At the end of the most tumultuous week of his presidency, Jimmy Carter is an openly serene and self-confident man, convinced that he has shaken his administration to the core and rid it of disloyalty and that achieving those goals was worth all the shock and uproar of the last few days.

Recalling the extraordinary events of the last few weeks, the president made his views and feelings known yesterday to reporters who were invited to the White House.

When he went to Camp David Early in the month and abruptly canceled an energy speech scheduled for July 5, he did not know what he was going to do. But in the 10 days he spent at the presidential retreat, much of what had been troubling him for months about American life in general and his own administration in particular began to come together.

By the time he returned to Washington from Maryland's Catoctin Mountains, he knew what he would do. He would make substantial changes in the personnel and in the operations of his White House staff and at the highest levels of the Cabinet. Most of the White House staff changes are to come.

In the purge of the Cabinet, accomplished with a stunning swiftness Carter had planned, the key test would be loyalty. For too long, the president believed, he had tolerated Cabinet officers who were working more for themselves than for him. The primary target of the purge would be the secretary he considered the most disloyal - Joseph A. Califano Jr. of Health, education and welfare.

Carter knew, too, how he wanted to accomplish the purge - all at once, getting it behind him. Better that, he felt, than to drag it out. He knew that this would send shock waves through official Washington and perhaps much of the country.

So be it, he told himself.

Now that it is over, the president is pleased with his work. No one, no other president, he believes, could have acted with more swiftness or decisiveness, qualities that he often has seemed to lack. He is convinced that in a week or so, when the dust has settled, the confusion that the last few days have caused and the criticism they have elicted in Congress and the public will subside. He has never been more confident, is perhaps a touch overconfident, but then that has always been his way.

Even in private, he gives the appearance of a man transformed. As in his televised speech to the nation last Sunday night, he is more animated than in the past, gesturing with a clenched right fist that slashed toward the table for emphasis.

His unexpected invitation to share with reporters his thoughts, feelings and recollections of the last few weeks was a sign of the transformation. Carter remains an intensely private person. He had planned to spend yesterday at Camp David, where he habitually retreats for solitude. But he canceled those plans and, yesterday morning, sat down and began to list the steps he should take in the aftermath of the governmental trauma he had wrought.

One of the first, he decided, should be to try to explain to the press, and through it the public, how and why the purge came about and what he sees for the future.

His assessment of the future is extraordinarily optimistic for a man who waited until he had dropped to a historic low in popular support to change both his manner of conducting the presidency and some of the key people round him.

Now, Carter believes, he is - or will be once there are some changes in subcabinet posts - surrounded by loyalists, team players, as he likes to think of them. Despite the week's turmoil, he does not believe his legislative program has been damaged. Some aspects of his energy proposals, particularly the so-called "windfall profits tax" on the oil industry, could be enacted before the August congressional recess.

But the shakeup is not over. There is the question of his White House staff, which is to be restructured and expanded soon. There is no sign that any of his senior aides from Georgia, whose loyalty has never been questioned, are in jeopardy. But the president wants more diversity in the views available to him, something he has been urged to get almost from the beginning of his administration.

Frank Moore, the much-criticized congressional relations chief, will remain the preeminent congressional liaison. But Hamilton Jordan, the new White House chief of staff, is to begin working closely with some key members of Congress to assist Moore's effort.

Carter has other things in mind, such as a regular domestic policy breakfast with key domestic Cabinet secretaries, similar to the foreign policy breakfasts he long has held. He candidly admits that his record in domestic policy does not match what he considers his substantial achievements in foreign policy.

And the president is rethinking his relationship with the press and how through it, he communicates to the public. He is not satisfied in having the Washington press corps as the primary vehicle for that Communication.

He still will hold televised press conferences in the nation's capital, but his promise of two month no longer holds. Instead, there will be more "town meetings" and regional press conference around the country. There are likely to be more invitations like the one yesterday for chats with the president, though the ground rules and dictums about what can and cannot be attributed directly to him will vary.

But some fundamentals will not change, Carter believes. In his own mind, he is still devoted to the concept of Cabinet government, allowing a maximum of latitude to his Cabinet secretaries.

Now that he has the team players he wants, allowing that latitude should be easier, the president thinks. Jordan may be chief of staff, imposing more discipline and order to the decision-making process, but the Cabinet secretaries will continue to have direct access to the president.

He has made it clear to his newly constituted Cabinet that they are to continue to make their own cases and disagree with him in private, but that once he has made a decision they are to adopt it as their own or resign. Carter recalls telling he original Cabinet that 2 1/2 years ago. But some didn't follow that and the president now believes he let them get away with defiance far too long.

Mostly, he thinks he let Califano get away with it. The president has laid down a rule for his staff and himself not to speak ill of any of the five departed Cabinet officials, and he openly admires what he considers the graceful and gentlemanly way Treasury Secretary W. Michael Blumenth took leave of his office.

But when he considers some of the acts of disloyalty that led to last week's drastic action, it is clearly Califano he has in mind. There is the example of a high-ranking official going a key congressional committee chairman to disagree with a presidential decision. That sort of thing, Carter believes, did no one any good and led to confusion about White House intentions and the portrait of disarray that so often plagued his administration.

And, of course, there is the question of the Califano version of their final meeting. At a press conference the day he was fired, Califano said the president gave him two reasons for the sacking - the HEW secretary's inability to get along with some key White House aides, specifically Jordan, Moore and press secretary Jody Powell, and the president's desire to get his Cabinet in line for the 1980 campaign. Califano also said Carter called him the greatest HEW secretary in history.

The president does not recall saying any of those things to Califano.

Califano has not retracted his version of that meeting. Yesterday, through a spokesman, he denied seeking to undermined presidential objectives, particularly the administration bill to create a Department of Education, which Califano said he actively worked for the bill and that White House officials had never expressed displeasure to him on his handling of that and other major pieces of legislation.

Carter considers the events behind him. A month before the president went to Camp David, Jordan had agreed to become chief of staff, the result of a plea by domestic policy adviser Stuart E. Eizenstat speaking for the entire senior staff. That should help the White House staff problem, Carter believes.

At Camp David he made the other key decisions, consulting only with Vice President Mondale. Califano would be fired. Blumenthal also would go, but in Carter's mind that was more a mutual agreement than a firing. To make the break clean and swfit, he decided also to move on the two resignations everyone knew would be coming soon - those of Attorney General Griffin B. Bell and Energy Secretary James R. Schlesinger Jr.

What he did not count on was Brock Adams, the secretary of transportation. He wanted Adams to stay, on condition that he fire his top deputy and invite his congressional relations chief to the Whitte House for some cautioning advice. After all, Carter told himself, he reluctantly had allowed Adams to prempt him 2 1/2 years ago when Adams brought so many from his Capitol Hill staff to the Transportation Department. It was time for a chance.

But Adams preempted him again, issuing a public statrment with his own conditions for remaining in the administration. So he, too, was fired.

Before leaving Camp Davis, Carter sent capsule previews of his Sunday night speech to 20 or 30 leaders around the world. The speech, and followup appearances last Monday in Kansas City and Detroit, went well.

With this background and these decisions made, the president convened a meeting with his Cabinet at the White House Tuesday morning. In the course of that meeting, he had some critical things to say about several of his appintees, among them Ambassador to the United Nations Andrew Young. But he was no harder on Young than on some of the others, and ended up praising Young for improved U.S relations with the Third World.

Carter also told the assembled sectaries that he was going to make some substantial changes in the Cabinet and White House staff.He reas to them from a list of options he was considering to accomplish the shakeup-one og which was that they all offer to resign.

The president's recollection of what happened next is not entirely clear. At some point, , Attorney General Bell, ever the lawyer, said they should submit their resignations in writing promptly. But Sectary of State Cyrus R. Vance argued that that was not necessary, that thay shoula offer the resignation orally then and there. Vance was supported by Defense Secretary Horald Brown, and the others quickly signaled their assent one way or another.

Then began the tumult. CAPTION: Picture, no caption, By Frank Johnston - The Washington Post