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wavelet3.c
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/*
=========================================================================
2-dimensional Daubechies D4 and Haar wavelet transforms on arbitrary
sized arrays of 3-tuples. Array boundaries are extended as constants,
which introduces padding coefficients.
Compile with -DWAVELET_TEST_2DPAD to build standalone unit tests.
The implementation here is mainly distilled from the following sources:
-- Filip Wasilewski's pywavelets:
https://github.com/PyWavelets/pywt/tree/master/pywt/_extensions/c
[D4 with boundary condition handling via padding, arbitrary sizes]
-- Ingrid Daubechies and Wim Sweldens, "Factoring Wavelet Tranforms into
Lifting Steps", section 7.5:
https://services.math.duke.edu/~ingrid/publications/J_Four_Anal_Appl_4_p247.pdf
[Lifting scheme on D4]
-- Ian Kaplan's webpages on wavelets and signal processing::
http://bearcave.com/misl/misl_tech/wavelets/daubechies/index.html
http://bearcave.com/misl/misl_tech/wavelets/lifting/basiclift.html
[Lifting scheme on D4]
-- Stefan Moebius' TurboWavelets.Net:
https://github.com/codeprof/TurboWavelets.Net/tree/master/TurboWavelets
[Boundary condition handling with arbitrary sizes, backreferencing]
-- "Numerical Recipes in C", chapter 13.10:
http://cacs.usc.edu/education/cs653/NRC-c13.10-Wavelets.pdf
[Linear algebra (matrix mult.) implementation of D4]
Roland Schregle (roland.schregle@{hslu.ch, gmail.com})
(c) Lucerne University of Applied Sciences and Arts,
supported by the Swiss National Science Foundation
(SNSF #179067, "Light Fields for Spatio-Temporal Glare Assessment")
=========================================================================
$Id$
*/
#include "wavelet2.h"
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <stdio.h>
/* Aggregated Dabuechies D4 coeffs for padding at left boundary */
static const WAVELET_COEFF h4Bound = H4NORM * (7 + SQRT3),
g4Bound = H4NORM * (1 + SQRT3);
/*
h4Bound = h4 [0] + h4 [1] + h4 [2];
g4Bound = g4 [0] + g4 [1] + g4 [2];
*/
static unsigned padHaarStep2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned len
)
/*
Single iteration of forward 2D Haar wavelet transform with padding on
array y of arbitrary size (len x len) containing 3-tuples. This variant
uses constant boundary extension. The transform is performed over y's
2nd axis (i.e. horizontally, assuming row-major addressing as per C
convention). Note the triplets per array element are _not_ decorrelated,
but transformed independently.
The wavelet coefficients are returned in the *TRANSPOSED* output array
yt, of identical dimensions to y. The transpose arranges the generated
coefficients vertically, and prepares the array for another transform
over its 2nd axis in a subsequent call (this time as input y). The
result of a subsequent transform restores yt to y's original orientation,
in which case both horizontal and vertical axes have been decorrelated.
Returns array dimension len on success, else 0.
*/
{
const unsigned hLen = -(-(signed)len >> 1);
int h, i, j, k;
#ifdef WAVELET_DBG
static unsigned axis = 0;
#endif
if (len < 2 || !y || !yt)
/* Input shorter than wavelet support, or no input/output */
return 0;
#ifdef WAVELET_DBG
clearCoeffs2(yt, len);
#endif
/* NOTE: yt is transposed on the fly such that the next function call
* transforms over the alternate axis. This is done by simply swapping
* the indices during assignment */
for (i = 0; i < len; i++) {
for (j = 0; j <= len - 2; j += 2) {
h = j >> 1;
for (k = 0; k < 3; k++) {
/* Smooth/approx/avg/lowpass */
yt [h ] [i] [k] = h2 * (
y [i] [j ] [k] +
y [i] [j + 1] [k]
);
/* Detail/diff/highpass */
yt [h + hLen] [i] [k] = h2 * (
y [i] [j ] [k] -
y [i] [j + 1] [k]
);
}
}
if (len & 1) {
/* Odd length; pad with last value as additional approx term */
for (k = 0; k < 3; k++)
/* Smooth/approx/avg/lowpass */
yt [hLen - 1] [i] [k] = y [i] [len - 1] [k];
}
}
#ifdef WAVELET_DBG
printf("%s FWD HAAR (%d x %d)\n", axis ? "VERT" : "HORIZ", len, len);
dumpCoeffs2(y, yt, len, len, 0);
putchar('\n');
axis ^= 1;
#endif
return len;
}
static unsigned padHaarInvStep2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned len
)
/*
Single iteration of inverse 2D Haar wavelet transform with padding on
array y of arbitrary size (len x len) containing 3-tuples. This reverses
the forward transform above. The transform is inverted over y's 2nd axis
(i.e. horizontally, assuming row-major addressing as per C convention).
The inverted coefficients are returned in the *TRANSPOSED* output array
yt, of identical dimensions to y. The transpose arranges the inverted
coefficients vertically, and prepares the array for another inverse
transform over its 2nd axis in a subsequent call (this time as input y).
The result of a subsequent inverse transform restores yt to y's original
orientation, in which case both horizontal and vertical axes have been
inversely transformed.
Returns array dimension len on success, else 0.
*/
{
const unsigned hLen = -(-(signed)len >> 1);
int h, i, j, k;
#ifdef WAVELET_DBG
static unsigned axis = 1;
#endif
if (len < 2 || !y || !yt)
/* Too few coeffs for reconstruction, or no input/output */
return 0;
#ifdef WAVELET_DBG
clearCoeffs2(yt, len);
#endif
/* NOTE: i, j are swapped relative to the forward transform, as axis
* order is now reversed. */
/* NOTE: yt is transposed on the fly such that the next function call
* inverts over the alternate axis. This is done by simply swapping
* the indices during assignment */
for (i = 0; i < len; i++) {
for (j = 0; j <= len - 2; j += 2) {
h = j >> 1;
for (k = 0; k < 3; k++) {
yt [i] [j ] [k] = h2 * (
y [h ] [i] [k] + /* Approx */
y [h + hLen] [i] [k] /* Detail */
);
yt [i] [j + 1] [k] = h2 * (
y [h ] [i] [k] - /* Approx */
y [h + hLen] [i] [k] /* Detail */
);
}
}
if (len & 1) {
/* Odd length; pad additional value from last approximation term */
for (k = 0; k < 3; k++)
yt [i] [len - 1] [k] = y [hLen - 1] [i] [k];
}
}
#ifdef WAVELET_DBG
printf("%s INV HAAR (%d x %d)\n", axis ? "VERT" : "HORIZ", len, len);
dumpCoeffs2(y, yt, len, len, 0);
putchar('\n');
axis ^= 1;
#endif
return len;
}
static unsigned padD4Step2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned yLen, unsigned ytOffset
)
/*
Single iteration of forward 2D Daubechies D4 wavelet transform with
boundary padding on array y containing samples of 3-tuples.
This variant uses constant boundary extension, which results in padding
coefficients. The transform is performed over y's 2nd axis (i.e.
horizontally, assuming row-major addressing as per C convention). Note
the triplets per array element are _not_ decorrelated, but transformed
independently.
The output wavelet coefficients are returned in the *TRANSPOSED* array
yt. The transpose arranges the generated coefficients vertically,
and prepares the array for another transform over its 2nd axis in a
subsequent call (this time as input y). The result of a subsequent
transform restores yt to y's original orientation, in which case both
horizontal and vertical axes have been decorrelated.
Both the input array y and output array yt must be large enough to also
accommodate the additional padding coefficients introduced at the
boundaries. The number of output coefficient pairs ytLen returned in yt
is obtained as return value, and can be interrogated beforehand without
performing a transform by passing either y or yt as NULL.
The approximation coefficients are returned in yt [0..ytLen-1] [i], while
the details are returned in yt [ytOffset..ytOffset+ytLen-1] [i]. The
offset ytOffset must be supplied by the caller to accommodate the detail
coefficients (plus padding!) without clobbering the approximation
coefficients (again, plus padding!). Consequently, there is a gap
between the approximation coefficients in the upper left of the matrix,
and the detail coefficients in the lower right. This gap shrinks and
shifts toward the upper left with each iteration.
The following schema indicates the matrix contents during the transform
(see the unit test output when compiled with WAVELET_TEST_2DPAD):
----> j
+----------+--------------+ +-----------+-------------+
| | y_ij | | | S(y_ji) | |
| +----------+ | (H_k xform)^T +-----------+ |
v | | ----------> | |
i | | +-----------+ |
| | | D(y_ji) | |
+-------------------------+ +-------------------------+
----> i
+----------+--------------+ +----------+---+----------+
| | S(y_ji) | | |S(S(y_ij))| |S(D(y_ij))|
| +----------+ | (V_k xform)^T +----------+ +----------+
v | | ----------> | |
j +----------+ | +----------+ +----------+
| D(y_ji) | | |D(S(y_ij))| |D(D(y_ij))|
+-------------------------+ +----------+---+----------+
... ... ...
... ... ...
+------+------+--------+--------+----------------+
|SS_n-1|SD_n-1| | | |
|------+------+ SD_n-2 | | |
+DS_n-1|DD_n-1+--------+ . . . | SD_0 |
+------+----+-+--------+ | |
| DS_n-2 | | DD_n-2 | +----------------+
(V_n-1 xform)^T +-----------+ +--------+ . . . |
----------> | . . . . . |
| . . . . . |
+----------------+ +----------------+
| | | |
| DS_0 | . . . . . . | DD_0 |
| | | |
| | | |
+----------------+--------------+----------------+
where i, j are the array indices of the outer resp. inner loop, S(y_ij)
D(y_ij) are approximation resp. details coefficients of input y_ij
(itself either the original signal or approximation/detail coefficients
from previous iterations), and H_k, V_k are the horizontal resp.
vertical transforms of the k-th (out of the maximum n) iteration.
*/
{
unsigned h, i, j, k, l, i0 = 0, iN;
/* Number of output coeff pairs ytLen, incl. boundary padding, and
dimension of entire array */
const unsigned ytLen = (yLen + 3) >> 1, ytTotalLen = ytOffset + ytLen;
#ifdef WAVELET_DBG
static unsigned axis = 0;
#endif
if (y && yt && yLen >= 2) {
/* FWD TRANSFORM GOTCHAS:
*
* i, j are swapped relative to the forward transform, as axis
* order is now reversed.
*
* yt is transposed on the fly such that the next function
* call transforms over the alternate axis. This is done by simply
* swapping the indices during assignment.
*
* In the initial horizontal transform, the input array only contains
* a set of approximation coefficients (or the original signal) at
* y [0..yLen-1] [0..yLen-1].
*
* In the subsequent vertical transform, the input array then contains
* two sets of coefficients from the preceding horizontal transform:
* approximation coeffs y [0..ytLen-1] [0..ytLen-1] and detail coeffs
* y [ytOffset..ytTotalLen-1] [ytOffset..ytTotalLen-1]. In this case,
* the loop below is iterated twice with an offset yOffset to select
* both sets of coefficients to transform. Note the detail coeffs are
* selected first to facilitate the looping logic; if i0==0 at the end
* of the loop (i.e. approx coeffs were selected), it terminates.
*/
do {
i0 ^= ytOffset * axis;
iN = i0 ? ytTotalLen : yLen;
for (i = i0; i < iN; i++) {
/* First iteration (j = -2); pad coeffs at left edge with
* constant boundary extension (note multiple factoring of
* y [i][0] via aggregated coefficients h4Bound and g4Bound) */
for (k = 0; k < 3; k++) {
/* Smooth/approx/avg/lowpass */
yt [0 ] [i] [k] =
h4Bound * y [i] [0] [k] +
h4 [3] * y [i] [1] [k];
/* Detail/diff/highpass */
yt [ytOffset] [i] [k] =
g4Bound * y [i] [0] [k] +
g4 [3] * y [i] [1] [k];
}
/* Intermediate and last iterations (j >= 0) */
for (j = 0; j < yLen; j += 2) {
h = (j >> 1) + 1;
for (k = 0; k < 3; k++) {
yt [h] [i] [k] = yt [h + ytOffset] [i] [k] = 0;
/* Convolve up to boundary of wavelet or input, whichever
* comes first */
for (l = j; l < min(j + 4, yLen); l++) {
/* Smooth/approx/avg/lowpass */
yt [h ] [i] [k] += h4 [l - j] * y [i] [l] [k];
/* Detail/diff/highpass */
yt [h + ytOffset] [i] [k] += g4 [l - j] * y [i] [l] [k];
}
/* If necessary, convolve beyond input boundary with
* constant extension (note multiple factoring of
* y [i] [yLen-1] via aggregated coefficients h4Bound and
* g4Bound). This is skipped if the wavelet boundary was
* already reached */
for (; l < j + 4; l++) {
/* Smooth/approx/avg/lowpass */
yt [h ] [i] [k] += h4 [l - j] *
y [i] [yLen - 1] [k];
/* Detail/diff/highpass */
yt [h + ytOffset] [i] [k] += g4 [l - j] *
y [i] [yLen - 1] [k];
}
}
}
}
} while (i0);
/* TODO: IS THIS NECESSARY??? */
#if 0
if (axis) {
/* Copy padding coeffs from preceding horizontal iteration */
for (i = yLen; i < ytTotalLen; i++)
for (j = 0; j < yLen; j++)
for (k = 0; k < 3; k++)
yt [j] [i] [k] = y [i] [j] [k];
}
#endif
#ifdef WAVELET_DBG
if (axis)
printf("VERT FWD D4 (%dx%d) H-approx, (%dx%d) H-detail\n"
"-> (%dx%d) V-approx of H-approx, (%dx%d) V-approx of H-detail,\n"
" (%dx%d) V-detail of H-approx, (%dx%d) V-detail of V-detail\n",
ytLen, yLen, ytLen, yLen,
ytLen, ytLen, ytLen, ytLen, ytLen, ytLen, ytLen, ytLen
);
else
printf(
"HORIZ FWD D4 (%dx%d) -> (%dx%d) H-approx, (%dx%d) H-detail\n",
yLen, yLen,
ytLen, yLen, ytLen, yLen
);
dumpCoeffs2(y, yt, ytTotalLen, ytTotalLen, 0);
putchar('\n');
axis ^= 1;
#endif
}
return ytLen;
}
static unsigned padD4InvStep2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned yLen, unsigned yOffset
)
/*
Single iteration of inverse 2D Daubechies D4 wavelet transform with
boundary padding on array y containg (yLen x yLen) approximation and
detail coefficients in 3-tuples. This reverses the forward transform
above. The transform is inverted over y's 2nd axis (i.e. horizontally,
assuming row-major addressing as per C convention).
The inverted coefficients are returned in the *TRANSPOSED* output array
yt. The transpose arranges the inverted coefficients vertically, and
prepares the array for another inverse transform over its 2nd axis in a
subsequent call (this time as input y). The result of a subsequent
inverse transform restores yt to y's original orientation, in which case
both horizontal and vertical axes have been inversely transformed.
The number of output coefficients is smaller than the input as padding
coefficients are collapsed at the boundaries during the inverse
transform. The number of output coefficients per dimension ytLen is
obtained as returned value, and can be interrogated beforehand without
performing a transform by passing either y or yt as NULL.
The inversion expects approximation coefficients at y [0..yLen/2-1] and
detail coefficients at y [yOffset..yOffset+yLen/2-1]. The offset yOffset
must be supplied by the caller to account for the fact that the number of
output coefficients ytLen is smaller than yLen due to the collapsed
padding coefficients. Consequently there is a gap between the inverted
coefficients in the upper left of the matrix, and the remaining detail
coefficients in the lower right. This gap opens with each iteration,
until all detail coefficients have been consumed by the inversion.
*/
{
unsigned h, i, j, k, l,
ytLen = yLen - 2; /* Max num output coeffs in yt */
const unsigned totalLen = yOffset + (yLen >> 1);
#ifdef WAVELET_DBG
static unsigned axis = 1;
#endif
if (y && yt && yLen >= 2) {
#ifdef WAVELET_DBG
/* Clear output array to facilitate debugging */
/* TODO; DO WE NEED THIS??? */
clearCoeffs2(yt, totalLen);
#endif
/* Reconstruct from approximation and detail coefficients */
for (i = 0; i < ytLen; i++)
for (j = 0; j < ytLen - 1; j += 2) {
h = j >> 1;
for (k = 0; k < 3; k++) {
yt [i] [j ] [k] =
h4 [2] * y [h ] [i] [k] + /* Approx */
g4 [2] * y [h + yOffset ] [i] [k] + /* Detail */
h4 [0] * y [h + 1 ] [i] [k] + /* Approx */
g4 [0] * y [h + 1 + yOffset] [i] [k]; /* Detail */
yt [i] [j + 1] [k] =
h4 [3] * y [h ] [i] [k] + /* Approx */
g4 [3] * y [h + yOffset ] [i] [k] + /* Detail */
h4 [1] * y [h + 1 ] [i] [k] + /* Approx */
g4 [1] * y [h + 1 + yOffset] [i] [k]; /* Detail */
}
}
ytLen = j;
/* TODO: IS THIS NECESSARY??? */
if (0 && axis) {
/* Copy padding coeffs for subsequent horizontal iteration */
for (i = ytLen; i < totalLen; i++)
for (j = 0; j < ytLen; j++)
for (k = 0; k < 3; k++)
yt [i] [j] [k] = y [j] [i] [k];
}
#ifdef WAVELET_DBG
printf("%s INV D4 (%d x %d) -> (%d x %d)\n", axis ? "VERT" : "HORIZ",
yLen, yLen, ytLen, ytLen
);
dumpCoeffs2(y, yt, totalLen, totalLen, 0);
putchar('\n');
axis ^= 1;
#endif
}
return ytLen;
}
unsigned padWaveletXform2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned yLen0
)
/* Perform full 2D multiresolution forward wavelet transform with padded
boundary coefficients on array y containing (yLen0 x yLen0) samples of
3-tuples. Note no intra-tuple transform occurs. An additional array yt
of identical dimension to y is required as buffer for intermediate
results.
The wavelet coefficients are returned in array y, containing the coarsest
approximation coefficients in y [0][0] followed by horizontal/vertical
detail coefficients in order of increasing resolution/frequency.
NOTE: Both y and yt must be large enough to accommodate the additional
padding coefficients introduced at the array boundaries during the
transform. It is the caller's responsibility to preallocate and
dimension these arrays accordingly with allocWaveletMatrix2(). The
maximum expected number of coefficients (which generally exceeds the
number of input samples yLen0) must be interrogated beforehand by calling
the function with y or yt set to NULL.
The returned value is the maximum number of output coefficients, or 0 if
the transform failed.
*/
{
/* Output size (number of coeffs, including boundary padding coeffs),
output array offset and pointers */
unsigned yLen, ytLen, ytOffset, totalLen = 0;
/* Transform if enough samples, else just return output size.
NOTE: the D4 transform will be skipped for input sizes yLen0 < 4. */
if (yLen0 >= 2) {
/* Figure out total number of coefficients (= maximum size of output
array including boundary padding) by summing the number of detail
coeffs returned by each xform iteration. */
for (yLen = yLen0, totalLen = 0;
yLen > 3;
totalLen += yLen = padD4Step2(NULL, NULL, yLen, 0)
);
/* Finally add number of approximation coeffs at coarsest resolution */
totalLen += yLen;
if (y && yt) {
/* Apply Daubechies D4 transform, accounting for boundary padding */
for (yLen = yLen0, ytOffset = totalLen;
yLen > 3;
yLen = ytLen
) {
/* Get num of coeff pairs returned by the next xform iteration,
and calculate the offset of detail coeffs in output array */
ytOffset -= ytLen = padD4Step2(NULL, NULL, yLen, 0);
/* Apply horizontal & vertical Daubechies D4 transform, swapping
input and transposed output array. The resulting detail
coefficients are prepended to those from the previous
iteration from position ytOffset; consequently, the returned
number of coefficient pairs is the input size for next
iteration */
if (!padD4Step2(y, yt, yLen, ytOffset) ||
!padD4Step2(yt, y, yLen, ytOffset)
)
return 0;
}
/* Apply horizontal & vertical Haar transform in penultimate and
final iterations (since yLen is odd) to decompose to a single
approximation coefficient y [0] [0] at the coarsest resolution;
all other coeffs are details. Obviously no boundary padding is
necessary here. */
for (; yLen >= 2; yLen--) {
if (!padHaarStep2(y, yt, yLen) || !padHaarStep2(yt, y, yLen))
return 0;
}
}
}
/* All coeffs now in y; return output size */
return totalLen;
}
unsigned padWaveletInvXform2 (WaveletMatrix2 y, WaveletMatrix2 yt,
unsigned yLen0, unsigned yLenOrg
)
/* Perform full 2D multiresolution inverse wavelet transform on array y
containing (yLen0 x yLen0) boundary padded wavelet coefficients as
3-tuples. The original number of samples (yLenOrg x yLenOrg) is required
for the reconstruction. An additional array yt of identical dimension to
y is required as buffer for intermediate results.
The reconstructed samples are returned in y. This is smaller than (yLen0
x yLen0) since the boundary coefficients from the forward transform are
collapsed.
The returned value is the reconstructed number of samples per dimension
(yLenOrg), or 0 if the inverse transform failed.
*/
{
unsigned yLen = 0, nextyLen, ytLen, ytOffset, i, j, d4Iter;
if (yLenOrg < 2)
/* Too few coefficients for reconstruction */
return 0;
/* Figure out num Daubechies iterations based on original num coeffs */
for (d4Iter = 0, yLen = yLenOrg;
yLen > 3;
d4Iter++, yLen = padD4Step2(NULL, NULL, yLen, 0)
);
/* Invert horizontal & vertical Haar transform at two coarsest levels */
for (yLen = 2; yLen <= min(3, yLen0); yLen++)
if (!padHaarInvStep2(y, yt, yLen) || !padHaarInvStep2(yt, y, yLen))
return 0;
/* Invert horiz & vert Daubechies D4 transform on subsequent levels */
for (i = d4Iter; i; i--) {
/* Get num detail coeffs and their offset for current iteration */
for (j = 0, ytOffset = yLen0, yLen = nextyLen = yLenOrg; j < i; j++) {
nextyLen = yLen;
ytOffset -= yLen = padD4Step2(NULL, NULL, yLen, 0);
}
if (!(ytLen = padD4InvStep2(y, yt, yLen << 1, ytOffset)) ||
!(ytLen = padD4InvStep2(yt, y, yLen << 1, ytOffset))
)
return 0;
#if 0
/* XXX: Drop excess reconstructed approximation coeffs to match number
of detail coeffs in next iteration. */
/* ??? */
yLen = min(ytLen, nextyLen);
#endif
}
return yLenOrg;
}
#ifdef WAVELET_TEST_2DPAD
#include <stdio.h>
#ifdef WAVELET_TEST_mRGBE
#include "mrgbe.h"
#endif
#define WAVELET_TEST_INIT 1
int main (int argc, char *argv [])
{
int i, j, k;
unsigned y0Len, yLen, numThresh = 0;
WaveletMatrix2 y0 = NULL, y = NULL, yt = NULL;
FILE *dataFile = NULL;
WAVELET_COEFF inData, thresh = 0;
#ifdef WAVELET_TEST_mRGBE
#define HUGE 1e10
mRGBE mrgbeCoeff;
mRGBERange mrgbeRange;
WaveletMatrix2 ymrgbe = NULL;
#endif
if (argc < 2) {
fprintf(stderr, "%s <dim> [threshold] [dataFile]\n", argv [0]);
fputs("Missing array dimension dim >= 2, "
"compression threshold >= 0\n", stderr
);
return -1;
}
if (!(y0Len = atoi(argv [1])) || y0Len < 2) {
fprintf(stderr, "Invalid array dimension %d\n", y0Len);
return -1;
}
if (argc > 2 && (thresh = atof(argv [2])) < 0) {
fprintf(stderr, "Invalid threshold %.3f\n", thresh);
return -1;
}
/* Get size of (padded) output array */
if (!(yLen = padWaveletXform2(NULL, NULL, y0Len))) {
fputs("Can't determine number of coefficients "
"(input too short?)\n", stderr
);
return -1;
}
/* Allocate & clear arrays for original and reconstruction */
if (!(y0 = allocWaveletMatrix2(y0Len)) ||
!(y = allocWaveletMatrix2(yLen)) ||
!(yt = allocWaveletMatrix2(yLen))
#ifdef WAVELET_TEST_mRGBE
|| !(ymrgbe = allocWaveletMatrix2(yLen))
#endif
) {
fprintf(stderr, "Failed allocating %dx%d array\n", yLen, yLen);
return -1;
}
clearCoeffs2(y0, y0Len);
clearCoeffs2(y, yLen);
clearCoeffs2(yt, yLen);
if (argc > 3) {
/* Load data from file; length must not exceed allocated */
if (!(dataFile = fopen(argv [3], "r"))) {
fprintf(stderr, "Failed opening data file %s\n", argv [3]);
return -1;
}
for (i = 0; i < y0Len; i++) {
for (j = 0; j < y0Len; j++) {
if (feof(dataFile)) {
fprintf(stderr,
"Premature end of file reading data from %s\n",
argv [2]
);
fclose(dataFile);
return -1;
}
/* Read next float, skipping any leading whitespace */
if (fscanf(dataFile, " %lf", &inData)) {
y0 [i][j][0] = y0 [i][j][1] = y0 [i][j][2] =
y [i][j][0] = y [i][j][1] = y [i][j][2] = inData;
}
else {
fprintf(stderr,
"Error reading from data file %s\n", argv [2]
);
fclose(dataFile);
return -1;
}
}
}
fclose(dataFile);
}
else {
/* Init input */
srand48(111);
for (i = 0; i < y0Len; i++) {
for (j = 0; j < y0Len; j++) {
for (k = 0; k < 3; k++) {
y0 [i][j][k] = y [i][j][k] =
#if WAVELET_TEST_INIT == 0
/* Random data, channel-independent */
drand48();
#elif WAVELET_TEST_INIT == 1
/* Random data, indentical for all channels */
k ? y [i][j][k - 1] : drand48();
#elif WAVELET_TEST_INIT == 2
/* Monotonically increasing along axis 0 */
i;
#elif WAVELET_TEST_INIT == 3
/* Monotonically increasing along axis 1 */
j;
#elif WAVELET_TEST_INIT == 4
/* Monotonically increasing along both axes */
i * j;
#elif WAVELET_TEST_INIT == 5
/* Monotonically increasing by linear index */
i * y0Len + j;
#endif
}
}
}
}
#ifdef WAVELET_DBG
puts("----------------------- FWD XFORM -------------------------\n");
#endif
/* Forward xform */
if (!padWaveletXform2(y, yt, y0Len)) {
fputs("Forward xform failed\n", stderr);
return -1;
}
/* Threshold coefficients; we use hard thresholding as it's easier to
* implement than soft thresholding, which requires sorting the
* coefficients. NOTE: the coarsest approximation coefficient at
* y [0][0] is omitted as it is essential for reconstruction! */
for (i = 0; i < yLen; i++)
for (j = 0; j < yLen; j++) {
if ((i | j) && coeffThresh(y [i][j], thresh)) {
y [i][j][0] = y [i][j][1] = y [i][j][2] = 0;
numThresh++;
#if 0
/* Replace thresholded values with random noise in range
[-threshold, threshold] */
y [i][j][0] = y [i][j][1] = y [i][j][2] = thresh * (
2 * drand48() - 1
);
#endif
}
}
#ifdef WAVELET_DBG
/* Dump coefficients */
puts("----------------------- COEFFICIENTS -------------------------\n");
dumpCoeffs2(y, NULL, yLen, 0, thresh);
if (numThresh)
printf("\n%d/%d coefficients thresholded = %.1f%% compression",
numThresh, yLen * yLen, 100. * numThresh / (yLen * yLen)
);
#endif
#ifdef WAVELET_TEST_mRGBE
/* Test mRGBE coefficient encoding */
mrgbeRange.min [0] = mrgbeRange.min [1] = mrgbeRange.min [2] = HUGE;
mrgbeRange.max [0] = mrgbeRange.max [1] = mrgbeRange.max [2] = 0;
clearCoeffs2(ymrgbe, yLen);
/* Find min/max coeff and init mRGBE range */
for (i = 0; i < yLen; i++)
for (j = 0; j < yLen; j++)
for (k = 0; k < 3; k++) {
inData = fabs(y [i][j][k]);
if (inData < mrgbeRange.min [k])
mrgbeRange.min [k] = inData;
if (inData > mrgbeRange.max [k])
mrgbeRange.max [k] = inData;
};
mRGBEinit(&mrgbeRange, mrgbeRange.min, mrgbeRange.max);
/* Encode coeffs to mRGBE and back, but preserve approximation
* coefficient at y [0][0] */
for (i = 0; i < yLen; i++)
for (j = 0; j < yLen; j++)
if (i | j) {
mrgbeCoeff = mRGBEencode(y [i][j], &mrgbeRange, 0);
mRGBEdecode(mrgbeCoeff, &mrgbeRange, ymrgbe [i][j]);
}
else for (k = 0; k < 3; k++)
ymrgbe [i][j][k] = y [i][j][k];
#ifdef WAVELET_DBG
/* Dump mRGBE-decoded coefficients */
puts("\n\n-------------------- mRGBE COEFFICIENTS ----------------------\n");
dumpCoeffs2(y, ymrgbe, yLen, yLen, 0);
#endif
#endif
#ifdef WAVELET_DBG
puts("\n----------------------- INV XFORM -------------------------\n");
#endif
/* Inverse xform (also using mRGBE coeffs if enabled) */
if (!padWaveletInvXform2(y, yt, yLen, y0Len)
#ifdef WAVELET_TEST_mRGBE
|| !padWaveletInvXform2(ymrgbe, yt, yLen, y0Len)
#endif
) {
fputs("\nInverse xform failed\n", stderr);
return -1;
}
#ifdef WAVELET_DBG
puts("\n--------------------- ORIG vs. INV XFORM ------------------------\n");
dumpCoeffs2(y0, y, y0Len, y0Len, 0);
#endif
printf("\nAvg RMSE = %.2f\n", rmseCoeffs2(y0, y, y0Len));
#ifdef WAVELET_TEST_mRGBE
#ifdef WAVELET_DBG
puts("\n------------------ ORIG vs. INV XFORM + mRGBE -------------------\n");
dumpCoeffs2(y0, ymrgbe, y0Len, y0Len, 0);
#endif
printf("\nAvg RMSE with mRGBE enc = %.2f\n",
rmseCoeffs2(y0, ymrgbe, y0Len)
);
#endif
freeWaveletMatrix2(y0, y0Len);
freeWaveletMatrix2(y, yLen);
freeWaveletMatrix2(yt, yLen);
#ifdef WAVELET_TEST_mRGBE
freeWaveletMatrix2(ymrgbe, yLen);
#endif
return 0;
}
#endif /* WAVELET_TEST_2DPAD */

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