Difference between revisions of "Hdot.m"

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#REDIRECT [[Ttclass/hdot.m]]
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{{DISPLAYTITLE:hdot.m}} __NOTOC__
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Hadamard route to Frobenius matrix product. This function computes the Frobenius inner product of two numerical arrays using elementwise multiplication.
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==Syntax==
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    H=hdot(A,B)
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==Parameters==
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    A,B - square matrices of the same size
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==Outputs==
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    H - Frobenius inner product of A and B
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==Notes==
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For matrices, the function is a faster replacement for `trace(A'*B)` because
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    trace(A'*B)=sum(conj(A).*B,'all')
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and the elementwise route only needs O(n<sup>2</sup>) multiplications for square n-by-n matrices, compared to O(n<sup>3</sup>) for matrix multiplication followed by the trace.
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==See also==
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[[ttclass/hdot.m]], [[cheap_norm.m]], [[krondelta.m]], [[tikhonov.m]], [[acomm.m]], [[arnoldi.m]], [[atranspose.m]], [[aux_mat.m]], [[binpack.m]], [[cheb_coeff.m]], [[clean_up.m]], [[dirdiff.m]], [[eigenfields.m]], [[expdrop.m]], [[expmint.m]], [[expmint2.m]], [[fftdiff.m]], [[fourdif.m]], [[fourlap.m]], [[frob_chop.m]], [[gaussfun.m]], [[herm_spline.m]], [[jacobianest.m]], [[keep_rank.m]], [[kronm_new.m]], [[logfactorial.m]], [[lorentzcon.m]], [[lorentzfun.m]], [[md5_hash.m]], [[mprealloc.m]], [[remncomm.m]], [[remtrace.m]], [[rspert.m]], [[rspt_eig.m]], [[snormpdf.m]], [[svd_shrink.m]], [[tikhoind.m]], [[trapdiff.m]], [[unit_oper.m]], [[unit_state.m]], [[vvpert.m]], [[Kernel_utilities]]
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''Version 2.11, authors: [[Ilya Kuprov]]''

Latest revision as of 06:48, 30 August 2026

Hadamard route to Frobenius matrix product. This function computes the Frobenius inner product of two numerical arrays using elementwise multiplication.

Syntax

    H=hdot(A,B)

Parameters

    A,B - square matrices of the same size

Outputs

    H - Frobenius inner product of A and B

Notes

For matrices, the function is a faster replacement for `trace(A'*B)` because

    trace(A'*B)=sum(conj(A).*B,'all')

and the elementwise route only needs O(n2) multiplications for square n-by-n matrices, compared to O(n3) for matrix multiplication followed by the trace.

See also

ttclass/hdot.m, cheap_norm.m, krondelta.m, tikhonov.m, acomm.m, arnoldi.m, atranspose.m, aux_mat.m, binpack.m, cheb_coeff.m, clean_up.m, dirdiff.m, eigenfields.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, fourdif.m, fourlap.m, frob_chop.m, gaussfun.m, herm_spline.m, jacobianest.m, keep_rank.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, remncomm.m, remtrace.m, rspert.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, trapdiff.m, unit_oper.m, unit_state.m, vvpert.m, Kernel_utilities

Version 2.11, authors: Ilya Kuprov