예제: 3차 스플라인 보간

lspline, pspline 및 cspline 함수를 사용하여 3차 스플라인(조각 다항식)을 만들고 데이터 점 사이를 보간합니다.

1. 행렬을 정의합니다.

2. csort 함수를 사용하여 Cu의 둘째 열이 오름차순으로 배열되도록 데이터를 정렬합니다.

스플라인 함수에 제공하는 x 값은 오름차순이어야 합니다.

3. x 및 y 데이터가 포함된 벡터를 만듭니다.

4. cspline 함수를 사용하여 3차 스플라인 벡터를 생성한 다음 interp 함수를 사용하여 보간 값을 얻습니다.

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5. lspline 함수를 사용하여 선형 스플라인 벡터를 생성한 다음 interp 함수를 사용하여 보간 값을 얻습니다.

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6. pspline 함수를 사용하여 포물선 스플라인 벡터를 생성한 다음 interp 함수를 사용하여 보간 값을 얻습니다.

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7. 원래 데이터 점과 3차 스플라인을 도표화합니다.

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8. 처음 두 개의 데이터 점을 확대합니다.

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세 개의 스플라인 함수를 통해 생성된 결과가 끝점을 제외하고는 거의 비슷한 것을 알 수 있습니다.

9. 보간된 선형 스플라인 벡터의 2차 도함수를 계산하여 도함수가 끝점에서 0과 같음을 보여줍니다.

10. 보간된 포물선 스플라인의 2차 도함수를 계산하여 끝점에서 도함수가 다음 번 가장 가까운 점의 값과 같음을 보여줍니다.

◦ 첫 번째 점과 두 번째 점에서 2차 도함수를 구해 두 값이 같음을 보여줍니다.

◦ 끝에서 두 번째 점과 마지막 점에서 2차 도함수를 구해 두 값이 같음을 보여줍니다.

스플라인 적합식의 도함수를 사용하여 보간된 곡선의 최대값과 최소값, 기울기 및 기타 수치를 구할 수 있습니다.