef 421 /*
JovanEps 2:273153e44338 422 Purpose:
JovanEps 2:273153e44338 423
JovanEps 2:273153e44338 424 DDOT forms the dot product of two vectors.
JovanEps 2:273153e44338 425
JovanEps 2:273153e44338 426 Discussion:
JovanEps 2:273153e44338 427
JovanEps 2:273153e44338 428 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 429
JovanEps 2:273153e44338 430 Modified:
JovanEps 2:273153e44338 431
JovanEps 2:273153e44338 432 30 March 2007
JovanEps 2:273153e44338 433
JovanEps 2:273153e44338 434 Author:
JovanEps 2:273153e44338 435
JovanEps 2:273153e44338 436 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 437 C version by John Burkardt
JovanEps 2:273153e44338 438
JovanEps 2:273153e44338 439 Reference:
JovanEps 2:273153e44338 440
JovanEps 2:273153e44338 441 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 442 LINPACK User's Guide,
JovanEps 2:273153e44338 443 SIAM, 1979.
JovanEps 2:273153e44338 444
JovanEps 2:273153e44338 445 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 446 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 447 Algorithm 539,
JovanEps 2:273153e44338 448 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 449 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 450
JovanEps 2:273153e44338 451 Parameters:
JovanEps 2:273153e44338 452
JovanEps 2:273153e44338 453 Input, int N, the number of entries in the vectors.
JovanEps 2:273153e44338 454
JovanEps 2:273153e44338 455 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 456
JovanEps 2:273153e44338 457 Input, int INCX, the increment between successive entries in DX.
JovanEps 2:273153e44338 458
JovanEps 2:273153e44338 459 Input, double DY[*], the second vector.
JovanEps 2:273153e44338 460
JovanEps 2:273153e44338 461 Input, int INCY, the increment between successive entries in DY.
JovanEps 2:273153e44338 462
JovanEps 2:273153e44338 463 Output, double DDOT, the sum of the product of the corresponding
JovanEps 2:273153e44338 464 entries of DX and DY.
JovanEps 0:43b96e9650ef 465 */
JovanEps 2:273153e44338 466 {
JovanEps 2:273153e44338 467 double dtemp;
JovanEps 2:273153e44338 468 int i;
JovanEps 2:273153e44338 469 int ix;
JovanEps 2:273153e44338 470 int iy;
JovanEps 2:273153e44338 471 int m;
JovanEps 2:273153e44338 472
JovanEps 2:273153e44338 473 dtemp = 0.0;
JovanEps 2:273153e44338 474
JovanEps 2:273153e44338 475 if ( n <= 0 ) {
JovanEps 2:273153e44338 476 return dtemp;
JovanEps 2:273153e44338 477 }
JovanEps 2:273153e44338 478 /*
JovanEps 2:273153e44338 479 Code for unequal increments or equal increments
JovanEps 2:273153e44338 480 not equal to 1.
JovanEps 2:273153e44338 481 */
JovanEps 2:273153e44338 482 if ( incx != 1 || incy != 1 ) {
JovanEps 2:273153e44338 483 if ( 0 <= incx ) {
JovanEps 2:273153e44338 484 ix = 0;
JovanEps 2:273153e44338 485 } else {
JovanEps 2:273153e44338 486 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 487 }
JovanEps 2:273153e44338 488
JovanEps 2:273153e44338 489 if ( 0 <= incy ) {
JovanEps 2:273153e44338 490 iy = 0;
JovanEps 2:273153e44338 491 } else {
JovanEps 2:273153e44338 492 iy = ( - n + 1 ) * incy;
JovanEps 2:273153e44338 493 }
JovanEps 2:273153e44338 494
JovanEps 2:273153e44338 495 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 496 dtemp = dtemp + dx[ix] * dy[iy];
JovanEps 2:273153e44338 497 ix = ix + incx;
JovanEps 2:273153e44338 498 iy = iy + incy;
JovanEps 2:273153e44338 499 }
JovanEps 2:273153e44338 500 }
JovanEps 2:273153e44338 501 /*
JovanEps 2:273153e44338 502 Code for both increments equal to 1.
JovanEps 2:273153e44338 503 */
JovanEps 2:273153e44338 504 else {
JovanEps 2:273153e44338 505 m = n % 5;
JovanEps 2:273153e44338 506
JovanEps 2:273153e44338 507 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 508 dtemp = dtemp + dx[i] * dy[i];
JovanEps 2:273153e44338 509 }
JovanEps 2:273153e44338 510
JovanEps 2:273153e44338 511 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 512 dtemp = dtemp + dx[i ] * dy[i ]
JovanEps 2:273153e44338 513 + dx[i+1] * dy[i+1]
JovanEps 2:273153e44338 514 + dx[i+2] * dy[i+2]
JovanEps 2:273153e44338 515 + dx[i+3] * dy[i+3]
JovanEps 2:273153e44338 516 + dx[i+4] * dy[i+4];
JovanEps 2:273153e44338 517 }
JovanEps 2:273153e44338 518 }
JovanEps 2:273153e44338 519 return dtemp;
JovanEps 2:273153e44338 520 }
JovanEps 2:273153e44338 521 /******************************************************************************/
JovanEps 2:273153e44338 522
JovanEps 2:273153e44338 523 int dgefa ( double a[], int lda, int n, int ipvt[] )
JovanEps 2:273153e44338 524
JovanEps 2:273153e44338 525 /******************************************************************************/
JovanEps 2:273153e44338 526 /*
JovanEps 2:273153e44338 527 Purpose:
JovanEps 2:273153e44338 528
JovanEps 2:273153e44338 529 DGEFA factors a real general matrix.
JovanEps 2:273153e44338 530
JovanEps 2:273153e44338 531 Modified:
JovanEps 2:273153e44338 532
JovanEps 2:273153e44338 533 16 May 2005
JovanEps 2:273153e44338 534
JovanEps 2:273153e44338 535 Author:
JovanEps 2:273153e44338 536
JovanEps 2:273153e44338 537 C version by John Burkardt.
JovanEps 2:273153e44338 538
JovanEps 2:273153e44338 539 Reference:
JovanEps 0:43b96e9650ef 540
JovanEps 2:273153e44338 541 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 2:273153e44338 542 LINPACK User's Guide,
JovanEps 2:273153e44338 543 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 2:273153e44338 544 3600 University City Science Center,
JovanEps 2:273153e44338 545 Philadelphia, PA, 19104-2688.
JovanEps 2:273153e44338 546 ISBN 0-89871-172-X
JovanEps 2:273153e44338 547
JovanEps 2:273153e44338 548 Parameters:
JovanEps 2:273153e44338 549
JovanEps 2:273153e44338 550 Input/output, double A[LDA*N].
JovanEps 2:273153e44338 551 On intput, the matrix to be factored.
JovanEps 2:273153e44338 552 On output, an upper triangular matrix and the multipliers used to obtain
JovanEps 2:273153e44338 553 it. The factorization can be written A=L*U, where L is a product of
JovanEps 2:273153e44338 554 permutation and unit lower triangular matrices, and U is upper triangular.
JovanEps 2:273153e44338 555
JovanEps 2:273153e44338 556 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 557
JovanEps 2:273153e44338 558 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 559
JovanEps 2:273153e44338 560 Output, int IPVT[N], the pivot indices.
JovanEps 2:273153e44338 561
JovanEps 2:273153e44338 562 Output, int DGEFA, singularity indicator.
JovanEps 2:273153e44338 563 0, normal value.
JovanEps 2:273153e44338 564 K, if U(K,K) == 0. This is not an error condition for this subroutine,
JovanEps 2:273153e44338 565 but it does indicate that DGESL or DGEDI will divide by zero if called.
JovanEps 2:273153e44338 566 Use RCOND in DGECO for a reliable indication of singularity.
JovanEps 2:273153e44338 567 */
JovanEps 2:273153e44338 568 {
JovanEps 2:273153e44338 569 int info;
JovanEps 2:273153e44338 570 int j;
JovanEps 2:273153e44338 571 int k;
JovanEps 2:273153e44338 572 int l;
JovanEps 2:273153e44338 573 double t;
JovanEps 2:273153e44338 574 /*
JovanEps 2:273153e44338 575 Gaussian elimination with partial pivoting.
JovanEps 2:273153e44338 576 */
JovanEps 2:273153e44338 577 info = 0;
JovanEps 2:273153e44338 578
JovanEps 2:273153e44338 579 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 580 /*
JovanEps 2:273153e44338 581 Find L = pivot index.
JovanEps 2:273153e44338 582 */
JovanEps 2:273153e44338 583 l = idamax ( n-k+1, a+(k-1)+(k-1)*lda, 1 ) + k - 1;
JovanEps 2:273153e44338 584 ipvt[k-1] = l;
JovanEps 2:273153e44338 585 /*
JovanEps 2:273153e44338 586 Zero pivot implies this column already triangularized.
JovanEps 2:273153e44338 587 */
JovanEps 2:273153e44338 588 if ( a[l-1+(k-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 589 info = k;
JovanEps 2:273153e44338 590 continue;
JovanEps 2:273153e44338 591 }
JovanEps 2:273153e44338 592 /*
JovanEps 2:273153e44338 593 Interchange if necessary.
JovanEps 2:273153e44338 594 */
JovanEps 2:273153e44338 595 if ( l != k ) {
JovanEps 2:273153e44338 596 t = a[l-1+(k-1)*lda];
JovanEps 2:273153e44338 597 a[l-1+(k-1)*lda] = a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 598 a[k-1+(k-1)*lda] = t;
JovanEps 2:273153e44338 599 }
JovanEps 2:273153e44338 600 /*
JovanEps 2:273153e44338 601 Compute multipliers.
JovanEps 2:273153e44338 602 */
JovanEps 2:273153e44338 603 t = -1.0 / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 604
JovanEps 2:273153e44338 605 dscal ( n-k, t, a+k+(k-1)*lda, 1 );
JovanEps 2:273153e44338 606 /*
JovanEps 2:273153e44338 607 Row elimination with column indexing.
JovanEps 2:273153e44338 608 */
JovanEps 2:273153e44338 609 for ( j = k+1; j <= n; j++ ) {
JovanEps 2:273153e44338 610 t = a[l-1+(j-1)*lda];
JovanEps 2:273153e44338 611 if ( l != k ) {
JovanEps 2:273153e44338 612 a[l-1+(j-1)*lda] = a[k-1+(j-1)*lda];
JovanEps 2:273153e44338 613 a[k-1+(j-1)*lda] = t;
JovanEps 2:273153e44338 614 }
JovanEps 2:273153e44338 615 daxpy ( n-k, t, a+k+(k-1)*lda, 1, a+k+(j-1)*lda, 1 );
JovanEps 2:273153e44338 616 }
JovanEps 2:273153e44338 617
JovanEps 0:43b96e9650ef 618 }
JovanEps 0:43b96e9650ef 619
JovanEps 2:273153e44338 620 ipvt[n-1] = n;
JovanEps 0:43b96e9650ef 621
JovanEps 2:273153e44338 622 if ( a[n-1+(n-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 623 info = n;
JovanEps 0:43b96e9650ef 624 }
JovanEps 0:43b96e9650ef 625
JovanEps 2:273153e44338 626 return info;
JovanEps 2:273153e44338 627 }
JovanEps 2:273153e44338 628 /******************************************************************************/
JovanEps 0:43b96e9650ef 629
JovanEps 2:273153e44338 630 void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job )
JovanEps 2:273153e44338 631
JovanEps 2:273153e44338 632 /******************************************************************************/
JovanEps 0:43b96e9650ef 633 /*
JovanEps 2:273153e44338 634 Purpose:
JovanEps 2:273153e44338 635
JovanEps 2:273153e44338 636 DGESL solves a real general linear system A * X = B.
JovanEps 2:273153e44338 637
JovanEps 2:273153e44338 638 Discussion:
JovanEps 2:273153e44338 639
JovanEps 2:273153e44338 640 DGESL can solve either of the systems A * X = B or A' * X = B.
JovanEps 2:273153e44338 641
JovanEps 2:273153e44338 642 The system matrix must have been factored by DGECO or DGEFA.
JovanEps 2:273153e44338 643
JovanEps 2:273153e44338 644 A division by zero will occur if the input factor contains a
JovanEps 2:273153e44338 645 zero on the diagonal. Technically this indicates singularity
JovanEps 2:273153e44338 646 but it is often caused by improper arguments or improper
JovanEps 2:273153e44338 647 setting of LDA. It will not occur if the subroutines are
JovanEps 2:273153e44338 648 called correctly and if DGECO has set 0.0 < RCOND
JovanEps 2:273153e44338 649 or DGEFA has set INFO == 0.
JovanEps 2:273153e44338 650
JovanEps 2:273153e44338 651 Modified:
JovanEps 2:273153e44338 652
JovanEps 2:273153e44338 653 16 May 2005
JovanEps 2:273153e44338 654
JovanEps 2:273153e44338 655 Author:
JovanEps 2:273153e44338 656
JovanEps 2:273153e44338 657 C version by John Burkardt.
JovanEps 2:273153e44338 658
JovanEps 2:273153e44338 659 Reference:
JovanEps 2:273153e44338 660
JovanEps 2:273153e44338 661 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 2:273153e44338 662 LINPACK User's Guide,
JovanEps 2:273153e44338 663 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 2:273153e44338 664 3600 University City Science Center,
JovanEps 2:273153e44338 665 Philadelphia, PA, 19104-2688.
JovanEps 2:273153e44338 666 ISBN 0-89871-172-X
JovanEps 2:273153e44338 667
JovanEps 2:273153e44338 668 Parameters:
JovanEps 2:273153e44338 669
JovanEps 2:273153e44338 670 Input, double A[LDA*N], the output from DGECO or DGEFA.
JovanEps 2:273153e44338 671
JovanEps 2:273153e44338 672 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 673
JovanEps 2:273153e44338 674 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 675
JovanEps 2:273153e44338 676 Input, int IPVT[N], the pivot vector from DGECO or DGEFA.
JovanEps 2:273153e44338 677
JovanEps 2:273153e44338 678 Input/output, double B[N].
JovanEps 2:273153e44338 679 On input, the right hand side vector.
JovanEps 2:273153e44338 680 On output, the solution vector.
JovanEps 0:43b96e9650ef 681
JovanEps 2:273153e44338 682 Input, int JOB.
JovanEps 2:273153e44338 683 0, solve A * X = B;
JovanEps 2:273153e44338 684 nonzero, solve A' * X = B.
JovanEps 2:273153e44338 685 */
JovanEps 2:273153e44338 686 {
JovanEps 2:273153e44338 687 int k;
JovanEps 2:273153e44338 688 int l;
JovanEps 2:273153e44338 689 double t;
JovanEps 2:273153e44338 690 /*
JovanEps 2:273153e44338 691 Solve A * X = B.
JovanEps 2:273153e44338 692 */
JovanEps 2:273153e44338 693 if ( job == 0 ) {
JovanEps 2:273153e44338 694 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 695 l = ipvt[k-1];
JovanEps 2:273153e44338 696 t = b[l-1];
JovanEps 2:273153e44338 697
JovanEps 2:273153e44338 698 if ( l != k ) {
JovanEps 2:273153e44338 699 b[l-1] = b[k-1];
JovanEps 2:273153e44338 700 b[k-1] = t;
JovanEps 2:273153e44338 701 }
JovanEps 2:273153e44338 702
JovanEps 2:273153e44338 703 daxpy ( n-k, t, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 704
JovanEps 2:273153e44338 705 }
JovanEps 0:43b96e9650ef 706
JovanEps 2:273153e44338 707 for ( k = n; 1 <= k; k-- ) {
JovanEps 2:273153e44338 708 b[k-1] = b[k-1] / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 709 t = -b[k-1];
JovanEps 2:273153e44338 710 daxpy ( k-1, t, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 711 }
JovanEps 2:273153e44338 712 }
JovanEps 2:273153e44338 713 /*
JovanEps 2:273153e44338 714 Solve A' * X = B.
JovanEps 2:273153e44338 715 */
JovanEps 2:273153e44338 716 else {
JovanEps 2:273153e44338 717 for ( k = 1; k <= n; k++ ) {
JovanEps 2:273153e44338 718 t = ddot ( k-1, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 719 b[k-1] = ( b[k-1] - t ) / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 720 }
JovanEps 0:43b96e9650ef 721
JovanEps 2:273153e44338 722 for ( k = n-1; 1 <= k; k-- ) {
JovanEps 2:273153e44338 723 b[k-1] = b[k-1] + ddot ( n-k, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 724 l = ipvt[k-1];
JovanEps 2:273153e44338 725
JovanEps 2:273153e44338 726 if ( l != k ) {
JovanEps 2:273153e44338 727 t = b[l-1];
JovanEps 2:273153e44338 728 b[l-1] = b[k-1];
JovanEps 2:273153e44338 729 b[k-1] = t;
JovanEps 2:273153e44338 730 }
JovanEps 2:273153e44338 731 }
JovanEps 2:273153e44338 732 }
JovanEps 2:273153e44338 733 return;
JovanEps 2:273153e44338 734 }
JovanEps 2:273153e44338 735 /******************************************************************************/
JovanEps 2:273153e44338 736
JovanEps 2:273153e44338 737 void dscal ( int n, double sa, double x[], int incx )
JovanEps 2:273153e44338 738
JovanEps 2:273153e44338 739 /******************************************************************************/
JovanEps 0:43b96e9650ef 740 /*
JovanEps 2:273153e44338 741 Purpose:
JovanEps 2:273153e44338 742
JovanEps 2:273153e44338 743 DSCAL scales a vector by a constant.
JovanEps 2:273153e44338 744
JovanEps 2:273153e44338 745 Modified:
JovanEps 2:273153e44338 746
JovanEps 2:273153e44338 747 30 March 2007
JovanEps 2:273153e44338 748
JovanEps 2:273153e44338 749 Author:
JovanEps 2:273153e44338 750
JovanEps 2:273153e44338 751 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 752 C version by John Burkardt
JovanEps 2:273153e44338 753
JovanEps 2:273153e44338 754 Reference:
JovanEps 2:273153e44338 755
JovanEps 2:273153e44338 756 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 757 LINPACK User's Guide,
JovanEps 2:273153e44338 758 SIAM, 1979.
JovanEps 2:273153e44338 759
JovanEps 2:273153e44338 760 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 761 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 762 Algorithm 539,
JovanEps 2:273153e44338 763 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 764 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 765
JovanEps 2:273153e44338 766 Parameters:
JovanEps 2:273153e44338 767
JovanEps 2:273153e44338 768 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 769
JovanEps 2:273153e44338 770 Input, double SA, the multiplier.
JovanEps 2:273153e44338 771
JovanEps 2:273153e44338 772 Input/output, double X[*], the vector to be scaled.
JovanEps 2:273153e44338 773
JovanEps 2:273153e44338 774 Input, int INCX, the increment between successive entries of X.
JovanEps 0:43b96e9650ef 775 */
JovanEps 2:273153e44338 776 {
JovanEps 2:273153e44338 777 int i;
JovanEps 2:273153e44338 778 int ix;
JovanEps 2:273153e44338 779 int m;
JovanEps 2:273153e44338 780
JovanEps 2:273153e44338 781 if ( n <= 0 ) {
JovanEps 2:273153e44338 782 } else if ( incx == 1 ) {
JovanEps 2:273153e44338 783 m = n % 5;
JovanEps 2:273153e44338 784
JovanEps 2:273153e44338 785 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 786 x[i] = sa * x[i];
JovanEps 2:273153e44338 787 }
JovanEps 0:43b96e9650ef 788
JovanEps 2:273153e44338 789 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 790 x[i] = sa * x[i];
JovanEps 2:273153e44338 791 x[i+1] = sa * x[i+1];
JovanEps 2:273153e44338 792 x[i+2] = sa * x[i+2];
JovanEps 2:273153e44338 793 x[i+3] = sa * x[i+3];
JovanEps 2:273153e44338 794 x[i+4] = sa * x[i+4];
JovanEps 2:273153e44338 795 }
JovanEps 2:273153e44338 796 } else {
JovanEps 2:273153e44338 797 if ( 0 <= incx ) {
JovanEps 2:273153e44338 798 ix = 0;
JovanEps 2:273153e44338 799 } else {
JovanEps 2:273153e44338 800 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 801 }
JovanEps 2:273153e44338 802
JovanEps 2:273153e44338 803 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 804 x[ix] = sa * x[ix];
JovanEps 2:273153e44338 805 ix = ix + incx;
JovanEps 2:273153e44338 806 }
JovanEps 2:273153e44338 807 }
JovanEps 2:273153e44338 808 return;
JovanEps 2:273153e44338 809 }
JovanEps 2:273153e44338 810 /******************************************************************************/
JovanEps 2:273153e44338 811
JovanEps 2:273153e44338 812 int idamax ( int n, double dx[], int incx )
JovanEps 2:273153e44338 813
JovanEps 2:273153e44338 814 /******************************************************************************/
JovanEps 0:43b96e9650ef 815 /*
JovanEps 2:273153e44338 816 Purpose:
JovanEps 2:273153e44338 817
JovanEps 2:273153e44338 818 IDAMAX finds the index of the vector element of maximum absolute value.
JovanEps 2:273153e44338 819
JovanEps 2:273153e44338 820 Discussion:
JovanEps 2:273153e44338 821
JovanEps 2:273153e44338 822 WARNING: This index is a 1-based index, not a 0-based index!
JovanEps 2:273153e44338 823
JovanEps 2:273153e44338 824 Modified:
JovanEps 2:273153e44338 825
JovanEps 2:273153e44338 826 30 March 2007
JovanEps 2:273153e44338 827
JovanEps 2:273153e44338 828 Author:
JovanEps 2:273153e44338 829
JovanEps 2:273153e44338 830 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 2:273153e44338 831 C version by John Burkardt
JovanEps 2:273153e44338 832
JovanEps 2:273153e44338 833 Reference:
JovanEps 2:273153e44338 834
JovanEps 2:273153e44338 835 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 2:273153e44338 836 LINPACK User's Guide,
JovanEps 2:273153e44338 837 SIAM, 1979.
JovanEps 2:273153e44338 838
JovanEps 2:273153e44338 839 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 2:273153e44338 840 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 2:273153e44338 841 Algorithm 539,
JovanEps 2:273153e44338 842 ACM Transactions on Mathematical Software,
JovanEps 2:273153e44338 843 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 844
JovanEps 2:273153e44338 845 Parameters:
JovanEps 2:273153e44338 846
JovanEps 2:273153e44338 847 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 848
JovanEps 2:273153e44338 849 Input, double X[*], the vector to be examined.
JovanEps 2:273153e44338 850
JovanEps 2:273153e44338 851 Input, int INCX, the increment between successive entries of SX.
JovanEps 2:273153e44338 852
JovanEps 2:273153e44338 853 Output, int IDAMAX, the index of the element of maximum
JovanEps 2:273153e44338 854 absolute value.
JovanEps 0:43b96e9650ef 855 */
JovanEps 2:273153e44338 856 {
JovanEps 2:273153e44338 857 double dmax;
JovanEps 2:273153e44338 858 int i;
JovanEps 2:273153e44338 859 int ix;
JovanEps 2:273153e44338 860 int value;
JovanEps 2:273153e44338 861
JovanEps 2:273153e44338 862 value = 0;
JovanEps 0:43b96e9650ef 863
JovanEps 2:273153e44338 864 if ( n < 1 || incx <= 0 ) {
JovanEps 2:273153e44338 865 return value;
JovanEps 2:273153e44338 866 }
JovanEps 2:273153e44338 867
JovanEps 2:273153e44338 868 value = 1;
JovanEps 2:273153e44338 869
JovanEps 2:273153e44338 870 if ( n == 1 ) {
JovanEps 2:273153e44338 871 return value;
JovanEps 2:273153e44338 872 }
JovanEps 0:43b96e9650ef 873
JovanEps 2:273153e44338 874 if ( incx == 1 ) {
JovanEps 2:273153e44338 875 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 876
JovanEps 2:273153e44338 877 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 878 if ( dmax < r8_abs ( dx[i] ) ) {
JovanEps 2:273153e44338 879 value = i + 1;
JovanEps 2:273153e44338 880 dmax = r8_abs ( dx[i] );
JovanEps 2:273153e44338 881 }
JovanEps 2:273153e44338 882 }
JovanEps 2:273153e44338 883 } else {
JovanEps 2:273153e44338 884 ix = 0;
JovanEps 2:273153e44338 885 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 886 ix = ix + incx;
JovanEps 2:273153e44338 887
JovanEps 2:273153e44338 888 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 889 if ( dmax < r8_abs ( dx[ix] ) ) {
JovanEps 2:273153e44338 890 value = i + 1;
JovanEps 2:273153e44338 891 dmax = r8_abs ( dx[ix] );
JovanEps 2:273153e44338 892 }
JovanEps 2:273153e44338 893 ix = ix + incx;
JovanEps 2:273153e44338 894 }
JovanEps 2:273153e44338 895 }
JovanEps 0:43b96e9650ef 896
JovanEps 2:273153e44338 897 return value;
JovanEps 2:273153e44338 898 }
JovanEps 2:273153e44338 899 /******************************************************************************/
JovanEps 2:273153e44338 900
JovanEps 2:273153e44338 901 double r8_abs ( double x )
JovanEps 2:273153e44338 902
JovanEps 2:273153e44338 903 /******************************************************************************/
JovanEps 2:273153e44338 904 /*
JovanEps 2:273153e44338 905 Purpose:
JovanEps 2:273153e44338 906
JovanEps 2:273153e44338 907 R8_ABS returns the absolute value of a R8.
JovanEps 0:43b96e9650ef 908
JovanEps 2:273153e44338 909 Modified:
JovanEps 2:273153e44338 910
JovanEps 2:273153e44338 911 02 April 2005
JovanEps 2:273153e44338 912
JovanEps 2:273153e44338 913 Author:
JovanEps 0:43b96e9650ef 914
JovanEps 2:273153e44338 915 John Burkardt
JovanEps 2:273153e44338 916
JovanEps 2:273153e44338 917 Parameters:
JovanEps 2:273153e44338 918
JovanEps 2:273153e44338 919 Input, double X, the quantity whose absolute value is desired.
JovanEps 2:273153e44338 920
JovanEps 2:273153e44338 921 Output, double R8_ABS, the absolute value of X.
JovanEps 2:273153e44338 922 */
JovanEps 0:43b96e9650ef 923 {
JovanEps 2:273153e44338 924 double value;
JovanEps 2:273153e44338 925
JovanEps 2:273153e44338 926 if ( 0.0 <= x ) {
JovanEps 2:273153e44338 927 value = x;
JovanEps 2:273153e44338 928 } else {
JovanEps 2:273153e44338 929 value = -x;
JovanEps 2:273153e44338 930 }
JovanEps 2:273153e44338 931 return value;
JovanEps 2:273153e44338 932 }
JovanEps 2:273153e44338 933 /******************************************************************************/
JovanEps 2:273153e44338 934
JovanEps 2:273153e44338 935 double r8_epsilon ( void )
JovanEps 0:43b96e9650ef 936
JovanEps 2:273153e44338 937 /******************************************************************************/
JovanEps 2:273153e44338 938 /*
JovanEps 2:273153e44338 939 Purpose:
JovanEps 2:273153e44338 940
JovanEps 2:273153e44338 941 R8_EPSILON returns the R8 round off unit.
JovanEps 2:273153e44338 942
JovanEps 2:273153e44338 943 Discussion:
JovanEps 2:273153e44338 944
JovanEps 2:273153e44338 945 R8_EPSILON is a number R which is a power of 2 with the property that,
JovanEps 2:273153e44338 946 to the precision of the computer's arithmetic,
JovanEps 2:273153e44338 947 1 < 1 + R
JovanEps 2:273153e44338 948 but
JovanEps 2:273153e44338 949 1 = ( 1 + R / 2 )
JovanEps 0:43b96e9650ef 950
JovanEps 2:273153e44338 951 Licensing:
JovanEps 2:273153e44338 952
JovanEps 2:273153e44338 953 This code is distributed under the GNU LGPL license.
JovanEps 2:273153e44338 954
JovanEps 2:273153e44338 955 Modified:
JovanEps 2:273153e44338 956
JovanEps 2:273153e44338 957 08 May 2006
JovanEps 2:273153e44338 958
JovanEps 2:273153e44338 959 Author:
JovanEps 2:273153e44338 960
JovanEps 2:273153e44338 961 John Burkardt
JovanEps 2:273153e44338 962
JovanEps 2:273153e44338 963 Parameters:
JovanEps 0:43b96e9650ef 964
JovanEps 2:273153e44338 965 Output, double R8_EPSILON, the double precision round-off unit.
JovanEps 2:273153e44338 966 */
JovanEps 0:43b96e9650ef 967 {
JovanEps 2:273153e44338 968 double r;
JovanEps 2:273153e44338 969
JovanEps 2:273153e44338 970 r = 1.0;
JovanEps 2:273153e44338 971
JovanEps 2:273153e44338 972 while ( 1.0 < ( double ) ( 1.0 + r ) ) {
JovanEps 2:273153e44338 973 r = r / 2.0;
JovanEps 2:273153e44338 974 }
JovanEps 2:273153e44338 975 r = 2.0 * r;
JovanEps 2:273153e44338 976
JovanEps 2:273153e44338 977 return r;
JovanEps 0:43b96e9650ef 978 }
JovanEps 2:273153e44338 979 /******************************************************************************/
JovanEps 0:43b96e9650ef 980
JovanEps 2:273153e44338 981 double r8_max ( double x, double y )
JovanEps 2:273153e44338 982
JovanEps 2:273153e44338 983 /******************************************************************************/
JovanEps 2:273153e44338 984 /*
JovanEps 2:273153e44338 985 Purpose:
JovanEps 2:273153e44338 986
JovanEps 2:273153e44338 987 R8_MAX returns the maximum of two R8's.
JovanEps 2:273153e44338 988
JovanEps 2:273153e44338 989 Modified:
JovanEps 2:273153e44338 990
JovanEps 2:273153e44338 991 18 August 2004
JovanEps 2:273153e44338 992
JovanEps 2:273153e44338 993 Author:
JovanEps 0:43b96e9650ef 994
JovanEps 2:273153e44338 995 John Burkardt
JovanEps 2:273153e44338 996
JovanEps 2:273153e44338 997 Parameters:
JovanEps 2:273153e44338 998
JovanEps 2:273153e44338 999 Input, double X, Y, the quantities to compare.
JovanEps 0:43b96e9650ef 1000
JovanEps 2:273153e44338 1001 Output, double R8_MAX, the maximum of X and Y.
JovanEps 2:273153e44338 1002 */
JovanEps 0:43b96e9650ef 1003 {
JovanEps 2:273153e44338 1004 double value;
JovanEps 2:273153e44338 1005
JovanEps 2:273153e44338 1006 if ( y < x ) {
JovanEps 2:273153e44338 1007 value = x;
JovanEps 2:273153e44338 1008 } else {
JovanEps 2:273153e44338 1009 value = y;
JovanEps 2:273153e44338 1010 }
JovanEps 2:273153e44338 1011 return value;
JovanEps 0:43b96e9650ef 1012 }
JovanEps 2:273153e44338 1013 /******************************************************************************/
JovanEps 2:273153e44338 1014
JovanEps 2:273153e44338 1015 double r8_random ( int iseed[4] )
JovanEps 2:273153e44338 1016
JovanEps 2:273153e44338 1017 /******************************************************************************/
JovanEps 2:273153e44338 1018 /*
JovanEps 2:273153e44338 1019 Purpose:
JovanEps 2:273153e44338 1020
JovanEps 2:273153e44338 1021 R8_RANDOM returns a uniformly distributed random number between 0 and 1.
JovanEps 2:273153e44338 1022
JovanEps 2:273153e44338 1023 Discussion:
JovanEps 0:43b96e9650ef 1024
JovanEps 2:273153e44338 1025 This routine uses a multiplicative congruential method with modulus
JovanEps 2:273153e44338 1026 2**48 and multiplier 33952834046453 (see G.S.Fishman,
JovanEps 2:273153e44338 1027 'Multiplicative congruential random number generators with modulus
JovanEps 2:273153e44338 1028 2**b: an exhaustive analysis for b = 32 and a partial analysis for
JovanEps 2:273153e44338 1029 b = 48', Math. Comp. 189, pp 331-344, 1990).
JovanEps 2:273153e44338 1030
JovanEps 2:273153e44338 1031 48-bit integers are stored in 4 integer array elements with 12 bits
JovanEps 2:273153e44338 1032 per element. Hence the routine is portable across machines with
JovanEps 2:273153e44338 1033 integers of 32 bits or more.
JovanEps 2:273153e44338 1034
JovanEps 2:273153e44338 1035 Parameters:
JovanEps 2:273153e44338 1036
JovanEps 2:273153e44338 1037 Input/output, integer ISEED(4).
JovanEps 2:273153e44338 1038 On entry, the seed of the random number generator; the array
JovanEps 2:273153e44338 1039 elements must be between 0 and 4095, and ISEED(4) must be odd.
JovanEps 2:273153e44338 1040 On exit, the seed is updated.
JovanEps 2:273153e44338 1041
JovanEps 2:273153e44338 1042 Output, double R8_RANDOM, the next pseudorandom number.
JovanEps 2:273153e44338 1043 */
JovanEps 1:be78b18b8347 1044 {
JovanEps 2:273153e44338 1045 int ipw2 = 4096;
JovanEps 2:273153e44338 1046 int it1;
JovanEps 2:273153e44338 1047 int it2;
JovanEps 2:273153e44338 1048 int it3;
JovanEps 2:273153e44338 1049 int it4;
JovanEps 2:273153e44338 1050 int m1 = 494;
JovanEps 2:273153e44338 1051 int m2 = 322;
JovanEps 2:273153e44338 1052 int m3 = 2508;
JovanEps 2:273153e44338 1053 int m4 = 2549;
JovanEps 2:273153e44338 1054 double r = 1.0 / 4096.0;
JovanEps 2:273153e44338 1055 double value;
JovanEps 2:273153e44338 1056 /*
JovanEps 2:273153e44338 1057 Multiply the seed by the multiplier modulo 2**48.
JovanEps 2:273153e44338 1058 */
JovanEps 2:273153e44338 1059 it4 = iseed[3] * m4;
JovanEps 2:273153e44338 1060 it3 = it4 / ipw2;
JovanEps 2:273153e44338 1061 it4 = it4 - ipw2 * it3;
JovanEps 2:273153e44338 1062 it3 = it3 + iseed[2] * m4 + iseed[3] * m3;
JovanEps 2:273153e44338 1063 it2 = it3 / ipw2;
JovanEps 2:273153e44338 1064 it3 = it3 - ipw2 * it2;
JovanEps 2:273153e44338 1065 it2 = it2 + iseed[1] * m4 + iseed[2] * m3 + iseed[3] * m2;
JovanEps 2:273153e44338 1066 it1 = it2 / ipw2;
JovanEps 2:273153e44338 1067 it2 = it2 - ipw2 * it1;
JovanEps 2:273153e44338 1068 it1 = it1 + iseed[0] * m4 + iseed[1] * m3 + iseed[2] * m2 + iseed[3] * m1;
JovanEps 2:273153e44338 1069 it1 = ( it1 % ipw2 );
JovanEps 2:273153e44338 1070 /*
JovanEps 2:273153e44338 1071 Return updated seed
JovanEps 2:273153e44338 1072 */
JovanEps 2:273153e44338 1073 iseed[0] = it1;
JovanEps 2:273153e44338 1074 iseed[1] = it2;
JovanEps 2:273153e44338 1075 iseed[2] = it3;
JovanEps 2:273153e44338 1076 iseed[3] = it4;
JovanEps 2:273153e44338 1077 /*
JovanEps 2:273153e44338 1078 Convert 48-bit integer to a real number in the interval (0,1)
JovanEps 2:273153e44338 1079 */
JovanEps 2:273153e44338 1080 value =
JovanEps 2:273153e44338 1081 r * ( ( double ) ( it1 )
JovanEps 2:273153e44338 1082 + r * ( ( double ) ( it2 )
JovanEps 2:273153e44338 1083 + r * ( ( double ) ( it3 )
JovanEps 2:273153e44338 1084 + r * ( ( double ) ( it4 ) ) ) ) );
JovanEps 2:273153e44338 1085
JovanEps 2:273153e44338 1086 return value;
JovanEps 2:273153e44338 1087 }
JovanEps 2:273153e44338 1088 /******************************************************************************/
JovanEps 2:273153e44338 1089
JovanEps 2:273153e44338 1090 double *r8mat_gen ( int lda, int n )
JovanEps 2:273153e44338 1091
JovanEps 2:273153e44338 1092 /******************************************************************************/
JovanEps 2:273153e44338 1093 /*
JovanEps 2:273153e44338 1094 Purpose:
JovanEps 2:273153e44338 1095
JovanEps 2:273153e44338 1096 R8MAT_GEN generates a random R8MAT.
JovanEps 2:273153e44338 1097
JovanEps 2:273153e44338 1098 Modified:
JovanEps 2:273153e44338 1099
JovanEps 2:273153e44338 1100 06 June 2005
JovanEps 2:273153e44338 1101
JovanEps 2:273153e44338 1102 Parameters:
JovanEps 2:273153e44338 1103
JovanEps 2:273153e44338 1104 Input, integer LDA, the leading dimension of the matrix.
JovanEps 2:273153e44338 1105
JovanEps 2:273153e44338 1106 Input, integer N, the order of the matrix.
JovanEps 2:273153e44338 1107
JovanEps 2:273153e44338 1108 Output, double R8MAT_GEN[LDA*N], the N by N matrix.
JovanEps 2:273153e44338 1109 */
JovanEps 2:273153e44338 1110 {
JovanEps 3:da1132c65314 1111 double *ba;
JovanEps 2:273153e44338 1112 int i;
JovanEps 2:273153e44338 1113 int init[4] = { 1, 2, 3, 1325 };
JovanEps 2:273153e44338 1114 int j;
JovanEps 2:273153e44338 1115
JovanEps 3:da1132c65314 1116 ba = ( double * ) malloc ( lda * n * sizeof ( double ) );
JovanEps 2:273153e44338 1117
JovanEps 2:273153e44338 1118 for ( j = 1; j <= n; j++ ) {
JovanEps 2:273153e44338 1119 for ( i = 1; i <= n; i++ ) {
JovanEps 3:da1132c65314 1120 ba[i-1+(j-1)*lda] = r8_random ( init ) - 0.5;
JovanEps 2:273153e44338 1121 }
JovanEps 1:be78b18b8347 1122 }
JovanEps 2:273153e44338 1123
JovanEps 3:da1132c65314 1124 return ba;
JovanEps 0:43b96e9650ef 1125 }