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Ik moet interpoleren en heb geen ideee hoe dit moet ik heb al meerdere malen bij google zitten zoeken maar helaas ben er wel achter dat ik linear moet interpoleren ik heb de volgende gegevens

329.90 = 1.69901E+00

330.05 = 1.69980E+00

nou wil ik 330 weten ????

mvg Erik

(1*329.90 + 2*330.05)/(1+2) = 330

(1*1.69901 + 2*1.69980)/(1+2) = 1.699536666 (evt. afronden)

Als je maar twee meetpunten hebt kun je weinig anders doen dan lineair interpoleren.

y(x) = Ax+B met A = (y₂-y₁)/(x₂-x₁) en B = y₁-Ax₁

x₁,y₁ en x₂,y₂ zijn de twee gegeven punten.

Ik zal ff uitleggen wat ik moet doen ik moet van de onderstaande gegevens een grafiek maken ( het is niet alles er is nog veel meer data maar is een beetje te veel m hier neer te zetten) En van die data wil ik dat het bijvoorbeeld begint bij 390 en dan 400 en dan 410 enz enz

maar ik heb geen hele getallen en werkt dat ook met die formule

389.83 2.22E-01

390.21 1.96E-01

390.59 2.83E-01

390.97 2.25E-01

391.34 2.19E-01

391.72 2.53E-01

392.1 1.58E-01

392.48 2.92E-01

392.86 2.02E-01

393.24 2.76E-01

393.61 3.54E-01

393.99 2.12E-01

394.37 2.51E-01

394.75 2.41E-01

395.13 2.76E-01

395.5 2.56E-01

395.88 2.78E-01

396.26 3.01E-01

396.64 3.37E-01

397.02 2.77E-01

397.39 2.96E-01

397.77 2.86E-01

398.15 2.98E-01

398.53 2.74E-01

398.9 3.48E-01

399.28 3.05E-01

399.66 3.59E-01

400.04 3.21E-01

400.41 3.31E-01

400.79 3.19E-01

401.17 3.34E-01

401.55 2.91E-01

401.92 3.39E-01

402.3 3.22E-01

402.68 2.78E-01

403.06 3.08E-01

403.43 3.19E-01

403.81 3.26E-01

404.19 3.19E-01

404.56 3.10E-01

404.94 3.26E-01

405.32 3.27E-01

405.7 3.48E-01

406.07 3.27E-01

406.45 3.21E-01

406.83 3.37E-01

407.2 3.67E-01

407.58 3.61E-01

407.96 3.80E-01

408.33 3.29E-01

408.71 3.45E-01

409.09 3.67E-01

409.46 3.52E-01

409.84 3.49E-01

410.22 3.61E-01

410.59 3.69E-01

410.97 3.50E-01

411.35 3.34E-01

411.72 3.64E-01

412.1 3.64E-01

412.48 3.80E-01

Je kan hier over afzonderlijke een lineaire interpolatie tussen 2 elementen gaan doen maar het lijkt me in dit geval beter om een lineaire regressie op het geheel te doen, een curve fit op deze gegevens.

okeej regesie klinkt leuk maar uhh..... hoe doe ik dat is er mischien een formule voor of zo ???? ( of mischien iets met excel heb alles daar instaan ! )

Excel is hier niet ideaal voor, maar toevallig kan het wel nog net met lineaire regressie werken geloof ik.

Maar ik heb je punten even geplot en een lineair verband komt niet echt boven water drijven...

Wil je dat het een rechte lijn is, die dus niet exact door al je meetpunten heen zal gaan? Of juist dat hij wel exact met alle meetpunten overeenkomt, waardoor het een beetje een bobbelige functie zal worden.

In het geval van lineaire regressie heb ik het je eens geprobeerd in Excel.

Ik vind de rechte 0.006x - 2.1076 met R = 0.6517 en dat is niet echt denderend...

De data is een iradiance specterum van een lichtbron ik heb deze data van een spectrometer waar ik mee werk. En het is blackbody curve dus het mag best hobbelig zijn.....

Niet met excel, maar iets anders:

Linear Fit: y=a+bx

Coefficient Data:

a = -2.1536063

b = 0.0061346103



De lineaire was wel niet de beste, kwadratische of polynomen (3e/4e-graad) fitten beter.

Dan ben je beter af met een stuksgewijze lineaire interpolatie (tussen elk paar opvolgende punten zo'n lineaire formule als ik hierboven gaf), of nog beter een cubische interpolatie.

Hieronder staat alle data...

379.21 3.65E-02

379.59 1.05E-01

379.97 2.57E-01

380.35 2.05E-01

380.73 3.38E-01

381.11 1.48E-01

381.49 1.91E-01

381.87 2.40E-01

382.25 1.94E-01

382.63 1.99E-01

383.01 2.81E-01

383.39 1.04E-01

383.77 2.03E-01

384.15 2.41E-01

384.53 1.76E-01

384.9 3.16E-01

385.28 2.58E-01

385.66 2.90E-01

386.04 1.81E-01

386.42 1.93E-01

386.8 1.88E-01

387.18 2.02E-01

387.56 2.68E-01

387.94 1.66E-01

388.31 1.38E-01

388.69 2.21E-01

389.07 1.72E-01

389.45 2.95E-01

389.83 2.22E-01

390.21 1.96E-01

390.59 2.83E-01

390.97 2.25E-01

391.34 2.19E-01

391.72 2.53E-01

392.1 1.58E-01

392.48 2.92E-01

392.86 2.02E-01

393.24 2.76E-01

393.61 3.54E-01

393.99 2.12E-01

394.37 2.51E-01

394.75 2.41E-01

395.13 2.76E-01

395.5 2.56E-01

395.88 2.78E-01

396.26 3.01E-01

396.64 3.37E-01

397.02 2.77E-01

397.39 2.96E-01

397.77 2.86E-01

398.15 2.98E-01

398.53 2.74E-01

398.9 3.48E-01

399.28 3.05E-01

399.66 3.59E-01

400.04 3.21E-01

400.41 3.31E-01

400.79 3.19E-01

401.17 3.34E-01

401.55 2.91E-01

401.92 3.39E-01

402.3 3.22E-01

402.68 2.78E-01

403.06 3.08E-01

403.43 3.19E-01

403.81 3.26E-01

404.19 3.19E-01

404.56 3.10E-01

404.94 3.26E-01

405.32 3.27E-01

405.7 3.48E-01

406.07 3.27E-01

406.45 3.21E-01

406.83 3.37E-01

407.2 3.67E-01

407.58 3.61E-01

407.96 3.80E-01

408.33 3.29E-01

408.71 3.45E-01

409.09 3.67E-01

409.46 3.52E-01

409.84 3.49E-01

410.22 3.61E-01

410.59 3.69E-01

410.97 3.50E-01

411.35 3.34E-01

411.72 3.64E-01

412.1 3.64E-01

412.48 3.80E-01

412.85 3.90E-01

413.23 3.88E-01

413.6 3.86E-01

413.98 3.82E-01

414.36 4.00E-01

414.73 3.84E-01

415.11 3.93E-01

415.48 4.16E-01

415.86 4.07E-01

416.24 3.89E-01

416.61 4.01E-01

416.99 3.97E-01

417.36 4.27E-01

417.74 4.17E-01

418.11 4.34E-01

418.49 4.30E-01

418.87 4.38E-01

419.24 4.22E-01

419.62 4.06E-01

419.99 4.17E-01

420.37 4.20E-01

420.74 4.25E-01

421.12 4.27E-01

421.49 4.43E-01

421.87 4.38E-01

422.25 4.53E-01

422.62 4.34E-01

423 4.42E-01

423.37 4.18E-01

423.75 4.58E-01

424.12 4.46E-01

424.5 4.43E-01

424.87 4.53E-01

425.25 4.52E-01

425.62 4.55E-01

426 4.59E-01

426.37 4.68E-01

426.75 4.99E-01

427.12 4.61E-01

427.5 4.73E-01

427.87 4.46E-01

428.24 4.77E-01

428.62 4.85E-01

428.99 4.66E-01

429.37 4.98E-01

429.74 4.91E-01

430.12 4.87E-01

430.49 4.87E-01

430.87 4.87E-01

431.24 4.63E-01

431.61 4.50E-01

431.99 4.77E-01

432.36 4.59E-01

432.74 4.69E-01

433.11 4.88E-01

433.49 4.70E-01

433.86 4.78E-01

434.23 4.87E-01

434.61 5.02E-01

434.98 4.84E-01

435.36 4.95E-01

435.73 5.08E-01

436.1 4.96E-01

436.48 5.06E-01

436.85 5.05E-01

437.22 4.99E-01

437.6 5.02E-01

437.97 5.01E-01

438.35 5.11E-01

438.72 5.10E-01

439.09 5.24E-01

439.47 5.25E-01

439.84 5.22E-01

440.21 5.41E-01

440.59 5.37E-01

440.96 5.54E-01

441.33 5.53E-01

441.71 5.56E-01

442.08 5.54E-01

442.45 5.58E-01

442.83 5.48E-01

443.2 5.84E-01

443.57 5.78E-01

443.95 5.66E-01

444.32 5.86E-01

444.69 5.73E-01

445.06 5.78E-01

445.44 5.87E-01

445.81 5.64E-01

446.18 6.09E-01

446.56 6.00E-01

446.93 5.93E-01

447.3 5.89E-01

447.67 5.90E-01

448.05 5.83E-01

448.42 5.86E-01

448.79 6.09E-01

449.16 6.22E-01

449.54 6.12E-01

449.91 5.93E-01

450.28 6.10E-01

450.65 6.08E-01

451.03 6.19E-01

451.4 6.31E-01

451.77 6.34E-01

452.14 6.28E-01

452.51 6.20E-01

452.89 6.36E-01

453.26 6.36E-01

453.63 6.28E-01

454 6.56E-01

454.37 6.42E-01

454.75 6.52E-01

455.12 6.35E-01

455.49 6.50E-01

455.86 6.58E-01

456.23 6.48E-01

456.6 6.85E-01

456.98 6.60E-01

457.35 6.59E-01

457.72 6.66E-01

458.09 6.71E-01

458.46 6.64E-01

458.83 6.77E-01

459.2 6.65E-01

459.58 6.88E-01

459.95 7.01E-01

460.32 6.99E-01

460.69 6.90E-01

461.06 6.92E-01

461.43 7.04E-01

461.8 6.84E-01

462.17 6.76E-01

462.55 6.75E-01

462.92 7.09E-01

463.29 7.18E-01

463.66 7.14E-01

464.03 6.93E-01

464.4 7.38E-01

464.77 7.30E-01

465.14 7.09E-01

465.51 7.24E-01

465.88 7.29E-01

466.25 7.42E-01

466.62 7.19E-01

466.99 7.42E-01

467.37 7.43E-01

467.74 7.46E-01

468.11 7.31E-01

468.48 7.36E-01

468.85 7.50E-01

469.22 7.29E-01

469.59 7.41E-01

469.96 7.69E-01

470.33 7.66E-01

470.7 7.44E-01

471.07 7.82E-01

471.44 7.69E-01

471.81 7.71E-01

472.18 7.79E-01

472.55 7.97E-01

472.92 7.73E-01

473.29 7.81E-01

473.66 7.94E-01

474.03 7.84E-01

474.4 7.98E-01

474.77 8.05E-01

475.14 8.09E-01

475.51 7.91E-01

475.88 8.29E-01

476.25 8.25E-01

476.61 7.93E-01

476.98 8.10E-01

477.35 8.26E-01

477.72 8.15E-01

478.09 8.22E-01

478.46 8.25E-01

478.83 8.08E-01

479.2 8.17E-01

479.57 8.16E-01

479.94 8.13E-01

480.31 8.19E-01

480.68 8.28E-01

481.05 8.17E-01

481.41 8.32E-01

481.78 8.09E-01

482.15 8.31E-01

482.52 8.34E-01

482.89 8.21E-01

483.26 8.34E-01

483.63 8.18E-01

484 8.33E-01

484.36 8.26E-01

484.73 8.35E-01

485.1 8.46E-01

485.47 8.46E-01

485.84 8.36E-01

486.21 8.49E-01

486.58 8.46E-01

486.94 8.48E-01

487.31 8.56E-01

487.68 8.47E-01

488.05 8.39E-01

488.42 8.40E-01

488.79 8.44E-01

489.15 8.45E-01

489.52 8.48E-01

489.89 8.54E-01

490.26 8.55E-01

490.63 8.57E-01

490.99 8.61E-01

491.36 8.62E-01

491.73 8.67E-01

492.1 8.68E-01

492.46 8.69E-01

492.83 8.73E-01

493.2 8.76E-01

493.57 8.78E-01

493.94 8.81E-01

494.3 9.02E-01

494.67 9.13E-01

495.04 9.11E-01

495.41 9.38E-01

495.77 9.67E-01

496.14 9.67E-01

496.51 9.22E-01

496.87 9.43E-01

497.24 9.41E-01

497.61 9.42E-01

497.98 9.63E-01

498.34 9.42E-01

498.71 9.53E-01

499.08 9.55E-01

499.44 9.72E-01

499.81 9.73E-01

500.18 9.76E-01

500.54 9.65E-01

500.91 9.76E-01

501.28 9.88E-01

501.64 9.91E-01

502.01 9.95E-01

502.38 9.96E-01

502.74 9.81E-01

503.11 9.97E-01

503.48 1.01E+00

503.84 1.00E+00

504.21 1.02E+00

504.58 1.03E+00

504.94 1.03E+00

505.31 1.03E+00

505.68 1.04E+00

506.04 1.04E+00

506.41 1.04E+00

506.77 1.04E+00

507.14 1.06E+00

507.51 1.06E+00

507.87 1.06E+00

508.24 1.08E+00

508.6 1.06E+00

508.97 1.06E+00

509.34 1.08E+00

509.7 1.07E+00

510.07 1.10E+00

510.43 1.09E+00

510.8 1.07E+00

511.16 1.09E+00

511.53 1.09E+00

511.9 1.10E+00

512.26 1.10E+00

512.63 1.11E+00

512.99 1.12E+00

513.36 1.10E+00

513.72 1.12E+00

514.09 1.10E+00

514.45 1.10E+00

514.82 1.11E+00

515.18 1.12E+00

515.55 1.13E+00

515.91 1.14E+00

516.28 1.12E+00

516.64 1.12E+00

517.01 1.14E+00

517.37 1.13E+00

517.74 1.14E+00

518.1 1.17E+00

518.47 1.16E+00

518.83 1.14E+00

519.2 1.15E+00

519.56 1.17E+00

519.93 1.16E+00

520.29 1.16E+00

520.66 1.16E+00

521.02 1.17E+00

521.39 1.18E+00

521.75 1.17E+00

522.11 1.17E+00

522.48 1.17E+00

522.84 1.19E+00

523.21 1.18E+00

523.57 1.20E+00

523.94 1.20E+00

524.3 1.20E+00

524.66 1.22E+00

525.03 1.20E+00

525.39 1.22E+00

525.76 1.21E+00

526.12 1.22E+00

526.48 1.20E+00

526.85 1.21E+00

527.21 1.23E+00

527.58 1.22E+00

527.94 1.23E+00

528.3 1.23E+00

528.67 1.24E+00

529.03 1.24E+00

529.39 1.24E+00

529.76 1.24E+00

530.12 1.23E+00

530.48 1.26E+00

530.85 1.25E+00

531.21 1.24E+00

531.57 1.24E+00

531.94 1.26E+00

532.3 1.25E+00

532.66 1.25E+00

533.03 1.24E+00

533.39 1.24E+00

533.75 1.24E+00

534.12 1.25E+00

534.48 1.24E+00

534.84 1.21E+00

535.2 1.21E+00

535.57 1.21E+00

535.93 1.21E+00

536.29 1.22E+00

536.66 1.22E+00

537.02 1.22E+00

537.38 1.23E+00

537.74 1.23E+00

538.11 1.23E+00

538.47 1.23E+00

538.83 1.24E+00

539.19 1.24E+00

539.56 1.24E+00

539.92 1.25E+00

540.28 1.25E+00

540.64 1.25E+00

541 1.26E+00

541.37 1.26E+00

541.73 1.26E+00

542.09 1.27E+00

542.45 1.27E+00

542.81 1.27E+00

543.18 1.27E+00

543.54 1.28E+00

543.9 1.28E+00

544.26 1.28E+00

544.62 1.29E+00

544.99 1.29E+00

545.35 1.29E+00

545.71 1.29E+00

546.07 1.30E+00

546.43 1.30E+00

546.79 1.30E+00

547.15 1.31E+00

547.52 1.31E+00

547.88 1.31E+00

548.24 1.31E+00

548.6 1.32E+00

548.96 1.32E+00

549.32 1.33E+00

549.68 1.33E+00

550.04 1.33E+00

550.41 1.33E+00

550.77 1.33E+00

551.13 1.34E+00

551.49 1.34E+00

551.85 1.34E+00

552.21 1.35E+00

552.57 1.35E+00

552.93 1.36E+00

553.29 1.35E+00

553.65 1.36E+00

554.01 1.36E+00

554.37 1.36E+00

554.74 1.37E+00

555.1 1.37E+00

555.46 1.37E+00

555.82 1.37E+00

556.18 1.38E+00

556.54 1.38E+00

556.9 1.39E+00

557.26 1.39E+00

557.62 1.65E+00

557.98 1.47E+00

558.34 1.46E+00

558.7 1.49E+00

559.06 1.48E+00

559.42 1.49E+00

559.78 1.49E+00

560.14 1.48E+00

560.5 1.48E+00

560.86 1.50E+00

561.22 1.50E+00

561.58 1.51E+00

561.94 1.50E+00

562.3 1.51E+00

562.66 1.50E+00

563.02 1.54E+00

563.38 1.52E+00

563.73 1.53E+00

564.09 1.54E+00

564.45 1.54E+00

564.81 1.56E+00

565.17 1.58E+00

565.53 1.55E+00

565.89 1.57E+00

566.25 1.55E+00

566.61 1.55E+00

566.97 1.55E+00

567.33 1.56E+00

567.69 1.58E+00

568.05 1.59E+00

568.4 1.58E+00

568.76 1.58E+00

569.12 1.56E+00

569.48 1.60E+00

569.84 1.60E+00

570.2 1.58E+00

570.56 1.56E+00

570.92 1.60E+00

571.27 1.58E+00

571.63 1.59E+00

571.99 1.60E+00

572.35 1.60E+00

572.71 1.62E+00

573.07 1.59E+00

573.42 1.62E+00

573.78 1.62E+00

574.14 1.62E+00

574.5 1.60E+00

574.86 1.62E+00

575.22 1.59E+00

575.57 1.61E+00

575.93 1.59E+00

576.29 1.60E+00

576.65 1.60E+00

577 1.57E+00

577.36 1.56E+00

577.72 1.55E+00

578.08 1.56E+00

578.44 1.56E+00

578.79 1.56E+00

579.15 1.57E+00

579.51 1.57E+00

579.87 1.57E+00

580.22 1.58E+00

580.58 1.58E+00

580.94 1.58E+00

581.3 1.58E+00

581.65 1.58E+00

582.01 1.59E+00

582.37 1.59E+00

582.72 1.60E+00

583.08 1.60E+00

583.44 1.60E+00

583.8 1.61E+00

584.15 1.61E+00

584.51 1.61E+00

584.87 1.61E+00

585.22 1.62E+00

585.58 1.62E+00

585.94 1.62E+00

586.29 1.63E+00

586.65 1.63E+00

587.01 1.63E+00

587.36 1.64E+00

587.72 1.64E+00

588.08 1.64E+00

588.43 1.65E+00

588.79 1.64E+00

589.15 1.65E+00

589.5 1.66E+00

589.86 1.66E+00

590.21 1.66E+00

590.57 1.66E+00

590.93 1.66E+00

591.28 1.67E+00

591.64 1.67E+00

592 1.67E+00

592.35 1.68E+00

592.71 1.68E+00

593.06 1.68E+00

593.42 1.69E+00

593.77 1.69E+00

594.13 1.69E+00

594.49 1.69E+00

594.84 1.69E+00

595.2 1.70E+00

595.55 1.70E+00

595.91 1.71E+00

596.26 1.71E+00

596.62 1.71E+00

596.97 1.71E+00

597.33 1.71E+00

597.69 1.72E+00

598.04 1.72E+00

598.4 1.73E+00

598.75 1.73E+00

599.11 1.73E+00

599.46 1.73E+00

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1003.21 3.18E+00

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1012.48 3.13E+00

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1013.06 2.97E+00

1013.35 2.01E+00

1013.63 3.43E+00

1013.92 3.14E+00

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1020.25 2.88E+00

1020.54 2.49E+00

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1021.11 2.59E+00

1021.4 3.22E+00

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1021.97 2.88E+00

1022.26 3.00E+00

1022.54 1.56E+00

1022.83 2.16E+00

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1024.26 2.35E+00

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1025.12 2.72E+00

1025.41 3.68E+00

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1027.12 9.90E-01

1027.41 3.64E+00

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1031.68 1.94E+00

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1032.25 2.58E+00

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1032.82 2.58E+00

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1033.39 2.43E+00

1033.67 3.91E+00

1033.96 1.80E+00

1034.24 2.60E+00

1034.53 2.86E+00

1034.81 3.01E+00

1035.09 1.56E+00

1035.38 1.24E+00

1035.66 2.71E+00

1035.94 4.23E-01

1036.23 2.48E+00

1036.51 3.29E+00

1036.8 2.09E+00

1037.08 3.33E+00

1037.36 2.40E+00

1037.65 2.85E+00

1037.93 2.44E+00

1038.21 2.71E+00

1038.49 3.39E+00

1038.78 3.08E+00

1039.06 3.30E+00

1039.34 3.13E+00

1039.63 3.25E+00

1039.91 3.15E+00

1040.19 2.35E+00

1040.48 2.30E+00

1040.76 2.30E+00

1041.04 2.49E+00

1041.32 3.18E+00

1041.61 2.31E+00

1041.89 1.94E+00

1042.17 3.10E+00

1042.45 4.19E+00

1042.74 3.08E+00

1043.02 4.92E+00

1043.3 2.27E+00

1043.58 1.42E+00

1043.86 1.77E+00

1044.15 2.65E+00

1044.43 3.71E+00

1044.71 2.50E+00

1044.99 2.43E+00

1045.27 2.84E+00

1045.55 2.38E+00

1045.84 2.41E+00

1046.12 8.10E+00

1046.4 1.80E+00

1046.68 2.99E+00

1046.96 3.84E+00

1047.24 1.70E+00

1047.52 4.01E+00

1047.81 1.77E+00

1048.09 3.62E+00

1048.37 2.00E+00

1048.65 2.32E+00

1048.93 4.04E+00

1049.21 4.71E+00

1049.49 3.00E+00

1049.77 1.84E+00

1050.05 1.70E+00

1050.33 1.34E+00

1050.61 1.81E+00

1050.89 2.54E+00

1051.17 2.68E+00

1051.46 2.57E+00

1051.74 2.99E+00

1052.02 3.29E+00

1052.3 1.72E+00

1052.58 2.12E+00

1052.86 5.39E+00

1053.14 1.75E+00

1053.42 2.15E+00

1053.7 1.97E+00

1053.98 2.82E+00

1054.26 2.05E+00

Ik dacht zelf eerst er een kruis product je op los laten maar da was ook geen optie....

Hiermee krijg ik fits met correlatie tot 0.92 ongeveer, met kwadratische en exponentiële fits.

De kwadratische geeft bvb:

Quadratic Fit: y=a+bx+cx^2

Coefficient Data:

a = -6.4589922

b = 0.020839973

c = -1.1438177e-005