AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
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Algorithm: Reverse UTPM of <strong>the</strong> Rectangular QR Decomposition<br />
input : [A] D = [A 0 , . . . , A D− 1], where A d ∈ R M×N , d = 0, . . . , D − 1, M ≥ N.<br />
output : [Q] D = [Q 0 , . . . , Q D− 1] m<strong>at</strong>rix with orthonormal column vectors, where Q d ∈ R M×N ,<br />
d = 0, . . . , D − 1<br />
output : [R] D = [R 0 , . . . , R D− 1] upper triangular, where R d ∈ R N×N , d = 0, . . . , D − 1<br />
input/output: [Ā] D = [Ā 0 , . . . , Ā D− 1], where Ā d ∈ R M×N , d = 0, . . . , D − 1, M ≥ N.<br />
input : [¯Q] D = [¯Q 0 , . . . , ¯Q D− 1], where ¯Q d ∈ R M×N , d = 0, . . . , D − 1<br />
input : [¯R] D = [¯R 0 , . . . , ¯R D− 1], where ¯R d ∈ R N×N , d = 0, . . . , D − 1<br />
[Ā] D = [Ā] D + ([¯Q] D − [Q] D [Q] T D [¯Q] D )[R] −T<br />
D )<br />
+[Q] D<br />
“[¯R] D + P L ◦ `[R] D [¯R] T D − [¯R] D [R] T D + [Q]T D [¯Q] D − [¯Q] T D [Q] ´ ”<br />
D [R]<br />
−T<br />
D<br />
Sebastian F. Walter, HU <strong>Berlin</strong> () Not So Short <strong>Tutorial</strong> OnAlgorithmic Differenti<strong>at</strong>ion Wednesday, 04.06.2010 27 / 39
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