Jovan Ivković / Mbed 2 deprecated Linpack

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Dependencies:   mbed

main.cpp@8:66f6deeb2556, 2017-01-03 (annotated)

Committer:
JovanEps
Date:
Tue Jan 03 22:29:43 2017 +0000
Revision:
8:66f6deeb2556
Parent:
7:931219974070
Child:
9:54628dc6805e
Child:
11:4e700bbf93d7
RC3 -WR

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 6:5e0f3eedaf66 51 while(1) {
JovanEps 6:5e0f3eedaf66 52
JovanEps 2:273153e44338 53 pc.printf("Starting benchmark...\n");
JovanEps 6:5e0f3eedaf66 54
JovanEps 2:273153e44338 55 do_benchmark();
JovanEps 6:5e0f3eedaf66 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 6:5e0f3eedaf66 64 {
JovanEps 0:43b96e9650ef 65
JovanEps 8:66f6deeb2556 66 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 67 /*
JovanEps 6:5e0f3eedaf66 68 Purpose:
JovanEps 2:273153e44338 69
JovanEps 6:5e0f3eedaf66 70 MAIN is the main program for LINPACK_BENCH.
JovanEps 0:43b96e9650ef 71
JovanEps 6:5e0f3eedaf66 72 Discussion:
JovanEps 2:273153e44338 73
JovanEps 6:5e0f3eedaf66 74 LINPACK_BENCH drives the double precision LINPACK benchmark program.
JovanEps 2:273153e44338 75
JovanEps 6:5e0f3eedaf66 76 Modified:
JovanEps 2:273153e44338 77
JovanEps 6:5e0f3eedaf66 78 25 July 2008
JovanEps 2:273153e44338 79
JovanEps 6:5e0f3eedaf66 80 Parameters:
JovanEps 0:43b96e9650ef 81
JovanEps 6:5e0f3eedaf66 82 N is the problem size.
JovanEps 6:5e0f3eedaf66 83 */
JovanEps 6:5e0f3eedaf66 84
JovanEps 4:557ad9613c6e 85 # define N 2
JovanEps 2:273153e44338 86 # define LDA ( N + 1 )
JovanEps 2:273153e44338 87
JovanEps 3:da1132c65314 88 //static double a[90];
JovanEps 2:273153e44338 89 static double *a;
JovanEps 2:273153e44338 90 static double a_max;
JovanEps 3:da1132c65314 91 //static double b[9];
JovanEps 2:273153e44338 92 static double *b;
JovanEps 2:273153e44338 93 static double b_max;
JovanEps 2:273153e44338 94 const double cray = 0.056;
JovanEps 2:273153e44338 95 static double eps;
JovanEps 2:273153e44338 96 int i;
JovanEps 2:273153e44338 97 int info;
JovanEps 3:da1132c65314 98 static int *ipvt;
JovanEps 2:273153e44338 99 int j;
JovanEps 2:273153e44338 100 int job;
JovanEps 2:273153e44338 101 double ops;
JovanEps 3:da1132c65314 102 static double *resid;
JovanEps 2:273153e44338 103 double resid_max;
JovanEps 2:273153e44338 104 double residn;
JovanEps 3:da1132c65314 105 static double *rhs;
JovanEps 3:da1132c65314 106 double t1 = 0.0;
JovanEps 3:da1132c65314 107 double t2 = 0.0;
JovanEps 2:273153e44338 108 static double time[6];
JovanEps 2:273153e44338 109 double total;
JovanEps 3:da1132c65314 110 double *x;
JovanEps 2:273153e44338 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 8:66f6deeb2556 121
JovanEps 6:5e0f3eedaf66 122 // ops = ( double ) ( 2 * N * N * N ) / 3.0 + 2.0 * ( double ) ( N * N );
JovanEps 6:5e0f3eedaf66 123 ops = ( double ) ( 2L * N * N * N ) / 3.0 + 2.0 * ( double ) ( (long)N * N ); // Arduino 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 8:66f6deeb2556 165 time[0] = 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 8:66f6deeb2556 178 time[1] = 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 2:273153e44338 223
JovanEps 2:273153e44338 224 time[2] = total;
JovanEps 2:273153e44338 225
JovanEps 4:557ad9613c6e 226 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 227 /*
JovanEps 8:66f6deeb2556 228 if ( total > 0.0 )
JovanEps 2:273153e44338 229 {
JovanEps 3:da1132c65314 230 time[3] = ( double ) ops / ( 1000000.0 * total );
JovanEps 4:557ad9613c6e 231 }
JovanEps 4:557ad9613c6e 232 else
JovanEps 2:273153e44338 233 {
JovanEps 2:273153e44338 234 time[3] = -1.0;
JovanEps 2:273153e44338 235 }
JovanEps 8:66f6deeb2556 236 */
JovanEps 4:557ad9613c6e 237
JovanEps 2:273153e44338 238 time[4] = 2.0 / time[3];
JovanEps 2:273153e44338 239 time[5] = total / cray;
JovanEps 2:273153e44338 240
JovanEps 4:557ad9613c6e 241 //pc.printf( " \n\n ");
JovanEps 8:66f6deeb2556 242 pc.printf( "\n Norm. Resid Resid MACHEP X[1] X[N]\n" );
JovanEps 8:66f6deeb2556 243 //pc.printf( "\n MACHEP X[1] X[N]\n" );
JovanEps 8:66f6deeb2556 244 pc.printf(" %4.6f ", residn);
JovanEps 8:66f6deeb2556 245 pc.printf(" %4.6f ", resid_max);
JovanEps 4:557ad9613c6e 246 pc.printf(" %14e", eps);
JovanEps 4:557ad9613c6e 247 pc.printf(" %14f", b[0]);
JovanEps 4:557ad9613c6e 248 pc.printf(" %14f ",b[N-1]);
JovanEps 4:557ad9613c6e 249 pc.printf("\n\n");
JovanEps 4:557ad9613c6e 250 //pc.printf( " %14f %14f %14e %14f %14f \n", residn, resid_max, eps, b[0], b[N-1] );
JovanEps 0:43b96e9650ef 251
JovanEps 2:273153e44338 252 pc.printf( " \n\n ");
JovanEps 6:5e0f3eedaf66 253 pc.printf( " Factor Solve Total MFLOPS Unit Cray-Ratio \n\n" );
JovanEps 4:557ad9613c6e 254
JovanEps 2:273153e44338 255 for(int ii=0; ii<6; ii++) {
JovanEps 4:557ad9613c6e 256 pc.printf(" %9f", time[ii]);
JovanEps 2:273153e44338 257 }
JovanEps 8:66f6deeb2556 258
JovanEps 4:557ad9613c6e 259 //pc.printf( " %9f %9f %9f %9f %9f %9f\n", time[0], time[1], time[2], time[3], time[4], time[5] );
JovanEps 8:66f6deeb2556 260
JovanEps 2:273153e44338 261 /*
JovanEps 2:273153e44338 262 Terminate.
JovanEps 7:931219974070 263 Free Mem
JovanEps 7:931219974070 264 */
JovanEps 7:931219974070 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 6:5e0f3eedaf66 314 {
JovanEps 2:273153e44338 315
JovanEps 7:931219974070 316 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 317 /*
JovanEps 6:5e0f3eedaf66 318 Purpose:
JovanEps 2:273153e44338 319
JovanEps 6:5e0f3eedaf66 320 DAXPY computes constant times a vector plus a vector.
JovanEps 2:273153e44338 321
JovanEps 6:5e0f3eedaf66 322 Discussion:
JovanEps 2:273153e44338 323
JovanEps 6:5e0f3eedaf66 324 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 325
JovanEps 6:5e0f3eedaf66 326 Modified:
JovanEps 2:273153e44338 327
JovanEps 6:5e0f3eedaf66 328 30 March 2007
JovanEps 2:273153e44338 329
JovanEps 6:5e0f3eedaf66 330 Author:
JovanEps 0:43b96e9650ef 331
JovanEps 6:5e0f3eedaf66 332 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 6:5e0f3eedaf66 333 C version by John Burkardt
JovanEps 2:273153e44338 334
JovanEps 6:5e0f3eedaf66 335 Reference:
JovanEps 2:273153e44338 336
JovanEps 6:5e0f3eedaf66 337 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 6:5e0f3eedaf66 338 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 339 SIAM, 1979.
JovanEps 2:273153e44338 340
JovanEps 6:5e0f3eedaf66 341 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 6:5e0f3eedaf66 342 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 6:5e0f3eedaf66 343 Algorithm 539,
JovanEps 6:5e0f3eedaf66 344 ACM Transactions on Mathematical Software,
JovanEps 6:5e0f3eedaf66 345 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 346
JovanEps 6:5e0f3eedaf66 347 Parameters:
JovanEps 2:273153e44338 348
JovanEps 6:5e0f3eedaf66 349 Input, int N, the number of elements in DX and DY.
JovanEps 2:273153e44338 350
JovanEps 6:5e0f3eedaf66 351 Input, double DA, the multiplier of DX.
JovanEps 2:273153e44338 352
JovanEps 6:5e0f3eedaf66 353 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 354
JovanEps 6:5e0f3eedaf66 355 Input, int INCX, the increment between successive entries of DX.
JovanEps 2:273153e44338 356
JovanEps 6:5e0f3eedaf66 357 Input/output, double DY[*], the second vector.
JovanEps 6:5e0f3eedaf66 358 On output, DY[*] has been replaced by DY[*] + DA * DX[*].
JovanEps 2:273153e44338 359
JovanEps 6:5e0f3eedaf66 360 Input, int INCY, the increment between successive entries of DY.
JovanEps 6:5e0f3eedaf66 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 6:5e0f3eedaf66 419 {
JovanEps 2:273153e44338 420
JovanEps 7:931219974070 421 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 422 /*
JovanEps 6:5e0f3eedaf66 423 Purpose:
JovanEps 2:273153e44338 424
JovanEps 6:5e0f3eedaf66 425 DDOT forms the dot product of two vectors.
JovanEps 2:273153e44338 426
JovanEps 6:5e0f3eedaf66 427 Discussion:
JovanEps 2:273153e44338 428
JovanEps 6:5e0f3eedaf66 429 This routine uses unrolled loops for increments equal to one.
JovanEps 2:273153e44338 430
JovanEps 6:5e0f3eedaf66 431 Modified:
JovanEps 2:273153e44338 432
JovanEps 6:5e0f3eedaf66 433 30 March 2007
JovanEps 2:273153e44338 434
JovanEps 6:5e0f3eedaf66 435 Author:
JovanEps 2:273153e44338 436
JovanEps 6:5e0f3eedaf66 437 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 6:5e0f3eedaf66 438 C version by John Burkardt
JovanEps 2:273153e44338 439
JovanEps 6:5e0f3eedaf66 440 Reference:
JovanEps 2:273153e44338 441
JovanEps 6:5e0f3eedaf66 442 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 6:5e0f3eedaf66 443 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 444 SIAM, 1979.
JovanEps 2:273153e44338 445
JovanEps 6:5e0f3eedaf66 446 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 6:5e0f3eedaf66 447 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 6:5e0f3eedaf66 448 Algorithm 539,
JovanEps 6:5e0f3eedaf66 449 ACM Transactions on Mathematical Software,
JovanEps 6:5e0f3eedaf66 450 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 451
JovanEps 6:5e0f3eedaf66 452 Parameters:
JovanEps 2:273153e44338 453
JovanEps 6:5e0f3eedaf66 454 Input, int N, the number of entries in the vectors.
JovanEps 2:273153e44338 455
JovanEps 6:5e0f3eedaf66 456 Input, double DX[*], the first vector.
JovanEps 2:273153e44338 457
JovanEps 6:5e0f3eedaf66 458 Input, int INCX, the increment between successive entries in DX.
JovanEps 2:273153e44338 459
JovanEps 6:5e0f3eedaf66 460 Input, double DY[*], the second vector.
JovanEps 2:273153e44338 461
JovanEps 6:5e0f3eedaf66 462 Input, int INCY, the increment between successive entries in DY.
JovanEps 2:273153e44338 463
JovanEps 6:5e0f3eedaf66 464 Output, double DDOT, the sum of the product of the corresponding
JovanEps 6:5e0f3eedaf66 465 entries of DX and DY.
JovanEps 6:5e0f3eedaf66 466 */
JovanEps 6:5e0f3eedaf66 467
JovanEps 2:273153e44338 468 double dtemp;
JovanEps 2:273153e44338 469 int i;
JovanEps 2:273153e44338 470 int ix;
JovanEps 2:273153e44338 471 int iy;
JovanEps 2:273153e44338 472 int m;
JovanEps 2:273153e44338 473
JovanEps 2:273153e44338 474 dtemp = 0.0;
JovanEps 2:273153e44338 475
JovanEps 2:273153e44338 476 if ( n <= 0 ) {
JovanEps 2:273153e44338 477 return dtemp;
JovanEps 2:273153e44338 478 }
JovanEps 2:273153e44338 479 /*
JovanEps 2:273153e44338 480 Code for unequal increments or equal increments
JovanEps 2:273153e44338 481 not equal to 1.
JovanEps 2:273153e44338 482 */
JovanEps 2:273153e44338 483 if ( incx != 1 || incy != 1 ) {
JovanEps 2:273153e44338 484 if ( 0 <= incx ) {
JovanEps 2:273153e44338 485 ix = 0;
JovanEps 2:273153e44338 486 } else {
JovanEps 2:273153e44338 487 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 488 }
JovanEps 2:273153e44338 489
JovanEps 2:273153e44338 490 if ( 0 <= incy ) {
JovanEps 2:273153e44338 491 iy = 0;
JovanEps 2:273153e44338 492 } else {
JovanEps 2:273153e44338 493 iy = ( - n + 1 ) * incy;
JovanEps 2:273153e44338 494 }
JovanEps 2:273153e44338 495
JovanEps 2:273153e44338 496 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 497 dtemp = dtemp + dx[ix] * dy[iy];
JovanEps 2:273153e44338 498 ix = ix + incx;
JovanEps 2:273153e44338 499 iy = iy + incy;
JovanEps 2:273153e44338 500 }
JovanEps 2:273153e44338 501 }
JovanEps 2:273153e44338 502 /*
JovanEps 2:273153e44338 503 Code for both increments equal to 1.
JovanEps 2:273153e44338 504 */
JovanEps 2:273153e44338 505 else {
JovanEps 2:273153e44338 506 m = n % 5;
JovanEps 2:273153e44338 507
JovanEps 2:273153e44338 508 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 509 dtemp = dtemp + dx[i] * dy[i];
JovanEps 2:273153e44338 510 }
JovanEps 2:273153e44338 511
JovanEps 2:273153e44338 512 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 513 dtemp = dtemp + dx[i ] * dy[i ]
JovanEps 2:273153e44338 514 + dx[i+1] * dy[i+1]
JovanEps 2:273153e44338 515 + dx[i+2] * dy[i+2]
JovanEps 2:273153e44338 516 + dx[i+3] * dy[i+3]
JovanEps 2:273153e44338 517 + dx[i+4] * dy[i+4];
JovanEps 2:273153e44338 518 }
JovanEps 2:273153e44338 519 }
JovanEps 2:273153e44338 520 return dtemp;
JovanEps 2:273153e44338 521 }
JovanEps 2:273153e44338 522 /******************************************************************************/
JovanEps 2:273153e44338 523
JovanEps 2:273153e44338 524 int dgefa ( double a[], int lda, int n, int ipvt[] )
JovanEps 6:5e0f3eedaf66 525 {
JovanEps 2:273153e44338 526
JovanEps 7:931219974070 527 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 528 /*
JovanEps 6:5e0f3eedaf66 529 Purpose:
JovanEps 2:273153e44338 530
JovanEps 6:5e0f3eedaf66 531 DGEFA factors a real general matrix.
JovanEps 2:273153e44338 532
JovanEps 6:5e0f3eedaf66 533 Modified:
JovanEps 2:273153e44338 534
JovanEps 6:5e0f3eedaf66 535 16 May 2005
JovanEps 2:273153e44338 536
JovanEps 6:5e0f3eedaf66 537 Author:
JovanEps 2:273153e44338 538
JovanEps 6:5e0f3eedaf66 539 C version by John Burkardt.
JovanEps 2:273153e44338 540
JovanEps 6:5e0f3eedaf66 541 Reference:
JovanEps 0:43b96e9650ef 542
JovanEps 6:5e0f3eedaf66 543 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 6:5e0f3eedaf66 544 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 545 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 6:5e0f3eedaf66 546 3600 University City Science Center,
JovanEps 6:5e0f3eedaf66 547 Philadelphia, PA, 19104-2688.
JovanEps 6:5e0f3eedaf66 548 ISBN 0-89871-172-X
JovanEps 2:273153e44338 549
JovanEps 6:5e0f3eedaf66 550 Parameters:
JovanEps 2:273153e44338 551
JovanEps 6:5e0f3eedaf66 552 Input/output, double A[LDA*N].
JovanEps 6:5e0f3eedaf66 553 On intput, the matrix to be factored.
JovanEps 6:5e0f3eedaf66 554 On output, an upper triangular matrix and the multipliers used to obtain
JovanEps 6:5e0f3eedaf66 555 it. The factorization can be written A=L*U, where L is a product of
JovanEps 6:5e0f3eedaf66 556 permutation and unit lower triangular matrices, and U is upper triangular.
JovanEps 2:273153e44338 557
JovanEps 6:5e0f3eedaf66 558 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 559
JovanEps 6:5e0f3eedaf66 560 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 561
JovanEps 6:5e0f3eedaf66 562 Output, int IPVT[N], the pivot indices.
JovanEps 2:273153e44338 563
JovanEps 6:5e0f3eedaf66 564 Output, int DGEFA, singularity indicator.
JovanEps 6:5e0f3eedaf66 565 0, normal value.
JovanEps 6:5e0f3eedaf66 566 K, if U(K,K) == 0. This is not an error condition for this subroutine,
JovanEps 6:5e0f3eedaf66 567 but it does indicate that DGESL or DGEDI will divide by zero if called.
JovanEps 6:5e0f3eedaf66 568 Use RCOND in DGECO for a reliable indication of singularity.
JovanEps 6:5e0f3eedaf66 569 */
JovanEps 6:5e0f3eedaf66 570
JovanEps 2:273153e44338 571 int info;
JovanEps 2:273153e44338 572 int j;
JovanEps 2:273153e44338 573 int k;
JovanEps 2:273153e44338 574 int l;
JovanEps 2:273153e44338 575 double t;
JovanEps 2:273153e44338 576 /*
JovanEps 2:273153e44338 577 Gaussian elimination with partial pivoting.
JovanEps 2:273153e44338 578 */
JovanEps 2:273153e44338 579 info = 0;
JovanEps 2:273153e44338 580
JovanEps 2:273153e44338 581 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 582 /*
JovanEps 2:273153e44338 583 Find L = pivot index.
JovanEps 2:273153e44338 584 */
JovanEps 2:273153e44338 585 l = idamax ( n-k+1, a+(k-1)+(k-1)*lda, 1 ) + k - 1;
JovanEps 2:273153e44338 586 ipvt[k-1] = l;
JovanEps 2:273153e44338 587 /*
JovanEps 2:273153e44338 588 Zero pivot implies this column already triangularized.
JovanEps 2:273153e44338 589 */
JovanEps 2:273153e44338 590 if ( a[l-1+(k-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 591 info = k;
JovanEps 2:273153e44338 592 continue;
JovanEps 2:273153e44338 593 }
JovanEps 2:273153e44338 594 /*
JovanEps 2:273153e44338 595 Interchange if necessary.
JovanEps 2:273153e44338 596 */
JovanEps 2:273153e44338 597 if ( l != k ) {
JovanEps 2:273153e44338 598 t = a[l-1+(k-1)*lda];
JovanEps 2:273153e44338 599 a[l-1+(k-1)*lda] = a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 600 a[k-1+(k-1)*lda] = t;
JovanEps 2:273153e44338 601 }
JovanEps 2:273153e44338 602 /*
JovanEps 2:273153e44338 603 Compute multipliers.
JovanEps 2:273153e44338 604 */
JovanEps 2:273153e44338 605 t = -1.0 / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 606
JovanEps 2:273153e44338 607 dscal ( n-k, t, a+k+(k-1)*lda, 1 );
JovanEps 2:273153e44338 608 /*
JovanEps 2:273153e44338 609 Row elimination with column indexing.
JovanEps 2:273153e44338 610 */
JovanEps 2:273153e44338 611 for ( j = k+1; j <= n; j++ ) {
JovanEps 2:273153e44338 612 t = a[l-1+(j-1)*lda];
JovanEps 2:273153e44338 613 if ( l != k ) {
JovanEps 2:273153e44338 614 a[l-1+(j-1)*lda] = a[k-1+(j-1)*lda];
JovanEps 2:273153e44338 615 a[k-1+(j-1)*lda] = t;
JovanEps 2:273153e44338 616 }
JovanEps 2:273153e44338 617 daxpy ( n-k, t, a+k+(k-1)*lda, 1, a+k+(j-1)*lda, 1 );
JovanEps 2:273153e44338 618 }
JovanEps 2:273153e44338 619
JovanEps 0:43b96e9650ef 620 }
JovanEps 0:43b96e9650ef 621
JovanEps 2:273153e44338 622 ipvt[n-1] = n;
JovanEps 0:43b96e9650ef 623
JovanEps 2:273153e44338 624 if ( a[n-1+(n-1)*lda] == 0.0 ) {
JovanEps 2:273153e44338 625 info = n;
JovanEps 0:43b96e9650ef 626 }
JovanEps 0:43b96e9650ef 627
JovanEps 2:273153e44338 628 return info;
JovanEps 2:273153e44338 629 }
JovanEps 2:273153e44338 630 /******************************************************************************/
JovanEps 0:43b96e9650ef 631
JovanEps 2:273153e44338 632 void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job )
JovanEps 6:5e0f3eedaf66 633 {
JovanEps 2:273153e44338 634
JovanEps 7:931219974070 635 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 636 /*
JovanEps 6:5e0f3eedaf66 637 Purpose:
JovanEps 2:273153e44338 638
JovanEps 6:5e0f3eedaf66 639 DGESL solves a real general linear system A * X = B.
JovanEps 2:273153e44338 640
JovanEps 6:5e0f3eedaf66 641 Discussion:
JovanEps 2:273153e44338 642
JovanEps 6:5e0f3eedaf66 643 DGESL can solve either of the systems A * X = B or A' * X = B.
JovanEps 2:273153e44338 644
JovanEps 6:5e0f3eedaf66 645 The system matrix must have been factored by DGECO or DGEFA.
JovanEps 2:273153e44338 646
JovanEps 6:5e0f3eedaf66 647 A division by zero will occur if the input factor contains a
JovanEps 6:5e0f3eedaf66 648 zero on the diagonal. Technically this indicates singularity
JovanEps 6:5e0f3eedaf66 649 but it is often caused by improper arguments or improper
JovanEps 6:5e0f3eedaf66 650 setting of LDA. It will not occur if the subroutines are
JovanEps 6:5e0f3eedaf66 651 called correctly and if DGECO has set 0.0 < RCOND
JovanEps 6:5e0f3eedaf66 652 or DGEFA has set INFO == 0.
JovanEps 2:273153e44338 653
JovanEps 6:5e0f3eedaf66 654 Modified:
JovanEps 2:273153e44338 655
JovanEps 6:5e0f3eedaf66 656 16 May 2005
JovanEps 2:273153e44338 657
JovanEps 6:5e0f3eedaf66 658 Author:
JovanEps 2:273153e44338 659
JovanEps 6:5e0f3eedaf66 660 C version by John Burkardt.
JovanEps 2:273153e44338 661
JovanEps 6:5e0f3eedaf66 662 Reference:
JovanEps 2:273153e44338 663
JovanEps 6:5e0f3eedaf66 664 Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
JovanEps 6:5e0f3eedaf66 665 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 666 SIAM, (Society for Industrial and Applied Mathematics),
JovanEps 6:5e0f3eedaf66 667 3600 University City Science Center,
JovanEps 6:5e0f3eedaf66 668 Philadelphia, PA, 19104-2688.
JovanEps 6:5e0f3eedaf66 669 ISBN 0-89871-172-X
JovanEps 2:273153e44338 670
JovanEps 6:5e0f3eedaf66 671 Parameters:
JovanEps 2:273153e44338 672
JovanEps 6:5e0f3eedaf66 673 Input, double A[LDA*N], the output from DGECO or DGEFA.
JovanEps 2:273153e44338 674
JovanEps 6:5e0f3eedaf66 675 Input, int LDA, the leading dimension of A.
JovanEps 2:273153e44338 676
JovanEps 6:5e0f3eedaf66 677 Input, int N, the order of the matrix A.
JovanEps 2:273153e44338 678
JovanEps 6:5e0f3eedaf66 679 Input, int IPVT[N], the pivot vector from DGECO or DGEFA.
JovanEps 2:273153e44338 680
JovanEps 6:5e0f3eedaf66 681 Input/output, double B[N].
JovanEps 6:5e0f3eedaf66 682 On input, the right hand side vector.
JovanEps 6:5e0f3eedaf66 683 On output, the solution vector.
JovanEps 0:43b96e9650ef 684
JovanEps 6:5e0f3eedaf66 685 Input, int JOB.
JovanEps 6:5e0f3eedaf66 686 0, solve A * X = B;
JovanEps 6:5e0f3eedaf66 687 nonzero, solve A' * X = B.
JovanEps 6:5e0f3eedaf66 688 */
JovanEps 6:5e0f3eedaf66 689
JovanEps 2:273153e44338 690 int k;
JovanEps 2:273153e44338 691 int l;
JovanEps 2:273153e44338 692 double t;
JovanEps 2:273153e44338 693 /*
JovanEps 2:273153e44338 694 Solve A * X = B.
JovanEps 2:273153e44338 695 */
JovanEps 2:273153e44338 696 if ( job == 0 ) {
JovanEps 2:273153e44338 697 for ( k = 1; k <= n-1; k++ ) {
JovanEps 2:273153e44338 698 l = ipvt[k-1];
JovanEps 2:273153e44338 699 t = b[l-1];
JovanEps 2:273153e44338 700
JovanEps 2:273153e44338 701 if ( l != k ) {
JovanEps 2:273153e44338 702 b[l-1] = b[k-1];
JovanEps 2:273153e44338 703 b[k-1] = t;
JovanEps 2:273153e44338 704 }
JovanEps 2:273153e44338 705
JovanEps 2:273153e44338 706 daxpy ( n-k, t, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 707
JovanEps 2:273153e44338 708 }
JovanEps 0:43b96e9650ef 709
JovanEps 2:273153e44338 710 for ( k = n; 1 <= k; k-- ) {
JovanEps 2:273153e44338 711 b[k-1] = b[k-1] / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 712 t = -b[k-1];
JovanEps 2:273153e44338 713 daxpy ( k-1, t, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 714 }
JovanEps 2:273153e44338 715 }
JovanEps 2:273153e44338 716 /*
JovanEps 2:273153e44338 717 Solve A' * X = B.
JovanEps 2:273153e44338 718 */
JovanEps 2:273153e44338 719 else {
JovanEps 2:273153e44338 720 for ( k = 1; k <= n; k++ ) {
JovanEps 2:273153e44338 721 t = ddot ( k-1, a+0+(k-1)*lda, 1, b, 1 );
JovanEps 2:273153e44338 722 b[k-1] = ( b[k-1] - t ) / a[k-1+(k-1)*lda];
JovanEps 2:273153e44338 723 }
JovanEps 0:43b96e9650ef 724
JovanEps 2:273153e44338 725 for ( k = n-1; 1 <= k; k-- ) {
JovanEps 2:273153e44338 726 b[k-1] = b[k-1] + ddot ( n-k, a+k+(k-1)*lda, 1, b+k, 1 );
JovanEps 2:273153e44338 727 l = ipvt[k-1];
JovanEps 2:273153e44338 728
JovanEps 2:273153e44338 729 if ( l != k ) {
JovanEps 2:273153e44338 730 t = b[l-1];
JovanEps 2:273153e44338 731 b[l-1] = b[k-1];
JovanEps 2:273153e44338 732 b[k-1] = t;
JovanEps 2:273153e44338 733 }
JovanEps 2:273153e44338 734 }
JovanEps 2:273153e44338 735 }
JovanEps 2:273153e44338 736 return;
JovanEps 2:273153e44338 737 }
JovanEps 2:273153e44338 738 /******************************************************************************/
JovanEps 2:273153e44338 739
JovanEps 2:273153e44338 740 void dscal ( int n, double sa, double x[], int incx )
JovanEps 6:5e0f3eedaf66 741 {
JovanEps 2:273153e44338 742
JovanEps 7:931219974070 743 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 744 /*
JovanEps 6:5e0f3eedaf66 745 Purpose:
JovanEps 2:273153e44338 746
JovanEps 6:5e0f3eedaf66 747 DSCAL scales a vector by a constant.
JovanEps 2:273153e44338 748
JovanEps 6:5e0f3eedaf66 749 Modified:
JovanEps 2:273153e44338 750
JovanEps 6:5e0f3eedaf66 751 30 March 2007
JovanEps 2:273153e44338 752
JovanEps 6:5e0f3eedaf66 753 Author:
JovanEps 2:273153e44338 754
JovanEps 6:5e0f3eedaf66 755 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 6:5e0f3eedaf66 756 C version by John Burkardt
JovanEps 2:273153e44338 757
JovanEps 6:5e0f3eedaf66 758 Reference:
JovanEps 2:273153e44338 759
JovanEps 6:5e0f3eedaf66 760 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 6:5e0f3eedaf66 761 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 762 SIAM, 1979.
JovanEps 2:273153e44338 763
JovanEps 6:5e0f3eedaf66 764 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 6:5e0f3eedaf66 765 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 6:5e0f3eedaf66 766 Algorithm 539,
JovanEps 6:5e0f3eedaf66 767 ACM Transactions on Mathematical Software,
JovanEps 6:5e0f3eedaf66 768 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 769
JovanEps 6:5e0f3eedaf66 770 Parameters:
JovanEps 2:273153e44338 771
JovanEps 6:5e0f3eedaf66 772 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 773
JovanEps 6:5e0f3eedaf66 774 Input, double SA, the multiplier.
JovanEps 2:273153e44338 775
JovanEps 6:5e0f3eedaf66 776 Input/output, double X[*], the vector to be scaled.
JovanEps 2:273153e44338 777
JovanEps 6:5e0f3eedaf66 778 Input, int INCX, the increment between successive entries of X.
JovanEps 6:5e0f3eedaf66 779 */
JovanEps 6:5e0f3eedaf66 780
JovanEps 2:273153e44338 781 int i;
JovanEps 2:273153e44338 782 int ix;
JovanEps 2:273153e44338 783 int m;
JovanEps 2:273153e44338 784
JovanEps 2:273153e44338 785 if ( n <= 0 ) {
JovanEps 2:273153e44338 786 } else if ( incx == 1 ) {
JovanEps 2:273153e44338 787 m = n % 5;
JovanEps 2:273153e44338 788
JovanEps 2:273153e44338 789 for ( i = 0; i < m; i++ ) {
JovanEps 2:273153e44338 790 x[i] = sa * x[i];
JovanEps 2:273153e44338 791 }
JovanEps 0:43b96e9650ef 792
JovanEps 2:273153e44338 793 for ( i = m; i < n; i = i + 5 ) {
JovanEps 2:273153e44338 794 x[i] = sa * x[i];
JovanEps 2:273153e44338 795 x[i+1] = sa * x[i+1];
JovanEps 2:273153e44338 796 x[i+2] = sa * x[i+2];
JovanEps 2:273153e44338 797 x[i+3] = sa * x[i+3];
JovanEps 2:273153e44338 798 x[i+4] = sa * x[i+4];
JovanEps 2:273153e44338 799 }
JovanEps 2:273153e44338 800 } else {
JovanEps 2:273153e44338 801 if ( 0 <= incx ) {
JovanEps 2:273153e44338 802 ix = 0;
JovanEps 2:273153e44338 803 } else {
JovanEps 2:273153e44338 804 ix = ( - n + 1 ) * incx;
JovanEps 2:273153e44338 805 }
JovanEps 2:273153e44338 806
JovanEps 2:273153e44338 807 for ( i = 0; i < n; i++ ) {
JovanEps 2:273153e44338 808 x[ix] = sa * x[ix];
JovanEps 2:273153e44338 809 ix = ix + incx;
JovanEps 2:273153e44338 810 }
JovanEps 2:273153e44338 811 }
JovanEps 2:273153e44338 812 return;
JovanEps 2:273153e44338 813 }
JovanEps 2:273153e44338 814 /******************************************************************************/
JovanEps 2:273153e44338 815
JovanEps 2:273153e44338 816 int idamax ( int n, double dx[], int incx )
JovanEps 6:5e0f3eedaf66 817 {
JovanEps 2:273153e44338 818
JovanEps 7:931219974070 819 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 820 /*
JovanEps 6:5e0f3eedaf66 821 Purpose:
JovanEps 2:273153e44338 822
JovanEps 6:5e0f3eedaf66 823 IDAMAX finds the index of the vector element of maximum absolute value.
JovanEps 2:273153e44338 824
JovanEps 6:5e0f3eedaf66 825 Discussion:
JovanEps 2:273153e44338 826
JovanEps 6:5e0f3eedaf66 827 WARNING: This index is a 1-based index, not a 0-based index!
JovanEps 2:273153e44338 828
JovanEps 6:5e0f3eedaf66 829 Modified:
JovanEps 2:273153e44338 830
JovanEps 6:5e0f3eedaf66 831 30 March 2007
JovanEps 2:273153e44338 832
JovanEps 6:5e0f3eedaf66 833 Author:
JovanEps 2:273153e44338 834
JovanEps 6:5e0f3eedaf66 835 FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
JovanEps 6:5e0f3eedaf66 836 C version by John Burkardt
JovanEps 2:273153e44338 837
JovanEps 6:5e0f3eedaf66 838 Reference:
JovanEps 2:273153e44338 839
JovanEps 6:5e0f3eedaf66 840 Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
JovanEps 6:5e0f3eedaf66 841 LINPACK User's Guide,
JovanEps 6:5e0f3eedaf66 842 SIAM, 1979.
JovanEps 2:273153e44338 843
JovanEps 6:5e0f3eedaf66 844 Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
JovanEps 6:5e0f3eedaf66 845 Basic Linear Algebra Subprograms for Fortran Usage,
JovanEps 6:5e0f3eedaf66 846 Algorithm 539,
JovanEps 6:5e0f3eedaf66 847 ACM Transactions on Mathematical Software,
JovanEps 6:5e0f3eedaf66 848 Volume 5, Number 3, September 1979, pages 308-323.
JovanEps 2:273153e44338 849
JovanEps 6:5e0f3eedaf66 850 Parameters:
JovanEps 2:273153e44338 851
JovanEps 6:5e0f3eedaf66 852 Input, int N, the number of entries in the vector.
JovanEps 2:273153e44338 853
JovanEps 6:5e0f3eedaf66 854 Input, double X[*], the vector to be examined.
JovanEps 2:273153e44338 855
JovanEps 6:5e0f3eedaf66 856 Input, int INCX, the increment between successive entries of SX.
JovanEps 2:273153e44338 857
JovanEps 6:5e0f3eedaf66 858 Output, int IDAMAX, the index of the element of maximum
JovanEps 6:5e0f3eedaf66 859 absolute value.
JovanEps 6:5e0f3eedaf66 860 */
JovanEps 6:5e0f3eedaf66 861
JovanEps 2:273153e44338 862 double dmax;
JovanEps 2:273153e44338 863 int i;
JovanEps 2:273153e44338 864 int ix;
JovanEps 2:273153e44338 865 int value;
JovanEps 2:273153e44338 866
JovanEps 2:273153e44338 867 value = 0;
JovanEps 0:43b96e9650ef 868
JovanEps 2:273153e44338 869 if ( n < 1 || incx <= 0 ) {
JovanEps 2:273153e44338 870 return value;
JovanEps 2:273153e44338 871 }
JovanEps 2:273153e44338 872
JovanEps 2:273153e44338 873 value = 1;
JovanEps 2:273153e44338 874
JovanEps 2:273153e44338 875 if ( n == 1 ) {
JovanEps 2:273153e44338 876 return value;
JovanEps 2:273153e44338 877 }
JovanEps 0:43b96e9650ef 878
JovanEps 2:273153e44338 879 if ( incx == 1 ) {
JovanEps 2:273153e44338 880 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 881
JovanEps 2:273153e44338 882 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 883 if ( dmax < r8_abs ( dx[i] ) ) {
JovanEps 2:273153e44338 884 value = i + 1;
JovanEps 2:273153e44338 885 dmax = r8_abs ( dx[i] );
JovanEps 2:273153e44338 886 }
JovanEps 2:273153e44338 887 }
JovanEps 2:273153e44338 888 } else {
JovanEps 2:273153e44338 889 ix = 0;
JovanEps 2:273153e44338 890 dmax = r8_abs ( dx[0] );
JovanEps 2:273153e44338 891 ix = ix + incx;
JovanEps 2:273153e44338 892
JovanEps 2:273153e44338 893 for ( i = 1; i < n; i++ ) {
JovanEps 2:273153e44338 894 if ( dmax < r8_abs ( dx[ix] ) ) {
JovanEps 2:273153e44338 895 value = i + 1;
JovanEps 2:273153e44338 896 dmax = r8_abs ( dx[ix] );
JovanEps 2:273153e44338 897 }
JovanEps 2:273153e44338 898 ix = ix + incx;
JovanEps 2:273153e44338 899 }
JovanEps 2:273153e44338 900 }
JovanEps 0:43b96e9650ef 901
JovanEps 2:273153e44338 902 return value;
JovanEps 2:273153e44338 903 }
JovanEps 2:273153e44338 904 /******************************************************************************/
JovanEps 2:273153e44338 905
JovanEps 2:273153e44338 906 double r8_abs ( double x )
JovanEps 6:5e0f3eedaf66 907 {
JovanEps 2:273153e44338 908
JovanEps 7:931219974070 909 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 910 /*
JovanEps 6:5e0f3eedaf66 911 Purpose:
JovanEps 2:273153e44338 912
JovanEps 6:5e0f3eedaf66 913 R8_ABS returns the absolute value of a R8.
JovanEps 0:43b96e9650ef 914
JovanEps 6:5e0f3eedaf66 915 Modified:
JovanEps 2:273153e44338 916
JovanEps 6:5e0f3eedaf66 917 02 April 2005
JovanEps 2:273153e44338 918
JovanEps 6:5e0f3eedaf66 919 Author:
JovanEps 0:43b96e9650ef 920
JovanEps 6:5e0f3eedaf66 921 John Burkardt
JovanEps 2:273153e44338 922
JovanEps 6:5e0f3eedaf66 923 Parameters:
JovanEps 2:273153e44338 924
JovanEps 6:5e0f3eedaf66 925 Input, double X, the quantity whose absolute value is desired.
JovanEps 2:273153e44338 926
JovanEps 6:5e0f3eedaf66 927 Output, double R8_ABS, the absolute value of X.
JovanEps 6:5e0f3eedaf66 928 */
JovanEps 6:5e0f3eedaf66 929
JovanEps 2:273153e44338 930 double value;
JovanEps 2:273153e44338 931
JovanEps 2:273153e44338 932 if ( 0.0 <= x ) {
JovanEps 2:273153e44338 933 value = x;
JovanEps 2:273153e44338 934 } else {
JovanEps 2:273153e44338 935 value = -x;
JovanEps 2:273153e44338 936 }
JovanEps 2:273153e44338 937 return value;
JovanEps 2:273153e44338 938 }
JovanEps 2:273153e44338 939 /******************************************************************************/
JovanEps 2:273153e44338 940
JovanEps 2:273153e44338 941 double r8_epsilon ( void )
JovanEps 6:5e0f3eedaf66 942 {
JovanEps 0:43b96e9650ef 943
JovanEps 7:931219974070 944 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 945 /*
JovanEps 6:5e0f3eedaf66 946 Purpose:
JovanEps 2:273153e44338 947
JovanEps 6:5e0f3eedaf66 948 R8_EPSILON returns the R8 round off unit.
JovanEps 2:273153e44338 949
JovanEps 6:5e0f3eedaf66 950 Discussion:
JovanEps 2:273153e44338 951
JovanEps 6:5e0f3eedaf66 952 R8_EPSILON is a number R which is a power of 2 with the property that,
JovanEps 6:5e0f3eedaf66 953 to the precision of the computer's arithmetic,
JovanEps 6:5e0f3eedaf66 954 1 < 1 + R
JovanEps 6:5e0f3eedaf66 955 but
JovanEps 6:5e0f3eedaf66 956 1 = ( 1 + R / 2 )
JovanEps 0:43b96e9650ef 957
JovanEps 6:5e0f3eedaf66 958 Licensing:
JovanEps 2:273153e44338 959
JovanEps 6:5e0f3eedaf66 960 This code is distributed under the GNU LGPL license.
JovanEps 2:273153e44338 961
JovanEps 6:5e0f3eedaf66 962 Modified:
JovanEps 2:273153e44338 963
JovanEps 6:5e0f3eedaf66 964 08 May 2006
JovanEps 2:273153e44338 965
JovanEps 6:5e0f3eedaf66 966 Author:
JovanEps 2:273153e44338 967
JovanEps 6:5e0f3eedaf66 968 John Burkardt
JovanEps 2:273153e44338 969
JovanEps 6:5e0f3eedaf66 970 Parameters:
JovanEps 0:43b96e9650ef 971
JovanEps 6:5e0f3eedaf66 972 Output, double R8_EPSILON, the double precision round-off unit.
JovanEps 6:5e0f3eedaf66 973 */
JovanEps 6:5e0f3eedaf66 974
JovanEps 2:273153e44338 975 double r;
JovanEps 2:273153e44338 976
JovanEps 2:273153e44338 977 r = 1.0;
JovanEps 2:273153e44338 978
JovanEps 2:273153e44338 979 while ( 1.0 < ( double ) ( 1.0 + r ) ) {
JovanEps 2:273153e44338 980 r = r / 2.0;
JovanEps 2:273153e44338 981 }
JovanEps 2:273153e44338 982 r = 2.0 * r;
JovanEps 2:273153e44338 983
JovanEps 2:273153e44338 984 return r;
JovanEps 0:43b96e9650ef 985 }
JovanEps 2:273153e44338 986 /******************************************************************************/
JovanEps 0:43b96e9650ef 987
JovanEps 2:273153e44338 988 double r8_max ( double x, double y )
JovanEps 6:5e0f3eedaf66 989 {
JovanEps 2:273153e44338 990
JovanEps 7:931219974070 991 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 992 /*
JovanEps 6:5e0f3eedaf66 993 Purpose:
JovanEps 2:273153e44338 994
JovanEps 6:5e0f3eedaf66 995 R8_MAX returns the maximum of two R8's.
JovanEps 2:273153e44338 996
JovanEps 6:5e0f3eedaf66 997 Modified:
JovanEps 2:273153e44338 998
JovanEps 6:5e0f3eedaf66 999 18 August 2004
JovanEps 2:273153e44338 1000
JovanEps 6:5e0f3eedaf66 1001 Author:
JovanEps 0:43b96e9650ef 1002
JovanEps 6:5e0f3eedaf66 1003 John Burkardt
JovanEps 2:273153e44338 1004
JovanEps 6:5e0f3eedaf66 1005 Parameters:
JovanEps 2:273153e44338 1006
JovanEps 6:5e0f3eedaf66 1007 Input, double X, Y, the quantities to compare.
JovanEps 0:43b96e9650ef 1008
JovanEps 6:5e0f3eedaf66 1009 Output, double R8_MAX, the maximum of X and Y.
JovanEps 6:5e0f3eedaf66 1010 */
JovanEps 6:5e0f3eedaf66 1011
JovanEps 2:273153e44338 1012 double value;
JovanEps 2:273153e44338 1013
JovanEps 2:273153e44338 1014 if ( y < x ) {
JovanEps 2:273153e44338 1015 value = x;
JovanEps 2:273153e44338 1016 } else {
JovanEps 2:273153e44338 1017 value = y;
JovanEps 2:273153e44338 1018 }
JovanEps 2:273153e44338 1019 return value;
JovanEps 0:43b96e9650ef 1020 }
JovanEps 2:273153e44338 1021 /******************************************************************************/
JovanEps 2:273153e44338 1022
JovanEps 2:273153e44338 1023 double r8_random ( int iseed[4] )
JovanEps 6:5e0f3eedaf66 1024 {
JovanEps 2:273153e44338 1025
JovanEps 7:931219974070 1026 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 1027 /*
JovanEps 6:5e0f3eedaf66 1028 Purpose:
JovanEps 2:273153e44338 1029
JovanEps 6:5e0f3eedaf66 1030 R8_RANDOM returns a uniformly distributed random number between 0 and 1.
JovanEps 2:273153e44338 1031
JovanEps 6:5e0f3eedaf66 1032 Discussion:
JovanEps 0:43b96e9650ef 1033
JovanEps 6:5e0f3eedaf66 1034 This routine uses a multiplicative congruential method with modulus
JovanEps 6:5e0f3eedaf66 1035 2**48 and multiplier 33952834046453 (see G.S.Fishman,
JovanEps 6:5e0f3eedaf66 1036 'Multiplicative congruential random number generators with modulus
JovanEps 6:5e0f3eedaf66 1037 2**b: an exhaustive analysis for b = 32 and a partial analysis for
JovanEps 6:5e0f3eedaf66 1038 b = 48', Math. Comp. 189, pp 331-344, 1990).
JovanEps 2:273153e44338 1039
JovanEps 6:5e0f3eedaf66 1040 48-bit integers are stored in 4 integer array elements with 12 bits
JovanEps 6:5e0f3eedaf66 1041 per element. Hence the routine is portable across machines with
JovanEps 6:5e0f3eedaf66 1042 integers of 32 bits or more.
JovanEps 2:273153e44338 1043
JovanEps 6:5e0f3eedaf66 1044 Parameters:
JovanEps 2:273153e44338 1045
JovanEps 6:5e0f3eedaf66 1046 Input/output, integer ISEED(4).
JovanEps 6:5e0f3eedaf66 1047 On entry, the seed of the random number generator; the array
JovanEps 6:5e0f3eedaf66 1048 elements must be between 0 and 4095, and ISEED(4) must be odd.
JovanEps 6:5e0f3eedaf66 1049 On exit, the seed is updated.
JovanEps 2:273153e44338 1050
JovanEps 6:5e0f3eedaf66 1051 Output, double R8_RANDOM, the next pseudorandom number.
JovanEps 6:5e0f3eedaf66 1052 */
JovanEps 6:5e0f3eedaf66 1053
JovanEps 2:273153e44338 1054 int ipw2 = 4096;
JovanEps 2:273153e44338 1055 int it1;
JovanEps 2:273153e44338 1056 int it2;
JovanEps 2:273153e44338 1057 int it3;
JovanEps 2:273153e44338 1058 int it4;
JovanEps 2:273153e44338 1059 int m1 = 494;
JovanEps 2:273153e44338 1060 int m2 = 322;
JovanEps 2:273153e44338 1061 int m3 = 2508;
JovanEps 2:273153e44338 1062 int m4 = 2549;
JovanEps 2:273153e44338 1063 double r = 1.0 / 4096.0;
JovanEps 2:273153e44338 1064 double value;
JovanEps 2:273153e44338 1065 /*
JovanEps 2:273153e44338 1066 Multiply the seed by the multiplier modulo 2**48.
JovanEps 2:273153e44338 1067 */
JovanEps 2:273153e44338 1068 it4 = iseed[3] * m4;
JovanEps 2:273153e44338 1069 it3 = it4 / ipw2;
JovanEps 2:273153e44338 1070 it4 = it4 - ipw2 * it3;
JovanEps 2:273153e44338 1071 it3 = it3 + iseed[2] * m4 + iseed[3] * m3;
JovanEps 2:273153e44338 1072 it2 = it3 / ipw2;
JovanEps 2:273153e44338 1073 it3 = it3 - ipw2 * it2;
JovanEps 2:273153e44338 1074 it2 = it2 + iseed[1] * m4 + iseed[2] * m3 + iseed[3] * m2;
JovanEps 2:273153e44338 1075 it1 = it2 / ipw2;
JovanEps 2:273153e44338 1076 it2 = it2 - ipw2 * it1;
JovanEps 2:273153e44338 1077 it1 = it1 + iseed[0] * m4 + iseed[1] * m3 + iseed[2] * m2 + iseed[3] * m1;
JovanEps 2:273153e44338 1078 it1 = ( it1 % ipw2 );
JovanEps 2:273153e44338 1079 /*
JovanEps 2:273153e44338 1080 Return updated seed
JovanEps 2:273153e44338 1081 */
JovanEps 2:273153e44338 1082 iseed[0] = it1;
JovanEps 2:273153e44338 1083 iseed[1] = it2;
JovanEps 2:273153e44338 1084 iseed[2] = it3;
JovanEps 2:273153e44338 1085 iseed[3] = it4;
JovanEps 2:273153e44338 1086 /*
JovanEps 2:273153e44338 1087 Convert 48-bit integer to a real number in the interval (0,1)
JovanEps 2:273153e44338 1088 */
JovanEps 2:273153e44338 1089 value =
JovanEps 2:273153e44338 1090 r * ( ( double ) ( it1 )
JovanEps 2:273153e44338 1091 + r * ( ( double ) ( it2 )
JovanEps 2:273153e44338 1092 + r * ( ( double ) ( it3 )
JovanEps 2:273153e44338 1093 + r * ( ( double ) ( it4 ) ) ) ) );
JovanEps 2:273153e44338 1094
JovanEps 2:273153e44338 1095 return value;
JovanEps 2:273153e44338 1096 }
JovanEps 2:273153e44338 1097 /******************************************************************************/
JovanEps 2:273153e44338 1098
JovanEps 2:273153e44338 1099 double *r8mat_gen ( int lda, int n )
JovanEps 6:5e0f3eedaf66 1100 {
JovanEps 2:273153e44338 1101
JovanEps 7:931219974070 1102 /******************************************************************************/
JovanEps 6:5e0f3eedaf66 1103 /*
JovanEps 6:5e0f3eedaf66 1104 Purpose:
JovanEps 2:273153e44338 1105
JovanEps 6:5e0f3eedaf66 1106 R8MAT_GEN generates a random R8MAT.
JovanEps 2:273153e44338 1107
JovanEps 6:5e0f3eedaf66 1108 Modified:
JovanEps 2:273153e44338 1109
JovanEps 6:5e0f3eedaf66 1110 06 June 2005
JovanEps 2:273153e44338 1111
JovanEps 6:5e0f3eedaf66 1112 Parameters:
JovanEps 2:273153e44338 1113
JovanEps 6:5e0f3eedaf66 1114 Input, integer LDA, the leading dimension of the matrix.
JovanEps 2:273153e44338 1115
JovanEps 6:5e0f3eedaf66 1116 Input, integer N, the order of the matrix.
JovanEps 2:273153e44338 1117
JovanEps 6:5e0f3eedaf66 1118 Output, double R8MAT_GEN[LDA*N], the N by N matrix.
JovanEps 6:5e0f3eedaf66 1119 */
JovanEps 6:5e0f3eedaf66 1120
JovanEps 3:da1132c65314 1121 double *ba;
JovanEps 2:273153e44338 1122 int i;
JovanEps 2:273153e44338 1123 int init[4] = { 1, 2, 3, 1325 };
JovanEps 2:273153e44338 1124 int j;
JovanEps 2:273153e44338 1125
JovanEps 3:da1132c65314 1126 ba = ( double * ) malloc ( lda * n * sizeof ( double ) );
JovanEps 2:273153e44338 1127
JovanEps 2:273153e44338 1128 for ( j = 1; j <= n; j++ ) {
JovanEps 2:273153e44338 1129 for ( i = 1; i <= n; i++ ) {
JovanEps 3:da1132c65314 1130 ba[i-1+(j-1)*lda] = r8_random ( init ) - 0.5;
JovanEps 2:273153e44338 1131 }
JovanEps 1:be78b18b8347 1132 }
JovanEps 2:273153e44338 1133
JovanEps 3:da1132c65314 1134 return ba;
JovanEps 0:43b96e9650ef 1135 }