0

I am trying to sample a multivariate Gaussian using mvnrnd, but when I run, the samples are NaN. For example (mu is a 1-by-50 vector, Sigma is a 50-by-50 matrix, and M equals 50):

Samp = mvnrnd(mu,Sigma,M)

When I run this and check the value of Samp from the command and variables in the workspace, it gives me NaN. Why? Is mvnrnd not working with larger dimensions?

* EDIT* Here are the values of mu:

mu =

  Columns 1 through 15

   14.3632    8.7442   -3.2029  -16.0259   -8.8725  -10.7675    9.2580   13.2556   -1.4326  -11.5970    1.9023   14.1793    9.9024  -12.7794   -0.2913

  Columns 16 through 30

   -4.3093  -15.2170   23.2225    4.5019   16.8539    0.6878    3.4329    1.9528    5.5965    0.1680    3.3895   15.1409   12.5796   11.8425    5.4299

  Columns 31 through 45

  -20.4517   12.3072   -7.5742  -14.9738   17.6118   -1.0414    3.2530   -0.1278    1.0009    3.2609   10.5319  -19.2158   -1.5661   -8.3426  -12.0159

  Columns 46 through 50

    6.3250   12.1056   11.5938   24.9523  -13.1602

The values of Sigma:

 1.0e+003 *

  Columns 1 through 15

    0.6526   -0.2398    0.2117    0.3901   -0.0241    0.1888   -0.2221    0.1173   -0.2380   -0.0327    0.0408    0.1229    0.0616    0.1475   -0.2264
   -0.2398    0.7744    0.0419   -0.4366   -0.1791   -0.0826    0.1756   -0.1534    0.3632   -0.1595    0.3086   -0.3319   -0.3392   -0.0717    0.1952
    0.2117    0.0419    0.7214   -0.2074    0.0711    0.2518   -0.1782   -0.2859   -0.1668   -0.0502   -0.0726    0.3005   -0.0525    0.1660   -0.0541
    0.3901   -0.4366   -0.2074    1.0006   -0.1486    0.0126   -0.0639    0.0847   -0.4875    0.2744   -0.3495    0.0131    0.5273    0.2531   -0.6108
   -0.0241   -0.1791    0.0711   -0.1486    0.5274   -0.1581   -0.1114   -0.1617   -0.1438   -0.0228    0.4721   -0.0968    0.0665    0.0576    0.1959
    0.1888   -0.0826    0.2518    0.0126   -0.1581    1.0361    0.1172    0.2760   -0.5648    0.5519   -0.3184    0.5437   -0.0191   -0.1152    0.0294
   -0.2221    0.1756   -0.1782   -0.0639   -0.1114    0.1172    0.4101    0.0368   -0.0796    0.0443   -0.1558    0.0977    0.1141   -0.0605    0.0048
    0.1173   -0.1534   -0.2859    0.0847   -0.1617    0.2760    0.0368    0.5609   -0.1075    0.2252   -0.1115    0.1774   -0.0141   -0.4447    0.0143
   -0.2380    0.3632   -0.1668   -0.4875   -0.1438   -0.5648   -0.0796   -0.1075    0.9745   -0.5401    0.1096   -0.4135   -0.4675   -0.0067    0.2081
   -0.0327   -0.1595   -0.0502    0.2744   -0.0228    0.5519    0.0443    0.2252   -0.5401    0.8966   -0.0644    0.0352    0.3309   -0.0716   -0.0799
    0.0408    0.3086   -0.0726   -0.3495    0.4721   -0.3184   -0.1558   -0.1115    0.1096   -0.0644    1.2591   -0.6571   -0.3052    0.0561    0.5633
    0.1229   -0.3319    0.3005    0.0131   -0.0968    0.5437    0.0977    0.1774   -0.4135    0.0352   -0.6571    0.7890    0.1215   -0.1922   -0.1545
    0.0616   -0.3392   -0.0525    0.5273    0.0665   -0.0191    0.1141   -0.0141   -0.4675    0.3309   -0.3052    0.1215    0.6406    0.0985   -0.3731
    0.1475   -0.0717    0.1660    0.2531    0.0576   -0.1152   -0.0605   -0.4447   -0.0067   -0.0716    0.0561   -0.1922    0.0985    0.6436   -0.0893
   -0.2264    0.1952   -0.0541   -0.6108    0.1959    0.0294    0.0048    0.0143    0.2081   -0.0799    0.5633   -0.1545   -0.3731   -0.0893    0.8214
   -0.0686    0.2110   -0.3078    0.0558   -0.0122    0.1147    0.1430    0.2891   -0.3322    0.3182    0.4246   -0.1755    0.1220   -0.2959    0.4601
    0.2857   -0.2873   -0.0581    0.2950    0.1501    0.2427    0.0816    0.0113   -0.3478    0.0397    0.0282    0.1461    0.1842    0.2372    0.0343
   -0.0803   -0.2141   -0.1914    0.0538   -0.1175   -0.1082   -0.0395    0.1628    0.1080    0.0010   -0.1534    0.0374   -0.0209   -0.0783    0.0447
   -0.3939    0.2945   -0.0432   -0.0477   -0.2129   -0.3433    0.1706   -0.2475    0.3644   -0.0215   -0.3702   -0.1953    0.1405    0.0665   -0.3338
   -0.0722   -0.0264    0.0008    0.3816   -0.3788    0.0074   -0.1099   -0.1504    0.0746    0.0737   -0.6089    0.0166    0.0902    0.2234   -0.2678
    0.1529   -0.5922   -0.2520    0.6748    0.1484    0.0973   -0.0401    0.0497   -0.3356    0.3686   -0.3625    0.0574    0.4848    0.2182   -0.4968
    0.0500    0.1051   -0.3110    0.1405    0.0029   -0.4277    0.0084    0.0768   -0.0301   -0.2538    0.5848   -0.3300   -0.1102   -0.0272    0.2356
   -0.1218   -0.1016    0.2996   -0.2520    0.2787   -0.2611    0.0569   -0.4067    0.1377   -0.4350   -0.1751    0.2062    0.0636    0.2057   -0.1183
    0.2696    0.1371   -0.1442    0.5029   -0.2059    0.3640    0.1549    0.3234   -0.5336    0.3734   -0.0536    0.0636    0.2701   -0.2389   -0.3367
   -0.1135    0.2516    0.0626   -0.4029    0.2331   -0.4780   -0.0001   -0.2735    0.4003   -0.3002    0.6077   -0.4151   -0.2260    0.1742    0.1648
   -0.0292   -0.4748   -0.3736    0.0169    0.1652    0.1030   -0.0086    0.4718   -0.1408    0.3198    0.1058    0.0903    0.0904   -0.3160    0.1783
    0.2547   -0.3759    0.0127    0.2648    0.0165    0.0835   -0.2337    0.0995   -0.0706    0.0958   -0.1449    0.0840    0.0818    0.0939   -0.0702
   -0.1816    0.0102    0.0898   -0.3345    0.2516   -0.2833   -0.1383   -0.2458    0.3455   -0.2373    0.0986   -0.1230   -0.0862    0.0791    0.2563
   -0.4171    0.4862    0.1516   -0.6891    0.0777    0.1910    0.1572    0.0256    0.0820   -0.2754   -0.0733    0.3196   -0.3359   -0.5783    0.2642
    0.0979   -0.1388    0.0024    0.0188   -0.1463   -0.3960    0.0223    0.0048    0.3365   -0.5037   -0.3112    0.1393   -0.0201    0.0032   -0.2922
    0.0948   -0.2636    0.3152    0.0659    0.2656   -0.0597   -0.2578   -0.1789   -0.2244   -0.0539    0.0389    0.1523    0.0280    0.0666   -0.2162
   -0.1445    0.2316    0.0613    0.0501   -0.0395   -0.2582    0.0113   -0.3707    0.2411   -0.0166   -0.0814   -0.3044    0.1419    0.3170   -0.0964
    0.1256   -0.5610   -0.1839    0.3283    0.0318    0.2282   -0.1754    0.1760   -0.1883    0.3672   -0.0763    0.0445    0.0492    0.1796   -0.0089
    0.1639    0.1968   -0.1370    0.0399   -0.1855   -0.3227   -0.1928    0.1799    0.3764   -0.2362    0.0825   -0.2515   -0.1152   -0.2144    0.0347
   -0.2864    0.3746   -0.2039   -0.2420   -0.3702   -0.1993    0.1265    0.1169    0.5200   -0.2245   -0.2712   -0.0906   -0.2380   -0.2680   -0.0291
    0.1612   -0.1498   -0.1399    0.0687    0.0545   -0.3288   -0.4044    0.1803    0.2788   -0.1633    0.2013   -0.2194   -0.1733   -0.1788    0.0570
    0.0210    0.0132    0.0418   -0.0458    0.3749   -0.8174   -0.3073   -0.2024    0.1391   -0.4363    0.6594   -0.3834   -0.0417   -0.0524    0.0248
   -0.1725   -0.4189   -0.3139    0.1701    0.2373   -0.0647   -0.0170    0.1205   -0.1555    0.4068    0.0057   -0.0915    0.3662   -0.0172    0.1566
   -0.0874   -0.2369    0.2437    0.1705   -0.3743   -0.0117    0.0462   -0.1165   -0.0344   -0.1393   -0.8038    0.4598    0.1061    0.1232   -0.4006
    0.3103   -0.3241   -0.1160    0.0813    0.2223   -0.0290   -0.1899    0.3164   -0.1250   -0.2822    0.1018    0.2295   -0.0279   -0.3269    0.1315
    0.0275   -0.0756   -0.0828   -0.0727    0.0860    0.1942    0.1057    0.1967   -0.0409    0.1347    0.0286    0.0873   -0.0564   -0.1634   -0.2309
   -0.1293    0.0226   -0.1196   -0.0434    0.0879   -0.0832   -0.0431   -0.0599    0.1180    0.1482    0.1804   -0.2526   -0.0167    0.0872    0.1069
    0.0780   -0.4398   -0.0265    0.4988    0.1396    0.1752    0.0595    0.0512   -0.7669    0.4653    0.0083    0.1777    0.4917    0.1050   -0.0940
   -0.0254   -0.0436    0.1248    0.0585   -0.2328    0.1872    0.1750   -0.1469    0.0017   -0.1329   -0.5634    0.3195    0.0734    0.2208   -0.0757
    0.1281   -0.0224    0.2863    0.0723   -0.4067   -0.0308    0.0180    0.0557    0.1420   -0.1877   -0.7327    0.3820    0.1499   -0.1069   -0.3878
   -0.1545   -0.2713   -0.3821    0.1368    0.0131   -0.0251    0.0240   -0.0059    0.0621   -0.1232   -0.1039   -0.0018   -0.1081    0.1816    0.2430
    0.0411   -0.0787    0.3134   -0.0046   -0.1013    0.3395   -0.1217    0.0351   -0.1643    0.2941   -0.3255    0.2577    0.0585   -0.0722   -0.1540
   -0.2357    0.3986   -0.1687   -0.2010   -0.3998    0.2651    0.2607    0.2268    0.1089    0.1718   -0.1816    0.0235   -0.1149   -0.2578    0.2615
    0.2349   -0.1041    0.1657    0.1751   -0.1983    0.3247    0.2915    0.0951   -0.3150    0.0387   -0.3997    0.4270    0.2562    0.0518   -0.2561
    0.0271   -0.3102   -0.0949    0.2027    0.0852    0.4680    0.0069    0.2586   -0.5133    0.6809    0.0700    0.0981    0.2209   -0.0654    0.0935

  Columns 16 through 30

   -0.0686    0.2857   -0.0803   -0.3939   -0.0722    0.1529    0.0500   -0.1218    0.2696   -0.1135   -0.0292    0.2547   -0.1816   -0.4171    0.0979
    0.2110   -0.2873   -0.2141    0.2945   -0.0264   -0.5922    0.1051   -0.1016    0.1371    0.2516   -0.4748   -0.3759    0.0102    0.4862   -0.1388
   -0.3078   -0.0581   -0.1914   -0.0432    0.0008   -0.2520   -0.3110    0.2996   -0.1442    0.0626   -0.3736    0.0127    0.0898    0.1516    0.0024
    0.0558    0.2950    0.0538   -0.0477    0.3816    0.6748    0.1405   -0.2520    0.5029   -0.4029    0.0169    0.2648   -0.3345   -0.6891    0.0188
   -0.0122    0.1501   -0.1175   -0.2129   -0.3788    0.1484    0.0029    0.2787   -0.2059    0.2331    0.1652    0.0165    0.2516    0.0777   -0.1463
    0.1147    0.2427   -0.1082   -0.3433    0.0074    0.0973   -0.4277   -0.2611    0.3640   -0.4780    0.1030    0.0835   -0.2833    0.1910   -0.3960
    0.1430    0.0816   -0.0395    0.1706   -0.1099   -0.0401    0.0084    0.0569    0.1549   -0.0001   -0.0086   -0.2337   -0.1383    0.1572    0.0223
    0.2891    0.0113    0.1628   -0.2475   -0.1504    0.0497    0.0768   -0.4067    0.3234   -0.2735    0.4718    0.0995   -0.2458    0.0256    0.0048
   -0.3322   -0.3478    0.1080    0.3644    0.0746   -0.3356   -0.0301    0.1377   -0.5336    0.4003   -0.1408   -0.0706    0.3455    0.0820    0.3365
    0.3182    0.0397    0.0010   -0.0215    0.0737    0.3686   -0.2538   -0.4350    0.3734   -0.3002    0.3198    0.0958   -0.2373   -0.2754   -0.5037
    0.4246    0.0282   -0.1534   -0.3702   -0.6089   -0.3625    0.5848   -0.1751   -0.0536    0.6077    0.1058   -0.1449    0.0986   -0.0733   -0.3112
   -0.1755    0.1461    0.0374   -0.1953    0.0166    0.0574   -0.3300    0.2062    0.0636   -0.4151    0.0903    0.0840   -0.1230    0.3196    0.1393
    0.1220    0.1842   -0.0209    0.1405    0.0902    0.4848   -0.1102    0.0636    0.2701   -0.2260    0.0904    0.0818   -0.0862   -0.3359   -0.0201
   -0.2959    0.2372   -0.0783    0.0665    0.2234    0.2182   -0.0272    0.2057   -0.2389    0.1742   -0.3160    0.0939    0.0791   -0.5783    0.0032
    0.4601    0.0343    0.0447   -0.3338   -0.2678   -0.4968    0.2356   -0.1183   -0.3367    0.1648    0.1783   -0.0702    0.2563    0.2642   -0.2922
    1.1641    0.1034   -0.0194   -0.3240   -0.0946   -0.3245    0.5362   -0.6197    0.5462   -0.2986    0.1476   -0.1007   -0.1329    0.2094   -0.5151
    0.1034    0.5320   -0.0902   -0.3749   -0.1158    0.3433   -0.0024    0.0443    0.1294   -0.1713    0.0906    0.1497   -0.0375   -0.2545   -0.1116
   -0.0194   -0.0902    0.2886   -0.0147    0.1016    0.0126    0.1733   -0.1194   -0.1837   -0.0298    0.2956    0.1006   -0.0653   -0.2525    0.1807
   -0.3240   -0.3749   -0.0147    0.7760    0.3068    0.0357   -0.2914    0.2226   -0.1225    0.1584   -0.3114   -0.2043    0.0994    0.0522    0.1904
   -0.0946   -0.1158    0.1016    0.3068    0.8276    0.1746   -0.1860   -0.1459    0.0079   -0.4393   -0.3581    0.1573    0.0312   -0.1168   -0.0679
   -0.3245    0.3433    0.0126    0.0357    0.1746    1.0148   -0.4049    0.0829    0.1196   -0.2878    0.2832    0.3084   -0.0141   -0.5111   -0.0565
    0.5362   -0.0024    0.1733   -0.2914   -0.1860   -0.4049    1.0361   -0.3308    0.1590    0.2469    0.1052   -0.1317   -0.2840   -0.2479    0.1052
   -0.6197    0.0443   -0.1194    0.2226   -0.1459    0.0829   -0.3308    0.7831   -0.4849    0.2867   -0.2149   -0.0856    0.3272    0.2165    0.3348
    0.5462    0.1294   -0.1837   -0.1225    0.0079    0.1196    0.1590   -0.4849    0.9412   -0.4123   -0.0770   -0.0688   -0.4534    0.1214   -0.2674
   -0.2986   -0.1713   -0.0298    0.1584   -0.4393   -0.2878    0.2469    0.2867   -0.4123    0.7798   -0.0243   -0.2134    0.0980   -0.2170    0.2545
    0.1476    0.0906    0.2956   -0.3114   -0.3581    0.2832    0.1052   -0.2149   -0.0770   -0.0243    0.8433    0.1766   -0.1008   -0.3012    0.0214
   -0.1007    0.1497    0.1006   -0.2043    0.1573    0.3084   -0.1317   -0.0856   -0.0688   -0.2134    0.1766    0.3139    0.0542   -0.3437   -0.0022
   -0.1329   -0.0375   -0.0653    0.0994    0.0312   -0.0141   -0.2840    0.3272   -0.4534    0.0980   -0.1008    0.0542    0.5184    0.2491   -0.0526
    0.2094   -0.2545   -0.2525    0.0522   -0.1168   -0.5111   -0.2479    0.2165    0.1214   -0.2170   -0.3012   -0.3437    0.2491    1.5153   -0.2274
   -0.5151   -0.1116    0.1807    0.1904   -0.0679   -0.0565    0.1052    0.3348   -0.2674    0.2545    0.0214   -0.0022   -0.0526   -0.2274    0.7070
   -0.3968   -0.0698   -0.0207   -0.0893   -0.0483    0.1385   -0.0376    0.2814   -0.1577    0.1031   -0.0168    0.0721    0.0247    0.0337    0.0821
   -0.0802   -0.0655   -0.1549    0.4400    0.3391    0.0921   -0.2724    0.1484   -0.1043    0.0449   -0.4317   -0.0374    0.2717   -0.0728   -0.1057
   -0.1999    0.1888    0.2938   -0.2767    0.1120    0.4970   -0.0022   -0.2160   -0.2068   -0.1046    0.5284    0.3405   -0.1427   -0.7204   -0.0466
    0.3181   -0.1686    0.0125    0.0108    0.1503   -0.2403    0.1669   -0.2955    0.1893   -0.1297   -0.1263    0.0829    0.1146    0.1083    0.0600
   -0.0343   -0.3779    0.1065    0.3992    0.2066   -0.3149   -0.0089   -0.0916   -0.0222    0.0032   -0.1363   -0.1702    0.0059    0.3385    0.2162
    0.0618   -0.1513    0.1417   -0.1844    0.0846    0.0036    0.1798   -0.2219   -0.0729   -0.0581    0.1733    0.2369    0.1535   -0.0489    0.0491
    0.0544   -0.2557    0.0243   -0.0554   -0.2783   -0.2822    0.6476    0.1633   -0.1530    0.4791   -0.0351   -0.0877    0.1246    0.0150    0.2277
    0.2663    0.1528    0.1494   -0.0407    0.0096    0.4694   -0.1303   -0.0893   -0.1266   -0.1709    0.4969    0.2061    0.2003   -0.3123   -0.2366
   -0.5369   -0.2308    0.2989    0.3189    0.4289   -0.0620   -0.0133    0.2445   -0.2775   -0.0713   -0.1156    0.0129   -0.2250   -0.2450    0.5264
    0.2755    0.2552    0.0031   -0.5586   -0.2286    0.0695    0.1570   -0.0321    0.1618   -0.3076    0.2594    0.2107    0.1243    0.3395    0.0260
   -0.4115   -0.0068   -0.0229    0.0189   -0.4013    0.2605   -0.2028    0.1050    0.0577    0.2234    0.3123   -0.0643   -0.1998   -0.0266    0.1533
    0.0066   -0.0327    0.0130    0.0817    0.0258    0.1196   -0.0610   -0.0605   -0.1290    0.1020    0.0831    0.0257    0.1124   -0.1464   -0.1545
    0.3602    0.2356    0.1184   -0.2522   -0.0306    0.2737    0.3444   -0.1652    0.2510   -0.1763    0.3047    0.0772   -0.3166   -0.4650   -0.1691
   -0.1881    0.1552    0.0119    0.1321    0.3246    0.0352   -0.2550    0.2124   -0.1284   -0.2292   -0.2541    0.0247    0.0387    0.0045    0.1263
   -0.2722   -0.2290    0.0889    0.3339    0.2808   -0.1718   -0.2520    0.1500    0.0115   -0.1775   -0.2271    0.0357   -0.0584    0.0010    0.4739
    0.0275    0.2651    0.2166   -0.2113    0.2603    0.2496    0.1726   -0.0389   -0.2758   -0.1997    0.1897    0.1525    0.0904   -0.1338   -0.0667
   -0.1500   -0.1471   -0.0139    0.0765    0.1940    0.0436   -0.3935   -0.0344    0.0330   -0.2192   -0.0419    0.0964   -0.0170    0.0823   -0.1049
    0.5355   -0.1411    0.0452    0.1215    0.1902   -0.4046    0.0411   -0.4058    0.2525   -0.2668   -0.0716   -0.1605   -0.1132    0.3145   -0.2036
   -0.0885    0.2229   -0.0299   -0.0124   -0.1432    0.0235   -0.0815    0.1245    0.2248   -0.0721   -0.0147   -0.0504   -0.3070   -0.2132    0.2714
    0.3065    0.1538    0.0976   -0.2684   -0.0850    0.2965   -0.0311   -0.3603    0.1956   -0.2121    0.4772    0.1421   -0.2157   -0.3283   -0.3742

  Columns 31 through 45

    0.0948   -0.1445    0.1256    0.1639   -0.2864    0.1612    0.0210   -0.1725   -0.0874    0.3103    0.0275   -0.1293    0.0780   -0.0254    0.1281
   -0.2636    0.2316   -0.5610    0.1968    0.3746   -0.1498    0.0132   -0.4189   -0.2369   -0.3241   -0.0756    0.0226   -0.4398   -0.0436   -0.0224
    0.3152    0.0613   -0.1839   -0.1370   -0.2039   -0.1399    0.0418   -0.3139    0.2437   -0.1160   -0.0828   -0.1196   -0.0265    0.1248    0.2863
    0.0659    0.0501    0.3283    0.0399   -0.2420    0.0687   -0.0458    0.1701    0.1705    0.0813   -0.0727   -0.0434    0.4988    0.0585    0.0723
    0.2656   -0.0395    0.0318   -0.1855   -0.3702    0.0545    0.3749    0.2373   -0.3743    0.2223    0.0860    0.0879    0.1396   -0.2328   -0.4067
   -0.0597   -0.2582    0.2282   -0.3227   -0.1993   -0.3288   -0.8174   -0.0647   -0.0117   -0.0290    0.1942   -0.0832    0.1752    0.1872   -0.0308
   -0.2578    0.0113   -0.1754   -0.1928    0.1265   -0.4044   -0.3073   -0.0170    0.0462   -0.1899    0.1057   -0.0431    0.0595    0.1750    0.0180
   -0.1789   -0.3707    0.1760    0.1799    0.1169    0.1803   -0.2024    0.1205   -0.1165    0.3164    0.1967   -0.0599    0.0512   -0.1469    0.0557
   -0.2244    0.2411   -0.1883    0.3764    0.5200    0.2788    0.1391   -0.1555   -0.0344   -0.1250   -0.0409    0.1180   -0.7669    0.0017    0.1420
   -0.0539   -0.0166    0.3672   -0.2362   -0.2245   -0.1633   -0.4363    0.4068   -0.1393   -0.2822    0.1347    0.1482    0.4653   -0.1329   -0.1877
    0.0389   -0.0814   -0.0763    0.0825   -0.2712    0.2013    0.6594    0.0057   -0.8038    0.1018    0.0286    0.1804    0.0083   -0.5634   -0.7327
    0.1523   -0.3044    0.0445   -0.2515   -0.0906   -0.2194   -0.3834   -0.0915    0.4598    0.2295    0.0873   -0.2526    0.1777    0.3195    0.3820
    0.0280    0.1419    0.0492   -0.1152   -0.2380   -0.1733   -0.0417    0.3662    0.1061   -0.0279   -0.0564   -0.0167    0.4917    0.0734    0.1499
    0.0666    0.3170    0.1796   -0.2144   -0.2680   -0.1788   -0.0524   -0.0172    0.1232   -0.3269   -0.1634    0.0872    0.1050    0.2208   -0.1069
   -0.2162   -0.0964   -0.0089    0.0347   -0.0291    0.0570    0.0248    0.1566   -0.4006    0.1315   -0.2309    0.1069   -0.0940   -0.0757   -0.3878
   -0.3968   -0.0802   -0.1999    0.3181   -0.0343    0.0618    0.0544    0.2663   -0.5369    0.2755   -0.4115    0.0066    0.3602   -0.1881   -0.2722
   -0.0698   -0.0655    0.1888   -0.1686   -0.3779   -0.1513   -0.2557    0.1528   -0.2308    0.2552   -0.0068   -0.0327    0.2356    0.1552   -0.2290
   -0.0207   -0.1549    0.2938    0.0125    0.1065    0.1417    0.0243    0.1494    0.2989    0.0031   -0.0229    0.0130    0.1184    0.0119    0.0889
   -0.0893    0.4400   -0.2767    0.0108    0.3992   -0.1844   -0.0554   -0.0407    0.3189   -0.5586    0.0189    0.0817   -0.2522    0.1321    0.3339
   -0.0483    0.3391    0.1120    0.1503    0.2066    0.0846   -0.2783    0.0096    0.4289   -0.2286   -0.4013    0.0258   -0.0306    0.3246    0.2808
    0.1385    0.0921    0.4970   -0.2403   -0.3149    0.0036   -0.2822    0.4694   -0.0620    0.0695    0.2605    0.1196    0.2737    0.0352   -0.1718
   -0.0376   -0.2724   -0.0022    0.1669   -0.0089    0.1798    0.6476   -0.1303   -0.0133    0.1570   -0.2028   -0.0610    0.3444   -0.2550   -0.2520
    0.2814    0.1484   -0.2160   -0.2955   -0.0916   -0.2219    0.1633   -0.0893    0.2445   -0.0321    0.1050   -0.0605   -0.1652    0.2124    0.1500
   -0.1577   -0.1043   -0.2068    0.1893   -0.0222   -0.0729   -0.1530   -0.1266   -0.2775    0.1618    0.0577   -0.1290    0.2510   -0.1284    0.0115
    0.1031    0.0449   -0.1046   -0.1297    0.0032   -0.0581    0.4791   -0.1709   -0.0713   -0.3076    0.2234    0.1020   -0.1763   -0.2292   -0.1775
   -0.0168   -0.4317    0.5284   -0.1263   -0.1363    0.1733   -0.0351    0.4969   -0.1156    0.2594    0.3123    0.0831    0.3047   -0.2541   -0.2271
    0.0721   -0.0374    0.3405    0.0829   -0.1702    0.2369   -0.0877    0.2061    0.0129    0.2107   -0.0643    0.0257    0.0772    0.0247    0.0357
    0.0247    0.2717   -0.1427    0.1146    0.0059    0.1535    0.1246    0.2003   -0.2250    0.1243   -0.1998    0.1124   -0.3166    0.0387   -0.0584
    0.0337   -0.0728   -0.7204    0.1083    0.3385   -0.0489    0.0150   -0.3123   -0.2450    0.3395   -0.0266   -0.1464   -0.4650    0.0045    0.0010
    0.0821   -0.1057   -0.0466    0.0600    0.2162    0.0491    0.2277   -0.2366    0.5264    0.0260    0.1533   -0.1545   -0.1691    0.1263    0.4739
    0.5618   -0.1389    0.1311   -0.2366   -0.2612    0.1054    0.4214   -0.0968    0.2378    0.0742    0.1362   -0.0443    0.1859   -0.1439   -0.0511
   -0.1389    0.5639   -0.2361    0.1229    0.0935   -0.0847   -0.0760    0.0770   -0.0814   -0.3276   -0.2688    0.1306   -0.2093    0.1579    0.0904
    0.1311   -0.2361    0.8412   -0.3004   -0.2777    0.1211   -0.2301    0.3626    0.1841   -0.0530    0.1751    0.1391    0.3622   -0.0307   -0.2654
   -0.2366    0.1229   -0.3004    0.7172    0.3009    0.4748    0.2397   -0.0594   -0.2792    0.3463   -0.3037   -0.0301   -0.3640   -0.1323    0.2454
   -0.2612    0.0935   -0.2777    0.3009    0.5920    0.0779   -0.0899   -0.2107    0.1831   -0.1457   -0.0197   -0.0219   -0.4566    0.0721    0.3146
    0.1054   -0.0847    0.1211    0.4748    0.0779    0.6433    0.4315    0.0993   -0.2028    0.4349   -0.1294    0.0469   -0.1881   -0.2934   -0.0284
    0.4214   -0.0760   -0.2301    0.2397   -0.0899    0.4315    1.1878   -0.0961   -0.0734    0.2712   -0.1223   -0.0191    0.1098   -0.4717   -0.1285
   -0.0968    0.0770    0.3626   -0.0594   -0.2107    0.0993   -0.0961    0.7490   -0.2378    0.1050   -0.0866    0.1984    0.3329   -0.0800   -0.2338
    0.2378   -0.0814    0.1841   -0.2792    0.1831   -0.2028   -0.0734   -0.2378    1.1624   -0.3832   -0.0479   -0.1837    0.2305    0.3955    0.6359
    0.0742   -0.3276   -0.0530    0.3463   -0.1457    0.4349    0.2712    0.1050   -0.3832    0.9227   -0.0834   -0.1482   -0.0324   -0.1425   -0.0706
    0.1362   -0.2688    0.1751   -0.3037   -0.0197   -0.1294   -0.1223   -0.0866   -0.0479   -0.0834    0.6686    0.0149   -0.0792   -0.1867   -0.1316
   -0.0443    0.1306    0.1391   -0.0301   -0.0219    0.0469   -0.0191    0.1984   -0.1837   -0.1482    0.0149    0.1645   -0.0320   -0.0962   -0.2218
    0.1859   -0.2093    0.3622   -0.3640   -0.4566   -0.1881    0.1098    0.3329    0.2305   -0.0324   -0.0792   -0.0320    0.9048   -0.0456   -0.1577
   -0.1439    0.1579   -0.0307   -0.1323    0.0721   -0.2934   -0.4717   -0.0800    0.3955   -0.1425   -0.1867   -0.0962   -0.0456    0.4988    0.3098
   -0.0511    0.0904   -0.2654    0.2454    0.3146   -0.0284   -0.1285   -0.2338    0.6359   -0.0706   -0.1316   -0.2218   -0.1577    0.3098    0.8820
   -0.0817   -0.0692    0.4338   -0.1519   -0.0458    0.0668   -0.2008    0.2467    0.0650    0.1479   -0.1583    0.0835    0.0988    0.2058   -0.3573
    0.1416    0.0187    0.0680   -0.0562   -0.0146   -0.0171   -0.2208   -0.0073    0.2197   -0.1295    0.0158   -0.0208    0.0281    0.0550    0.2491
   -0.4990    0.0574   -0.2256    0.2206    0.3842   -0.1397   -0.4567   -0.0353   -0.0290   -0.1550   -0.2281   -0.0193   -0.1279    0.1608    0.1671
   -0.1164   -0.1255   -0.0674   -0.2109   -0.0759   -0.4299   -0.3661   -0.1675    0.3490   -0.1026    0.1468   -0.2091    0.2150    0.2954    0.3980
    0.0063   -0.2136    0.4850   -0.2805   -0.3146   -0.0851   -0.2834    0.4075   -0.1096   -0.0682    0.1309    0.1055    0.5218   -0.1392   -0.2866

  Columns 46 through 50

   -0.1545    0.0411   -0.2357    0.2349    0.0271
   -0.2713   -0.0787    0.3986   -0.1041   -0.3102
   -0.3821    0.3134   -0.1687    0.1657   -0.0949
    0.1368   -0.0046   -0.2010    0.1751    0.2027
    0.0131   -0.1013   -0.3998   -0.1983    0.0852
   -0.0251    0.3395    0.2651    0.3247    0.4680
    0.0240   -0.1217    0.2607    0.2915    0.0069
   -0.0059    0.0351    0.2268    0.0951    0.2586
    0.0621   -0.1643    0.1089   -0.3150   -0.5133
   -0.1232    0.2941    0.1718    0.0387    0.6809
   -0.1039   -0.3255   -0.1816   -0.3997    0.0700
   -0.0018    0.2577    0.0235    0.4270    0.0981
   -0.1081    0.0585   -0.1149    0.2562    0.2209
    0.1816   -0.0722   -0.2578    0.0518   -0.0654
    0.2430   -0.1540    0.2615   -0.2561    0.0935
    0.0275   -0.1500    0.5355   -0.0885    0.3065
    0.2651   -0.1471   -0.1411    0.2229    0.1538
    0.2166   -0.0139    0.0452   -0.0299    0.0976
   -0.2113    0.0765    0.1215   -0.0124   -0.2684
    0.2603    0.1940    0.1902   -0.1432   -0.0850
    0.2496    0.0436   -0.4046    0.0235    0.2965
    0.1726   -0.3935    0.0411   -0.0815   -0.0311
   -0.0389   -0.0344   -0.4058    0.1245   -0.3603
   -0.2758    0.0330    0.2525    0.2248    0.1956
   -0.1997   -0.2192   -0.2668   -0.0721   -0.2121
    0.1897   -0.0419   -0.0716   -0.0147    0.4772
    0.1525    0.0964   -0.1605   -0.0504    0.1421
    0.0904   -0.0170   -0.1132   -0.3070   -0.2157
   -0.1338    0.0823    0.3145   -0.2132   -0.3283
   -0.0667   -0.1049   -0.2036    0.2714   -0.3742
   -0.0817    0.1416   -0.4990   -0.1164    0.0063
   -0.0692    0.0187    0.0574   -0.1255   -0.2136
    0.4338    0.0680   -0.2256   -0.0674    0.4850
   -0.1519   -0.0562    0.2206   -0.2109   -0.2805
   -0.0458   -0.0146    0.3842   -0.0759   -0.3146
    0.0668   -0.0171   -0.1397   -0.4299   -0.0851
   -0.2008   -0.2208   -0.4567   -0.3661   -0.2834
    0.2467   -0.0073   -0.0353   -0.1675    0.4075
    0.0650    0.2197   -0.0290    0.3490   -0.1096
    0.1479   -0.1295   -0.1550   -0.1026   -0.0682
   -0.1583    0.0158   -0.2281    0.1468    0.1309
    0.0835   -0.0208   -0.0193   -0.2091    0.1055
    0.0988    0.0281   -0.1279    0.2150    0.5218
    0.2058    0.0550    0.1608    0.2954   -0.1392
   -0.3573    0.2491    0.1671    0.3980   -0.2866
    0.7949   -0.2198   -0.0021   -0.2056    0.0743
   -0.2198    0.3682    0.0427    0.0429    0.1559
   -0.0021    0.0427    0.7153    0.0822    0.0522
   -0.2056    0.0429    0.0822    0.6820    0.0415
    0.0743    0.1559    0.0522    0.0415    0.6538

EDIT

This is how i tried to go around with my problem:

Sig = cov(x);   % Covariance calculation of a 12x50 matrix
 A = chol(Sig);
 Sigma = A*A';
p = mvnrnd(mu,Sigma,20);

but when i run this, it gives me this error:

Matrix must be positive definite.
Error at A = chol(Sig);

Still my matrix is not positive definite. Any idea how to fix this?

elizwet
  • 11
  • 4
  • Is `sigma` symmetric positive definite? What do you get from `[T,err] = cholcov(sigma);`? What is `err`? – horchler Jul 27 '13 at 19:53
  • Yes, mvnrnd DOES work with higher dimensions. But beyond the issue of positive definiteness, what version of MATLAB are you using? What are the values of mu and sigma? Are they real? At least tell us what eig produces for Sigma. What are the min and max eigenvalues? –  Jul 27 '13 at 20:18
  • @horchler, err is zero(err = 0). – elizwet Jul 28 '13 at 01:47
  • @woodchips, my matlab version is R2008b. My mu and sigma are all real. – elizwet Jul 28 '13 at 01:50
  • You still did not tell us what the eigenvalues are though, the most important piece of information you could give us. –  Jul 28 '13 at 01:53
  • I read from the mvnrnd documentation saying: [T,p] = chol(sigma); if (p~=0) r = nan; return; end here my p is zero, so that is why I am having NaN. How can I fix this then – elizwet Jul 28 '13 at 01:53
  • Here are the eig: E = 1.0e+003 * -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.3178 1.8892 1.9005 2.2103 2.6608 3.0017 3.3238 3.5207 4.8989 6.1014 7.1987 – elizwet Jul 28 '13 at 01:57
  • Sorry, but you need to learn to use better formatting. Those numbers that look like zeros are NOT really zero. Regardless, they are NEGATIVE. This matrix is NOT positive definite. It does NOT correspond to a valid covariance matrix, so mvnrnd MUST fail. –  Jul 28 '13 at 01:59
  • @woodchips, sorry about the mess. I am new here and am learning how to use it efficiently. Ok, since my matrix is not positive definite, how can I make it positive definite so that I can fix this error? – elizwet Jul 28 '13 at 02:07
  • My R2012b version `mvnrand` and `chol`/`cholcov` (used under the hood) were updated in 2011 and 2010, respectively, so they've seen some changes since. BTW, there's no point in giving a 50-by-50 matrix copy-and-pasted from the the command window when you only have `format short` turned on. The proper way to share such a thing is via a `.mat` file (see `save`). – horchler Jul 28 '13 at 02:25
  • @horchler, thanks for the suggestion and advice on the formatting. We have all come to the agreement that my Sigma is not positive semidefinite, now I am asking how I can make my Sigma positive semidefinite so as to fix this error. – elizwet Jul 28 '13 at 02:38
  • I have no idea how you're obtaining your covariance matrix (which could be the issue itself), but otherwise, you'll need know the difference between covariance and correlation to look into methods for finding the "[nearest correlation matrix](http://nickhigham.wordpress.com/2013/02/13/the-nearest-correlation-matrix/)" and "[nearest covariance matrix](http://www.maths.manchester.ac.uk/~clucas/)". This area has been active recently. – horchler Jul 28 '13 at 02:39
  • I just use the matlab function cov to calculate the covariance. – elizwet Jul 28 '13 at 02:48
  • Does anyone have any idea on how to make a covariance matrix which is non positive define to a positive define one? i read from here and other places and they suggesting different idea. I use topdm function from Matlab Central, but it did not work for me. i saw lots of suggestion which cannot work for me. So suggest deleting some data which i don't want to go for. Is there any way i can make a covariance matrix positive definite? – elizwet Jul 28 '13 at 19:00
  • I am still looking at how to make my covariance matrix a positive definite in matlab. Does anyone have any idea how to do this? – elizwet Jul 30 '13 at 12:06

1 Answers1

0

I've seen this question before. How do you compute the nearest Symmetric, Positive Definite matrix (often abbreviated SPD) to a given matrix? I was unsatisfied with what I found on the MATLAB Central file exchange, so I just posted nearestSPD on the FEX.

Starting from a matrix that is complete crap in terms of being SPD...

U = randn(100);
tic,Uj = nearestSPD(U);toc
Elapsed time is 0.006049 seconds.

The ultimate test of course, is to use chol. If chol returns a second argument that is zero, then MATLAB (and mvnrnd) will be happy!

[R,p] = chol(Uj);
p
p =
     0

mvnrnd(zeros(1,100),Uj,1)
ans =
  Columns 1 through 13
   -2.1788   -1.1002    2.1801   -3.3030   -2.5108    0.1486   -0.7695   -1.6912    3.7952   -1.0618    0.7432    1.8749    1.1410
  Columns 14 through 26
   -0.0626   -1.2843    1.4384   -3.9369   -0.1819    1.9848    2.7395    2.0121   -0.2007   -0.3842    0.0343    0.4587    0.4310
  Columns 27 through 39
   -1.2035   -0.3946   -1.5155   -1.8792   -2.4681    0.7230   -1.2775   -0.8252    1.3161    0.4606   -2.0888   -4.0684   -0.5214
  Columns 40 through 52
    1.5011   -0.5847   -1.7154    0.8114    1.3967    1.2961   -1.4040    1.7476   -0.6991   -0.8323    0.5736    1.8499   -0.0301
  Columns 53 through 65
   -2.9938    0.6624   -0.0497   -0.5262    1.8294    1.8198    1.6230   -1.1492    0.8652    0.7090    0.1075    1.4513    1.6283
  Columns 66 through 78
    0.9870   -1.5733   -0.3842   -0.8873   -0.3926    1.1245    1.7367    1.3051   -2.3758   -0.7082   -4.0189   -2.5654   -0.0725
  Columns 79 through 91
   -2.0292    2.0114    0.0484   -1.7458    0.3135   -0.1224    3.0652   -0.4663   -2.0318    1.4760    0.5025   -0.8270    1.5677
  Columns 92 through 100
   -0.4954   -1.1622   -1.5471    1.1630   -1.6892   -1.1148   -0.8012    1.0580   -2.1881
  • Can the above your function convert a covariance matrix with is not positive definite to a positive definite matrix? If you look at my edit on my post, i am presently trying that technique, but still not fixing the problem. – elizwet Jul 30 '13 at 14:18
  • That is the point of the tool. It does exactly that, converting a matrix into the closest possible matrix, which is indeed symmetric and positive definite, thus a viable covariance matrix. –  Jul 30 '13 at 17:42
  • Thanks for the tool. I just want to ask you the difference between positive definite and positive semidefinite. I was made to understand that a positive semidefinite may not necessary be positive definite. Can you clarify this to me please. – elizwet Jul 30 '13 at 17:51
  • Positive semi-definite allows for a zero eigenvalue. Thats what the "semi" tells you. A matrix with a zero eigenvalue will be singular, so not invertible. A truly positive definite matrix will have no zero eigenvalues. My tool ensures the result will pass the chol test, although it may still have some essentially numerically zero eigenvalues. This is done by what should be essentially insignificant alterations to the result after the main work is done. –  Jul 30 '13 at 18:14
  • One more question, When is a covariance matrix a positive semidefinite matrix? when is it positive definite? Does the number of elements in the covariance matrix matters for a positive definiteness? Does the number of observation in the matrix whose covariance is going to be calculated using Cov in matlab? If so, how do you fix the problem in a case where the observation whose covariance is to be calculated is very few? – elizwet Jul 31 '13 at 19:02
  • Having too little data will cause the covariance matrix to be singular. The solution is simple (in theory) - get more data. You essentially have too little information to estimate all the parameters you need. –  Aug 01 '13 at 01:46
  • This most eb the case. I tried to estimate the covariance of a 12x50 matrix, but ran into this problem. Now can you people recommend a method i can use to add more data as woodchips suggested and an explanation of how this method works? – elizwet Aug 01 '13 at 15:13