[
https://issues.apache.org/jira/browse/MATH-1557?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
Randy Strauss updated MATH-1557:
--------------------------------
Attachment: real-eigen-vectors-test-case.txt
> Enhancement request: Complex Eigen Vectors
> ------------------------------------------
>
> Key: MATH-1557
> URL: https://issues.apache.org/jira/browse/MATH-1557
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 3.6.1
> Reporter: Randy Strauss
> Priority: Major
> Attachments: real-eigen-vectors-test-case.txt
>
>
> I have a real hamiltonian matrix and need to get complex eigenvalues and
> eigenvectors, just like MatLab produces (I'm moving code from MatLab to Java).
> To give you a test case:
> I wrap a RealMatrix in an RMatrix and add a name, to help with testing
> and use this to set a single or multiple values on a single row, starting at
> col c:
> {{ public void set(int r, int c, double...val) {...
> }}
> Methods to create the hamiltonian matrix, the real and imaginary parts of the
> eigenvectors (which this library creates) and the real and imaginary parts of
> the eigenvectors follow. Note that the eigenvalues (evals) come as a
> diagonal matrix.
> (Meanwhile, I'll try the ojAlg library... The only other one I haven't
> investigated is JEigen, a wrapper around the C++ eigen library...)
> {{RMatrix getHam() {}}
> {{ RMatrix mm = RMatrix.zeros(24,24).setName("ml:Ham()");}}
> {{ mm.set(0,9, 1.0);}}
> {{ mm.set(1,10, 1.0);}}
> {{ mm.set(2,11, 1.0);}}
> {{ mm.set(3,6, 1.0);}}
> {{ mm.set(4,7, 1.0);}}
> {{ mm.set(5,8, 1.0);}}
> {{ mm.set(6,18, -50.2882527112151934);}}
> {{ mm.set(7,19, -50.2882527112151934);}}
> {{ mm.set(8,20, -104.6706084865823385);}}
> {{ mm.set(9,3, -0.0000000000000012, -9.8066499999999994);}}
> {{ mm.set(10,3, 9.8066499999999994, -0.0000000000000012);}}
> {{ mm.set(11,23, -2.6882428037761028);}}
> {{ mm.set(12,0, -1000.0);}}
> {{ mm.set(13,1, -1000.0);}}
> {{ mm.set(14,2, -50000.0);}}
> {{ mm.set(15,3, -1000.0);}}
> {{ mm.setRow(15,21, 0.0000000000000012, -9.8066499999999994);}}
> {{ mm.set(16,4, -1000.0);}}
> {{ mm.setRow(16,21, 9.8066499999999994, 0.0000000000000012);}}
> {{ mm.set(17,5, -20.0);}}
> {{ mm.set(18,6, -10.0);}}
> {{ mm.set(18,15, -1.0);}}
> {{ mm.set(19,7, -10.0);}}
> {{ mm.set(19,16, -1.0);}}
> {{ mm.set(20,8, -5.0);}}
> {{ mm.set(20,17, -1.0);}}
> {{ mm.set(21,9, -100.0);}}
> {{ mm.set(21,12, -1.0);}}
> {{ mm.set(22,10, -100.0);}}
> {{ mm.set(22,13, -1.0);}}
> {{ mm.set(23,11, -4000.0);}}
> {{ mm.set(23,14, -1.0);}}
> {{return mm;}}
> {{ }}}
> {{RMatrix getRealEvals() {
> RMatrix mm = RMatrix.zeros(24,24).setName("ml:realEvals");
> mm.set(0,0, -19.2515559709009736);
> mm.set(1,1, 19.2515559709010127);
> mm.set(2,2, -11.0808348997399158);
> mm.set(3,3, 11.0808348997399193);
> mm.set(4,4, -2.7428623037015809);
> mm.set(5,5, -2.7428623037015809);
> mm.set(6,6, 2.7428623037015827);
> mm.set(7,7, 2.7428623037015827);
> mm.set(8,8, -103.636174429371124);
> mm.set(9,9, 103.6361744293712093);
> mm.set(10,10, -19.251555970901066);
> mm.set(11,11, 19.2515559709010518);
> mm.set(12,12, -11.0808348997399442);
> mm.set(13,13, 11.0808348997399424);
> mm.set(14,14, -22.7886373854221205);
> mm.set(15,15, 22.7886373854220921);
> mm.set(16,16, -2.7428623037015889);
> mm.set(17,17, -2.7428623037015889);
> mm.set(18,18, 2.742862303701588);
> mm.set(19,19, 2.742862303701588);
> mm.set(20,20, -3.5375930728932987);
> mm.set(21,21, -2.0077471326476353);
> mm.set(22,22, 2.0077471326476282);
> mm.set(23,23, 3.5375930728932929);
> return mm;
> }
> RMatrix getImagEvals() {
> RMatrix mm = RMatrix.zeros(24,24).setName("ml:imagEvals");
> mm.set(4,4, 1.6690370723880767);
> mm.set(5,5, -1.6690370723880767);
> mm.set(6,6, 1.6690370723880767);
> mm.set(7,7, -1.6690370723880767);
> mm.set(16,16, 1.6690370723880816);
> mm.set(17,17, -1.6690370723880816);
> mm.set(18,18, 1.6690370723880807);
> mm.set(19,19, -1.6690370723880807);
> return mm;
> }
> RMatrix getRealEvecs() {
> RMatrix mm = RMatrix.zeros(24,24).setName("ml:realEvecs");
> mm.set(0,0, 0.0004832230449602, -0.0004832230449602, -0.0009379501782333,
> 0.0009379501782333, 0.0025918144777927, 0.0025918144777927,
> 0.0025918144777927, 0.0025918144777927, -0.0, 0.0, -0.0, -0.0, -0.0, 0.0,
> 0.0, -0.0, 0.0, 0.0, -0.0, -0.0, 0.0, -0.0, 0.0, -0.0);
> mm.set(1,8, -0.0, 0.0, 0.0004832230449602, 0.0004832230449602,
> -0.0009379501782333, 0.0009379501782333, -0.0, -0.0, -0.0025918144777927,
> -0.0025918144777927, 0.0025918144777927, 0.0025918144777927, 0.0, 0.0, -0.0,
> -0.0);
> mm.set(2,8, 0.0002484038122836, -0.0002484038122836, 0.0, -0.0, 0.0, -0.0,
> 0.0, 0.0, 0.0, 0.0, -0.0, -0.0, 0.0000707518552269, 0.0, -0.0,
> 0.0000707518552269);
> mm.set(3,0, -0.0, 0.0, 0.0, -0.0, 0.0, 0.0, 0.0, 0.0, -0.0, 0.0,
> 0.0182624329599153, 0.0182624329599153, -0.0117436760551143,
> 0.0117436760551143, 0.0, -0.0, 0.0002203558678773, 0.0002203558678773,
> -0.0002203558678772, -0.0002203558678772, -0.0, -0.0, -0.0, -0.0);
> mm.set(4,0, -0.0182624329599153, 0.0182624329599153, 0.0117436760551143,
> -0.0117436760551143, 0.0002203558678772, 0.0002203558678772,
> 0.0002203558678772, 0.0002203558678772, 0.0, -0.0, -0.0, -0.0, 0.0, -0.0,
> -0.0, 0.0, -0.0, -0.0, 0.0, 0.0, 0.0, 0.0, -0.0, 0.0);
> mm.set(5,0, -0.0, -0.0, 0.0, 0.0, -0.0, -0.0, 0.0, 0.0, 0.0,
> 0.0000000000000002, 0.0, -0.0000000000000001, -0.0000000000000001, -0.0,
> -0.0428074741554847, -0.0428074741554848, -0.0000000000000001,
> -0.0000000000000001, -0.0, -0.0, -0.0, 0.0979346456757011, 0.097934645675701,
> -0.0);
> mm.set(6,0, 0.0, 0.0, -0.0, -0.0, -0.0, -0.0, 0.0, 0.0, -0.0000000000000002,
> -0.0000000000000002, -0.3515802502926373, 0.3515802502926377,
> 0.1301297354827506, 0.1301297354827507, -0.0000000000000002, -0.0,
> -0.0059148347790043, -0.0059148347790043, -0.0059148347790042,
> -0.0059148347790042, 0.0, -0.0, 0.0, -0.0);
> mm.set(7,0, 0.3515802502926374, 0.3515802502926376, -0.1301297354827509,
> -0.1301297354827506, -0.0059148347790042, -0.0059148347790042,
> 0.0059148347790041, 0.0059148347790041, 0.0, 0.0, 0.0, -0.0, -0.0, -0.0,
> 0.0000000000000001, 0.0000000000000001, 0.0, 0.0, 0.0, 0.0, 0.0, -0.0, -0.0,
> -0.0);
> mm.set(8,8, 0.0000000000000001, -0.0000000000000023, -0.0000000000000002,
> -0.0000000000000003, 0.0, 0.0, 0.9755240059151693, -0.9755240059151695,
> -0.0000000000000002, -0.0000000000000002, -0.0000000000000002,
> -0.0000000000000002, 0.0, -0.196628004042251, 0.1966280040422509, -0.0);
> mm.set(9,0, -0.0093027954964812, -0.0093027954964812, 0.0103932710691854,
> 0.0103932710691854, -0.0044767115132939, -0.0044767115132939,
> 0.0044767115132939, 0.0044767115132939, 0.0, 0.0, 0.0, -0.0, 0.0, 0.0, -0.0,
> -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.0, 0.0, -0.0);
> mm.set(10,0, 0.0, 0.0, -0.0, -0.0, 0.0, 0.0, -0.0, -0.0, 0.0, 0.0,
> -0.0093027954964812, 0.0093027954964812, 0.0103932710691854,
> 0.0103932710691854, -0.0, -0.0, 0.0044767115132939, 0.0044767115132939,
> 0.0044767115132939, 0.0044767115132939, 0.0, 0.0, -0.0, -0.0);
> mm.set(11,8, -0.0257436208187483, -0.0257436208187483, -0.0, -0.0, 0.0, 0.0,
> 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.0002502912729449, -0.0, 0.0,
> 0.0002502912729449);
> mm.set(12,0, 0.0251004669799487, 0.0251004669799487, -0.0846461649072455,
> -0.0846461649072456, 0.9449305837536955, 0.9449305837536955,
> -0.9449305837536957, -0.9449305837536957, -0.0, -0.0, -0.0, 0.0, -0.0, -0.0,
> 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.0, -0.0, 0.0);
> mm.set(13,8, -0.0000000000000015, -0.0000000000000004, 0.0251004669799488,
> -0.0251004669799487, -0.0846461649072455, -0.0846461649072455,
> -0.0000000000000004, 0.0000000000000001, -0.9449305837536948,
> -0.9449305837536948, -0.9449305837536955, -0.9449305837536955,
> 0.0000000000000001, 0.0000000000000013, 0.0000000000000009,
> 0.0000000000000005);
> mm.set(14,8, 0.1198441633200829, 0.1198441633200825, -0.0, -0.0, -0.0, 0.0,
> 0.0000000000000001, -0.0000000000000001, 0.0000000000000006,
> 0.0000000000000006, 0.0000000000000005, 0.0000000000000005,
> 0.9999999119316623, -0.0000000000000004, -0.0000000000000014,
> -0.9999999119316623);
> mm.set(15,0, -0.0000000000000001, -0.0000000000000001, 0.0000000000000001,
> 0.0000000000000001, 0.0, 0.0, -0.0, -0.0, -0.0000000000000047,
> 0.0000000000000008, 0.9246701470035759, -0.9246701470035759,
> -0.9835697352164537, -0.9835697352164535, 0.0000000000000004,
> -0.0000000000000002, 0.0570691616413982, 0.0570691616413982,
> 0.0570691616413963, 0.0570691616413963, -0.0000000000000002,
> -0.0000000000000001, -0.0000000000000001, 0.0000000000000001);
> mm.set(16,0, -0.9246701470035759, -0.9246701470035759, 0.9835697352164536,
> 0.9835697352164536, 0.0570691616413962, 0.0570691616413962,
> -0.0570691616413952, -0.0570691616413952, 0.0, 0.0, -0.0000000000000001,
> 0.0000000000000001, 0.0000000000000002, 0.0000000000000002,
> -0.0000000000000001, -0.0000000000000001, -0.0, -0.0, -0.0, -0.0, 0.0,
> 0.0000000000000001, 0.0000000000000001, -0.0);
> mm.set(17,8, -0.0000000000000004, 0.0000000000000007, 0.0000000000000001,
> 0.0000000000000001, -0.0000000000000001, 0.0000000000000001,
> -0.0375691388927618, 0.0375691388927611, -0.0000000000000005,
> -0.0000000000000005, 0.0000000000000003, 0.0000000000000003,
> -0.0000000000000001, 0.9755675312214632, -0.9755675312214632,
> 0.0000000000000002);
> mm.set(18,0, 0.0, -0.0, -0.0, 0.0, -0.0, -0.0, -0.0, -0.0,
> -0.0000000000000002, -0.0, -0.1345933990914463, -0.1345933990914461,
> 0.0286736173299098, -0.0286736173299096, -0.0000000000000001, 0.0,
> -0.0006000508905014, -0.0006000508905014, 0.0006000508905015,
> 0.0006000508905015, -0.0, -0.0, -0.0, 0.0);
> mm.set(19,0, 0.1345933990914462, -0.1345933990914462, -0.0286736173299099,
> 0.0286736173299098, -0.0006000508905014, -0.0006000508905014,
> -0.0006000508905014, -0.0006000508905014, 0.0, 0.0, 0.0, 0.0, -0.0, 0.0, 0.0,
> -0.0, 0.0, 0.0, -0.0, -0.0, 0.0, 0.0, -0.0, 0.0);
> mm.set(20,8, -0.0000000000000001, 0.0000000000000003, -0.0,
> 0.0000000000000001, 0.0, -0.0, 0.2123887799355335, 0.2123887799355333,
> -0.0000000000000001, -0.0000000000000001, -0.0, -0.0, 0.0,
> -0.0037716348172817, -0.0037716348172816, -0.0);
> mm.set(21,0, -0.0470184895203464, 0.0470184895203463, 0.0861560478654635,
> -0.0861560478654635, -0.0077681276851642, -0.0077681276851642,
> -0.0077681276851642, -0.0077681276851642, 0.0, -0.0, 0.0, 0.0, 0.0, -0.0,
> -0.0, 0.0, -0.0, -0.0, 0.0, 0.0, -0.0, -0.0, 0.0, 0.0);
> mm.set(22,8, -0.0000000000000011, -0.0000000000000002, -0.0470184895203463,
> -0.0470184895203464, 0.0861560478654634, -0.0861560478654634,
> -0.0000000000000001, 0.0, 0.007768127685165, 0.007768127685165,
> -0.0077681276851632, -0.0077681276851632, 0.0000000000000002,
> 0.0000000000000007, -0.0000000000000001, 0.0000000000000001);
> mm.set(23,8, -0.9924588559737858, 0.9924588559737859, -0.0, 0.0,
> -0.0000000000000001, -0.0, -0.0, -0.0000000000000001, -0.0, -0.0, 0.0, 0.0,
> -0.0003293707964667, -0.0, 0.0, -0.0003293707964667);
> return mm;
> }
> @Override RMatrix getImagEvecs() {
> RMatrix mm = RMatrix.zeros(24,24).setName("ml:imagEvecs");
> mm.set(0,4, -0.0015771241751182, 0.0015771241751182, 0.0015771241751182,
> -0.0015771241751182);
> mm.set(0,16, 0.0, -0.0, -0.0, 0.0);
> mm.set(1,16, 0.0015771241751182, -0.0015771241751182, 0.0015771241751182,
> -0.0015771241751182);
> mm.set(2,16, -0.0, 0.0, 0.0, -0.0);
> mm.set(3,4, 0.0, -0.0, -0.0, 0.0);
> mm.set(3,16, 0.0031817321876536, -0.0031817321876536, 0.0031817321876535,
> -0.0031817321876535);
> mm.set(4,4, 0.0031817321876535, -0.0031817321876535, -0.0031817321876535,
> 0.0031817321876535);
> mm.set(4,16, -0.0, 0.0, -0.0, 0.0);
> mm.set(5,4, 0.0, -0.0, 0.0, -0.0);
> mm.set(5,16, 0.0, -0.0, -0.0, 0.0);
> mm.set(6,4, -0.0, 0.0, -0.0, 0.0);
> mm.set(6,16, -0.0083592711653836, 0.0083592711653836, 0.0083592711653836,
> -0.0083592711653836);
> mm.set(7,4, -0.0083592711653836, 0.0083592711653836, -0.0083592711653835,
> 0.0083592711653835);
> mm.set(7,16, 0.0, -0.0, -0.0, 0.0);
> mm.set(8,16, 0.0000000000000001, -0.0000000000000001, 0.0000000000000001,
> -0.0000000000000001);
> mm.set(9,4, 0.0086516688963765, -0.0086516688963765, 0.0086516688963765,
> -0.0086516688963765);
> mm.set(9,16, 0.0, -0.0, -0.0, 0.0);
> mm.set(10,4, -0.0, 0.0, -0.0, 0.0);
> mm.set(10,16, -0.0086516688963765, 0.0086516688963765, 0.0086516688963765,
> -0.0086516688963765);
> mm.set(11,16, -0.0, 0.0, 0.0, -0.0);
> mm.set(12,16, 0.0, -0.0, -0.0, 0.0);
> mm.set(14,16, 0.0000000000000003, -0.0000000000000003, -0.0000000000000007,
> 0.0000000000000007);
> mm.set(15,4, 0.0, -0.0, 0.0, -0.0);
> mm.set(15,16, 0.0838820942848218, -0.0838820942848218, -0.0838820942848232,
> 0.0838820942848232);
> mm.set(16,4, 0.0838820942848225, -0.0838820942848225, 0.0838820942848227,
> -0.0838820942848227);
> mm.set(16,16, -0.0, 0.0, 0.0, -0.0);
> mm.set(17,16, 0.0, -0.0, 0.0, -0.0);
> mm.set(18,4, -0.0, 0.0, 0.0, -0.0);
> mm.set(18,16, -0.0002596282538929, 0.0002596282538929, -0.0002596282538928,
> 0.0002596282538928);
> mm.set(19,4, -0.000259628253893, 0.000259628253893, 0.000259628253893,
> -0.000259628253893);
> mm.set(19,16, 0.0, -0.0, 0.0, -0.0);
> mm.set(20,16, 0.0, -0.0, 0.0, -0.0);
> mm.set(21,4, 0.310697914145376, -0.310697914145376, -0.3106979141453762,
> 0.3106979141453762);
> mm.set(21,16, 0.0, -0.0, 0.0, -0.0);
> mm.set(22,16, -0.310697914145378, 0.310697914145378, -0.310697914145376,
> 0.310697914145376);
> mm.set(23,16, 0.0000000000000001, -0.0000000000000001, -0.0, 0.0);
> return mm;
> }
> }}
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