2aa85cdb-1110-4faf-b934-ad44ab574a17 10 4 5 fraction

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Pad a Matrix

x y φ x y * :

Ω 812 φ matrix maple :

Explain ::

Ω 12345678910111224681012141618202224369121518212427303336481216202428323640444851015202530354045505560612182430364248546066727142128354249566370778481624324048566472808896812 mat

This padding is the basic padding to zoom a grayscale image. RGB requires each R,G,B similar padding. This demo is for a matrix. If the matrix is a grayscale, in 'A' we plug its Fourier 3D "cfft(M)" and recover the zoomed image "scale[Re(icfft(S))]. Note the symmetry for even row/col in Ω .

M nc nr Pad A M : insert 'nc' cols i 1 A rows range j 1 nc range vert i j el 0 : for for a A 1 A rows 1 A cols 2 / Floor submatrix : b A 1 A rows A cols 2 / Floor 1 + A cols submatrix : S a vert b augment transpose : insert 'nr' rows in the transpose 'S' i 1 S rows range j 1 nr range horiz i j el 0 : for for a S 1 S rows 1 S cols 2 / Floor submatrix : b S 1 S rows S cols 2 / Floor 1 + S cols submatrix : S a horiz b augment transpose : 111 line :

Ω 33 Pad 123456000789101112246810120001416182022243691215180002124273033364812162024000283236404448000000000000000000000000000000000000000000000510152025300003540455055606121824303600042485460667271421283542000495663707784816243240480005664728088961115 mat