splitting_bregman分裂算法用于求解最优化问题.zip

/* File Name: MIRDWT.c Last Modification Date: 06/14/95 16:22:45 Current Version: MIRDWT.c 2.4 File Creation Date: Wed Oct 12 08:44:43 1994 Author: Markus Lang <lang@jazz.rice.edu> Copyright (c) 2000 RICE UNIVERSITY. All rights reserved. Created by Markus Lang, Department of ECE, Rice University. This software is distributed and licensed to you on a non-exclusive basis, free-of-charge. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistribution of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistribution in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. All advertising materials mentioning features or use of this software must display the following acknowledgment: This product includes software developed by Rice University, Houston, Texas and its contributors. 4. Neither the name of the University nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY WILLIAM MARSH RICE UNIVERSITY, HOUSTON, TEXAS, AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL RICE UNIVERSITY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTIONS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE), PRODUCT LIABILITY, OR OTHERWISE ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. For information on commercial licenses, contact Rice University's Office of Technology Transfer at techtran@rice.edu or (713) 348-6173 Change History: Fixed the code such that 1D vectors passed to it can be in either passed as a row or column vector. Also took care of the code such that it will compile with both under standard C compilers as well as for ANSI C compilers Jan Erik Odegard <odegard@ece.rice.edu> Wed Jun 14 1995 Fix minor bug to allow maximum number of levels MATLAB description: %function x = mirdwt(yl,yh,h,L); % % function computes the inverse redundant discrete wavelet transform y for a % 1D or 2D input signal. redundant means here that the subsampling after % each stage of the forward transform has been omitted. yl contains the % lowpass and yl the highpass components as computed, e.g., by mrdwt. In % case of a 2D signal the ordering in yh is [lh hl hh lh hl ... ] (first % letter refers to row, second to column filtering). % % Input: % yl : lowpass component % yh : highpass components % h : scaling filter % L : number of levels. in case of a 1D signal length(yl) must be % divisible by 2^L; in case of a 2D signal the row and the % column dimension must be divisible by 2^L. % % Output: % x : finite length 1D or 2D signal % % see also: mdwt, midwt, mrdwt */ #include <math.h> #include <stdio.h> #define max(a, b) ((a) > (b) ? (a) : (b)) #define mat(a, i, j) (*(a + (m*(j)+i))) /* macro for matrix indices */ #ifdef __STDC__ MIRDWT(double *x, int m, int n, double *h, int lh, int L, double *yl, double *yh) #else MIRDWT(x, m, n, h, lh, L, yl, yh) double *x, *h, *yl, *yh; int m, n, lh, L; #endif { double *g0, *g1, *ydummyll, *ydummylh, *ydummyhl; double *ydummyhh, *xdummyl , *xdummyh, *xh; long i, j; int actual_L, actual_m, actual_n, c_o_a, ir, n_c, n_cb, n_c_o, lhm1; int ic, n_r, n_rb, n_r_o, c_o_a_p2n, sample_f; xh = (double *)mxCalloc(m*n,sizeof(double)); xdummyl = (double *)mxCalloc(max(m,n),sizeof(double)); xdummyh = (double *)mxCalloc(max(m,n),sizeof(double)); ydummyll = (double *)mxCalloc(max(m,n)+lh-1,sizeof(double)); ydummylh = (double *)mxCalloc(max(m,n)+lh-1,sizeof(double)); ydummyhl = (double *)mxCalloc(max(m,n)+lh-1,sizeof(double)); ydummyhh = (double *)mxCalloc(max(m,n)+lh-1,sizeof(double)); g0 = (double *)mxCalloc(lh,sizeof(double)); g1 = (double *)mxCalloc(lh,sizeof(double)); if (n==1){ n = m; m = 1; } /* analysis lowpass and highpass */ for (i=0; i<lh; i++){ g0[i] = h[i]/2; g1[i] = h[lh-i-1]/2; } for (i=1; i<=lh; i+=2) g1[i] = -g1[i]; lhm1 = lh - 1; /* 2^L */ sample_f = 1; for (i=1; i<L; i++) sample_f = sample_f*2; actual_m = m/sample_f; actual_n = n/sample_f; /* restore yl in x */ for (i=0;i<m*n;i++) x[i] = yl[i]; /* main loop */ for (actual_L=L; actual_L >= 1; actual_L--){ /* actual (level dependent) column offset */ if (m==1) c_o_a = n*(actual_L-1); else c_o_a = 3*n*(actual_L-1); c_o_a_p2n = c_o_a + 2*n; /* go by columns in case of a 2D signal*/ if (m>1){ n_rb = m/actual_m; /* # of row blocks per column */ for (ic=0; ic<n; ic++){ /* loop over column */ for (n_r=0; n_r<n_rb; n_r++){ /* loop within one column */ /* store in dummy variables */ ir = -sample_f + n_r; for (i=0; i<actual_m; i++){ ir = ir + sample_f; ydummyll[i+lhm1] = mat(x, ir, ic); ydummylh[i+lhm1] = mat(yh, ir, c_o_a+ic); ydummyhl[i+lhm1] = mat(yh, ir,c_o_a+n+ic); ydummyhh[i+lhm1] = mat(yh, ir, c_o_a_p2n+ic); } /* perform filtering and adding: first LL/LH, then HL/HH */ bpconv(xdummyl, actual_m, g0, g1, lh, ydummyll, ydummylh); bpconv(xdummyh, actual_m, g0, g1, lh, ydummyhl, ydummyhh); /* store dummy variables in matrices */ ir = -sample_f + n_r; for (i=0; i<actual_m; i++){ ir = ir + sample_f; mat(x, ir, ic) = xdummyl[i]; mat(xh, ir, ic) = xdummyh[i]; } } } } /* go by rows */ n_cb = n/actual_n; /* # of column blocks per row */ for (ir=0; ir<m; ir++){ /* loop over rows */ for (n_c=0; n_c<n_cb; n_c++){ /* loop within one row */ /* store in dummy variable */ ic = -sample_f + n_c; for (i=0; i<actual_n; i++){ ic = ic + sample_f; ydummyll[i+lhm1] = mat(x, ir, ic); if (m>1) ydummyhh[i+lhm1] = mat(xh, ir, ic); else ydummyhh[i+lhm1] = mat(yh, ir, c_o_a+ic); } /* perform filtering lowpass/highpass */ bpconv(xdummyl, actual_n, g0, g1, lh, ydummyll, ydummyhh); /* restore dummy variables in matrices */ ic = -sample_f + n_c; for (i=0; i<actual_n; i++){ ic = ic + sample_f; mat(x, ir, ic) = xdummyl[i]; } } } sample_f = sample_f/2; actual_m = actual_m*2; actual_n = actual_n*2; } } #ifdef __STDC__ bpconv(double *x_out, int lx, double *g0, double *g1, int lh, double *x_inl, double *x_inh) #else bpconv(x_out, lx, g0, g1, lh, x_inl, x_inh) double *x_inl, *x_inh, *g0, *g1, *x_out; int lx, lh; #endif { int i, j; double x0; for (i=lh-2; i > -1; i--){ x_inl[i] = x_inl[lx+i]; x_inh[i] = x_inh[lx+i]; } for (i=0; i<lx; i++){ x0 = 0; for (j=0; j<lh; j++) x0 = x0 + x_inl[j+i]*g0[lh-1-j] + x_inh[j+i]*g1[lh-1-j]; x_out[i] = x0; } }