You left an important chunk of the code and have not shown how the sensor is connected to the Uno. If I had all of the code I could connect a HMC5883 to my Uno and test the code.
In the meantime, have you run an I2C scanner to verify that the I2C bus sees the HMC? What does the scanner report.
// I2C scanner by Nick Gammon. Thanks Nick.
#include <Wire.h>
void setup() {
Serial.begin (115200); //***** make sure serial monitor baud matches *****
// Leonardo: wait for serial port to connect
while (!Serial)
{
}
Serial.println ();
Serial.println ("I2C scanner. Scanning ...");
byte count = 0;
Wire.begin();
for (byte i = 1; i < 120; i++)
{
Wire.beginTransmission (i);
if (Wire.endTransmission () == 0)
{
Serial.print ("Found address: ");
Serial.print (i, DEC);
Serial.print (" (0x");
Serial.print (i, HEX);
Serial.println (")");
count++;
delay (1); // maybe unneeded?
} // end of good response
} // end of for loop
Serial.println ("Done.");
Serial.print ("Found ");
Serial.print (count, DEC);
Serial.println (" device(s).");
} // end of setup
void loop() {}