Correct: He called me to repair the computer. I am here to repair the computer. He invited me to repair the computer. (NOT for repairing)
We don't use 'for' before a verb to talk about purpose. Instead, we use to + infinitive.
She went to Canada to attend the conference. He is studying everyday to improve his English. I am going to New York to visit my grandmother. I went there to buy a watch.
[[ We can use for before a noun to talk about a purpose.
I went to Paris for an interview. He went to the pub for a drink. He is studying hard for the exam.
We can use 𝗳𝗼𝗿 before a verb to talk about the purpose of a thing. (the reason why we use it)
We use an altimeter 𝗳𝗼𝗿 measur𝗶𝗻𝗴 height above sea level. That stuff is (used) 𝗳𝗼𝗿 clean𝗶𝗻𝗴 leather. The garden shears are used 𝗳𝗼𝗿 clip𝗽𝗶𝗻𝗴 the hedge. He wears these old trousers 𝗳𝗼𝗿 paint𝗶𝗻𝗴.]]