QR分解求矩阵全部特征值

/** * Matrix.java */ package structure; import java.io.Serializable; /** * <p>鍩虹鏁版嵁绫伙紝琛ㄧず鐭╅樀銆傚悜閲忋?鐭╅樀閮界敱姝ょ被琛ㄧず銆?/p> * @author Nano.Michael * @version 1.0.0 * @date 2013-8-20 * @author (latest modification by Nano.Michael) * @since 1.0.0 */ public class Matrix implements Serializable{ private static final long serialVersionUID = 1L; /** * 鐭╅樀鐨勫垪鏁? */ protected int cols = 0; /** * 鐭╅樀鐨勮鏁? */ protected int rows = 0; /** * 淇濆瓨鐭╅樀鐨勬暟鎹? */ protected double[] d = null; /** * 鏁版嵁鍒楁暟锛屾渶鍘熷鐭╅樀鐨勫垪鏁? */ protected int dCols = 0; /** * 鐩稿浜庢渶鍘熷鐭╅樀锛堢敱鏋勯?鏂规硶寰楀埌锛夌殑琛岃寖鍥达紝鏈?垵杩欎釜瀛楁搴旇绛変簬Range.all()锛屽綋rowRange琚０鏄庯紝鍒欒繖涓煩闃电殑琛屽紑濮? * 涓嬫爣鐩稿浜庢渶鍒濈殑鐭╅樀鐨勮涓簉owRange.begin()锛岀煩闃电殑琛岀粨鏉熶笅鏍囩浉瀵逛簬鏈?垵鐨勭煩闃佃涓簉owRange.end()銆備妇涓垪瀛愶細 * 褰?code>rowRange.start==2</code>涓?code>rowRange.end==5</code>鏃讹紝閭ｄ箞杩欎釜鐭╅樀鐩稿浜庢渶鍘熷鐭╅樀鐨勮鐨勫紑濮? * 鍜岀粨鏉熶笅鏍囦负2鍜?銆傝繖涓瓧娈典竴鑸敱锛? * @see #at(Range, Range) * @see #set(Range, Range, Matrix) * 浣跨敤 */ protected Range rowRange = null; /** * 鐩稿浜庢渶鍘熷鐭╅樀鐨勫垪鑼冨洿锛岃В閲婂悓 * @see #rowRange */ protected Range colRange = null; private Matrix(){ } /** * 浣跨敤澹版槑鐨勮鏁皉ows鍜屽垪鏁癱ols鏋勯?涓?釜鐭╅樀锛屾鏃跺唴瀛樺凡缁忚鍒嗛厤 * @param rows 鐭╅樀琛屾暟銆? * @param cols 鐭╅樀鍒楁暟 */ public Matrix(int rows, int cols){ this(rows, cols, new double[cols * rows]); } /** * 浣跨敤澹版槑鐨勮鏁板拰鍒楁暟浠ュ強棰勫厛鍒嗛厤鐨勫弻绮惧害娴偣鍨嬫暟鎹瀯閫犱竴涓煩闃点? * <br><b><i>NOTICE:</i></b> 濡傛灉鐭╅樀鐨勫ぇ灏忥紙绛変簬琛屾暟*鍒楁暟锛夊皬浜庨鍏堝瓨鍌ㄧ殑鏁版嵁鐨勯暱搴︼紝绋嬪簭鑳藉姝ｅ父鐨勮繍琛岋紝浣嗘槸骞朵笉 * 鎺ㄨ崘杩欐牱鍋氥? * @see #Matrix(int, int) * @param rows 鐭╅樀琛屾暟銆? * @param cols 鐭╅樀鍒楁暟銆? * @param data 棰勫厛瀛樺偍鐨勬暟鎹? */ public Matrix(int rows, int cols, double[] data){ if (cols <= 0 || rows <= 0) throw new IllegalArgumentException("Matrix, columns and rows must be positive integer."); if (cols * rows > data.length) throw new IllegalArgumentException("Matrix, the size of the matrix does not match the length of the data."); this.cols = cols; this.rows = rows; this.d = data; this.dCols = cols; rowRange = new Range(0, rows); colRange = new Range(0, cols); } /** * 鍒ゆ柇涓?釜鐭╅樀鏄惁涓哄悜閲忥紙鍒楀悜閲忔垨琛屽悜閲忥級 * @return */ public boolean isVector(){ return (rows!= 1&&cols!=1); } /** * 鍒ゆ柇鐭╅樀鏄惁涓鸿鍚戦噺 * @return */ public boolean isRowVector(){ return rows==1; } /** * 鍒ゆ柇鐭╅樀鏄惁涓哄垪鍚戦噺 * @return */ public boolean isColumnVector(){ return cols==1; } /** * 鍒ゆ柇涓や釜鐭╅樀鏄惁鏄悓鍨嬬煩闃碉紙鍗宠鍒楃浉绛夛級 * @param x * @return 鍚屽瀷杩斿洖<code>true</code>锛屽弽涔嬪垯鍙? */ public boolean sameType(Matrix x){ return (rows==x.rows&&cols==x.cols); } /** * 鍒ゆ柇鏄惁涓烘柟闃点? * @return */ public boolean isSquare(){ return rows==cols; } /** * 寰楀埌鐭╅樀澶у皬锛坰ize=rows*columns锛? * @return */ public int size(){ return rows*cols; } /** * 璁＄畻鐭╅樀鐨勭粷瀵瑰? * @param reserve 鎸囩ず鏄惁淇濈暀鍘熷鐭╅樀锛岃嫢<code>reserve==false</code>锛屾柟娉曞皢浣跨敤缁濆鍊肩煩闃垫浛鎹㈠師濮嬬煩闃点? * @return 鐭╅樀鐨勭粷瀵瑰?鐭╅樀 * @see #abs() */ public Matrix abs(boolean reserve){ Matrix x = reserve?new Matrix(rows,cols):this; for (int i=0; i<rows; i++) for (int j=0; j<cols; j++){ double d = at(i, j); x.set(i, j, d>=0.?d:-d); } return x; } /** * 璁＄畻鐭╅樀鐨勭粷瀵瑰?銆? * <br><br><b><i>NOTICE:</i></b>鏂规硶灏嗘浛鎹㈠師濮嬬煩闃点? * @return 鐭╅樀鐨勭粷瀵瑰?鐭╅樀銆? * @see #abs(boolean) */ public Matrix abs(){ return abs(false); } /** * 灏嗙煩闃垫竻闆躲? */ public void clear(){ for (int i = 0; i < rows; i++) for (int j = 0; j < cols; j++) set(i, j, 0); } /** * 灏嗙煩闃垫嫹璐濆埌鍙﹀涓?釜鐭╅樀锛屾鏃讹紝杩欎袱涓煩闃靛繀椤绘槸鍚屽瀷鐨勶紝鏁版嵁灏嗗畬鍏ㄦ嫹璐濆埌鏂扮殑鐭╅樀锛屼絾鏄柊鐨勭煩闃靛皢鍜屽綋鍓嶇殑鐭╅樀 * 鏄畬鍏ㄧ嫭绔嬬殑銆? * @param x 鐩爣鐭╅樀銆? */ public void copyTo(Matrix x){ if (x.rows != rows || x.cols != cols) throw new IllegalArgumentException("Matrix copy, size not match."); for (int i = 0; i < rows; i++) for (int j = 0; j < cols; j++) x.set(i, j, at(i, j)); } /** * 灏嗙煩闃佃浆鎹负1缁存暟缁勶紝姝ゆ椂鏂规硶浠ヨ浠庡乏鑷冲彸锛屼互鍒椾粠涓婅嚦涓嬮『搴忓皢鐭╅樀杞崲涓?缁存暟缁勩? * <br><b><i>NOTICE:</i></b>寰楀埌鐨勫皢鏄煩闃典腑鏁扮粍鐨勬嫹璐濓紝濡傛灉涓嶆兂鍐嶅彟澶栧紑杈熷瓨鍌ㄧ┖闂达紝璇蜂娇鐢▄@link #data()}鏂规硶锛? * 浣嗘槸姝ゆ柟娉曡繑鍥炵煩闃靛叏閮ㄥ厓绱狅紝涓嶈兘寰楀埌瀛愮煩闃碉紙鐢辨柟娉曪細{@link #at(Range, Range)}锛寋@link #col(int)}锛寋@link #row(int)} * 寰楀埌锛夌殑鍏冪礌銆? * @return */ public double[] toArray(){ double[] x = new double[size()]; int c = 0; for (int i=0; i<rows; i++){ for (int j=0; j<cols; j++){ x[c] = at(i, j); c++; } } return x; } /** * 灏嗙煩闃佃浆鎹负2缁存暟缁勩? * <br><b><i>NOTICE:</i></b> 寰楀埌鐨勫皢鏄煩闃典腑鏁扮粍鐨勬嫹璐濄? * @return */ public double[][] to2DArray(){ double[][] x = new double[rows][cols]; for (int i=0; i<rows; i++) for (int j=0; j<cols; j++) x[i][j] = at(i,j); return x; } /** * 鑾峰彇瀛樺偍浜庣煩闃典腑鐨勬暟鎹? * @return 鏁版嵁 */ public double[] data(){ return this.d; } /** * 鑾峰彇鐭╅樀鐨勫垪鏁般? * @return 鐭╅樀鐨勫垪鏁般? */ public int columns(){ return this.cols; } /** * 鑾峰彇鐭╅樀鐨勮鏁般? * @return 鐭╅樀琛屾暟銆? */ public int rows(){ return this.rows; } /** * 鑾峰彇鐭╅樀鍦ㄨ涓嬫爣涓篿澶勭殑琛屽悜閲忋? * @param i 琛屼笅鏍囥? * @return 鐗瑰畾鐨勮鍚戦噺銆? */ public Matrix row(int i){ return at(new Range(i, i+1), Range.all()); } /** * 鑾峰彇鐭╅樀鍦ㄥ垪涓嬫爣涓篿澶勭殑鍒楀悜閲忋? * @param i 鍒椾笅鏍囥? * @return 鐗瑰畾鐨勫垪鍚戦噺銆? */ public Matrix col(int i){ return at(Range.all(), new Range(i, i+1)); } /** * 鏋勯?涓?釜浠庝互pitch涓洪棿闅斾粠begin鍒癳nd閫掑鐨勫悜閲忋? * @param begin 鍚戦噺寮?鏁版嵁 * @param pitch 闂撮殧 * @param end 鍚戦噺缁撴潫 * @return */ public static Matrix increment(double begin, double pitch, double end){ int r = (int)((end-begin)/pitch); if (r<=0) throw new IllegalArgumentException("Matrix increment, end must greater than begin."); Matrix x = new Matrix(r, 1); double pre = begin; for (int i=0; i<x.rows; i++){ x.set(i, pre); pre += pitch; } return x; } /** * 鏋勯?涓?釜鐭╅樀褰㈠ A=u*I, I 鏄崟浣嶅悜閲? u 鏄竴涓爣閲忋? * @param size 鐭╅樀鐨勮竟闀裤? (size=rows=columns) * @param scale 缂╂斁姣斿垪銆? * @return A * @see #unit(int) */ public static Matrix unit(int size, double scale){ Matrix x = new Matrix(size, size); for (int i = 0; i < size; i++) x.set(i, i, scale); return x; } /** * 鏋勯?涓?釜鍗曚綅鐭╅樀銆? * @param size 鐭╅樀杈归暱銆?size=rows=columns) * @return 鍗曚綅鐭╅樀銆? * @see #unit(int, double) */ public static Matrix unit(int size){ return unit(size, 1.); } /** * 鏋勯?涓?釜鎵?湁鍏冪礌鍏锋湁鐩稿悓鏁版嵁鐨勭煩闃碉紝褰㈠锛欰=N*scale锛孨涓?鐭╅樀锛宻cale涓虹缉鏀炬瘮渚嬨? * @param rows 鐭╅樀琛屾暟銆? * @param cols 鐭╅樀鍒楁暟銆? * @param scale 缂╂斁姣斾緥銆? * @return A * @see #ones(int, int) */ public static Matrix ones(int rows, int cols, double scale){ Matrix x = new Matrix(rows, cols); for (int i = 0; i < x.rows; i++) for (int j = 0; j < x.cols; j++) x.set(i, j, scale); return x; } /** * 鏋勯?涓?釜鎵?湁鍏冪礌涓?鐨勭煩闃点? * @param rows 鐭╅樀琛屾暟銆? * @param cols 鐭╅樀鍒楁暟銆? * @return A * @see #ones(