Esempio: regressione di funzione razionale 2

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rationalfitnp - Nessun polo

Utilizzare le funzioni rationalfit e rationalfitnp per eseguire la regressione di funzione razionale. Quando si utilizza la funzione rationalfitnp anziché la funzione rationalfit, nella soluzione del problema dei minimi quadrati viene verificata la presenza di radici del denominatore nell'intervallo di fit. Se non vi sono poli, viene restituito il fit generale. Se vi sono poli, vengono aggiunti ulteriori vincoli al problema di ottimizzazione non lineare.

1. Definire un insieme di dati modificando lievemente la funzione inversa di x.

2. Specificare un ordine per il numeratore e il denominatore della funzione razionale.

La funzione adattata è riportata di seguito.

Fare clic per copiare questa espressione

3. Definire un limite di confidenza e un vettore di deviazioni standard.

4. Chiamare le funzioni rationalfit e rationalfitnp.

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Per param1 e param2, la prima colonna contiene i parametri e le colonne rimanenti contengono i limiti inferiori e superiori per ogni parametro al limite di confidenza definito in precedenza.

5. Tracciare il grafico dell'insieme di dati e delle due curve di regressione.

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Il polo è stato rimosso dalla funzione rationalfitnp: Il polinomio denominatore viene trasformato nella forma seguente:

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Per evitare il polo, sono stati aggiunti vincoli:

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LeastSquaresFit

Confrontare le curve di fit restituite da rationalfitnp e da LeastSquaresFit. La funzione LeastSquaresFit esegue lo stesso algoritmo di rationalfitnp, ma richiede valori ipotizzati e limiti di confidenza per i parametri. Questa operazione è consigliabile quando si desidera che il termine costante sia nel numeratore anziché nel denominatore.

1. Definire la funzione adattata.

2. Definire valori ipotizzati per i parametri.

3. Definire condizioni di limite inferiore e superiore per i parametri.

4. Chiamare la funzione LeastSquaresFit.

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5. Tracciare il grafico dell'insieme di dati e delle curve di fit restituite dalle funzioni rationalfitnp e LeastSquaresFit.

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Qualsiasi metodo di filtro o di trasformazione dei dati che inclina i dati verso una linea retta prima di eseguire un fit di funzione razionale aggiunge una velocità di convergenza considerevole alla funzione rational e potrebbe avere il vantaggio collaterale di eliminare i poli indesiderati.

Argomenti correlati

Regressione di funzione razionale

Funzioni LeastSquaresFit e confidence

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