/// <summary>
/// find some eigenvalues and -vectors of symmetric (hermitian) matrix
/// </summary>
/// <param name="A">input matrix, Size [n x n], symmetric (hermitian for complex A) </param>
/// <param name="V">output: n eigenvectors as columns. Size [n x n]. If V is null on input, the eigenvectors will not be computed and V is not changed. </param>
/// <param name="rangeStart">The eigenvalues will be returned by increasing size. This will determine the number of the first eigenvalue to be returned.</param>
/// <param name="rangeEnd">Determine the number of the last eigenvalue to be returned.</param>
/// <returns>diagonal matrix of size [n,n] with eigenvalues of A on the main diagonal.</returns>
/// <remarks><para>For computation the Lapack functions dsyevr, ssyevr, chesvr and zheesv are used. </para>
/// <para>Since A is symmetric, the eigenvalues will always be real. Therefore the return value will be of the same inner type as A.</para></remarks>
/// <exception cref="ILNumerics.Exceptions.ILArgumentException">if A is not square or <paramref name="rangeEnd"/> < <paramref name="rangeStart"/> or if either one is <= 0.</exception>
public static /*!HC:HCCls1*/ ILArray<double> eigSymm (/*!HC:HCCls1*/ ILArray<double> A, ref /*!HC:HCCls1*/ ILArray<double> V, /*!HC:HCArrReal*/ double rangeStart, /*!HC:HCArrReal*/ double rangeEnd) {
if (A.IsEmpty) {
V = /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
return /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
}
int n = A.Dimensions[0];
if (n != A.Dimensions[1])
throw new ILArgumentException("eigSymm: input matrix A must be square and symmetric/hermitian.");
/*!HC:HCCls1*/ ILArray<double> ret = null;
int m = 0,ldz = 0,info = 0;
if (rangeStart > rangeEnd)
throw new ILArgumentException("eigSymm: invalid range of eigenvalues requested");
/*!HC:HCCls1*/ ILArray<double> tmpA = A.copyUpperTriangle(n);
/*!HC:HCClsReal*/ ILArray<double> w = new /*!HC:HCClsReal*/ ILArray<double> (new /*!HC:HCArrReal*/ double [n],1,n);
/*!HC:HCArr1*/ double [] z;
char jobz;
if (object.Equals(V,null)) {
z = new /*!HC:HCArr1*/ double [1];
jobz = 'N';
ldz = 1;
} else {
z = new /*!HC:HCArr1*/ double [n * n];
jobz = 'V';
ldz = n;
}
int [] isuppz = new int[2 * n];
/*!HC:lapack_???evr*/ Lapack.dsyevr (jobz,'V','U',n,tmpA.m_data,n,rangeStart,rangeEnd,0,0,0, ref m,w.m_data,z,ldz,isuppz,ref info);
ret = ILMath.diag(/*!HC:HCClsConv3*/ /**/ (w));
if (jobz == 'V') {
V = new /*!HC:HCCls1*/ ILArray<double> (z,n,n);
V = V[null,ILMath.vector(0,m-1)];
}
/// <summary>
/// find all eigenvalues of symmetric (hermitian) matrix
/// </summary>
/// <param name="A">input matrix, Size [n x n], symmetric (hermitian for complex A) </param>
/// <returns>array of size [n,1] with eigenvalues of A.</returns>
/// <remarks><para>For computation the Lapack functions dsyevr, ssyevr, chesvr and zheesv are used. </para>
/// <para>Since A is symmetric, the eigenvalues will always be real. Therefore the return value will be of the same inner type as A.</para></remarks>
/// <exception cref="ILNumerics.Exceptions.ILArgumentException">if A is not square.</exception>
public static /*!HC:HCCls1*/ ILArray<double> eigSymm (/*!HC:HCCls1*/ ILArray<double> A) {
if (A.IsEmpty) {
return /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
}
int n = A.Dimensions[0];
if (n != A.Dimensions[1])
throw new ILArgumentException("eigSymm: input matrix A must be square and symmetric/hermitian.");
/*!HC:HCCls1*/ ILArray<double> ret = null;
int m = 0,info = 0;
/*!HC:HCCls1*/ ILArray<double> tmpA = A.copyUpperTriangle(n);
/*!HC:HCClsReal*/ ILArray<double> w = new /*!HC:HCClsReal*/ ILArray<double> (new /*!HC:HCArrReal*/ double [n],1,n);
/*!HC:HCArr1*/ double [] z = new /*!HC:HCArr1*/ double [1]; ;
int [] isuppz = new int[2 * n];
/*!HC:lapack_???evr*/ Lapack.dsyevr ('N','A','U',n,tmpA.m_data,n,0,0,0,0,0,ref m,w.m_data,z,1,isuppz,ref info);
ret = /*!HC:HCClsConv3*/ /**/ (w);
return ret;
}
/// <summary>
/// find all eigenvalues and -vectors of symmetric (hermitian) matrix
/// </summary>
/// <param name="A">input matrix, Size [n x n], symmetric (hermitian for complex A) </param>
/// <param name="V">output: n eigenvectors as columns. Size [n x n]. If V is null on input, the eigenvectors will not be computed and V is not changed. </param>
/// <returns>diagonal matrix of size [n,n] with eigenvalues of A on the main diagonal.</returns>
/// <remarks><para>For computation the Lapack functions dsyevr, ssyevr, chesvr and zheesv are used. </para>
/// <para>Since A is symmetric, the eigenvalues will always be real. Therefore the return value will be of the same inner type as A.</para></remarks>
/// <exception cref="ILNumerics.Exceptions.ILArgumentException">if A is not square.</exception>
public static /*!HC:HCCls1*/ ILArray<double> eigSymm (/*!HC:HCCls1*/ ILArray<double> A, ref /*!HC:HCCls1*/ ILArray<double> V) {
if (A.IsEmpty) {
V = /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
return /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
}
int n = A.Dimensions[0];
if (n != A.Dimensions[1])
throw new ILArgumentException("eigSymm: input matrix A must be square and symmetric/hermitian.");
/*!HC:HCCls1*/ ILArray<double> ret = null;
int m = 0,ldz = 0,info = 0;
/*!HC:HCCls1*/ ILArray<double> tmpA = A.copyUpperTriangle(n);
/*!HC:HCClsReal*/ ILArray<double> w = new /*!HC:HCClsReal*/ ILArray<double> (new /*!HC:HCArrReal*/ double [n],n,1);
/*!HC:HCArr1*/ double [] z;
char jobz;
if (object.Equals(V,null)) {
z = new /*!HC:HCArr1*/ double [1];
jobz = 'N';
ldz = 1;
} else {
z = new /*!HC:HCArr1*/ double [n * n];
jobz = 'V';
ldz = n;
}
int [] isuppz = new int[2 * n];
/*!HC:lapack_???evr*/ Lapack.dsyevr (jobz,'A','U',n,tmpA.m_data,n,1,n,0,0,0,ref m,w.m_data,z,ldz,isuppz,ref info);
if (info != 0)
throw new ILException("eigSymm: error returned from lapack: " + info);
if (jobz == 'V') {
V = new /*!HC:HCCls1*/ ILArray<double> (z,n,n);
V = V[null,ILMath.vector(0,m-1)];
ret = ILMath.diag(/*!HC:HCClsConv3*/ /**/ (w));
} else {
ret = /*!HC:HCClsConv3*/ /**/ (w);
}
return ret;
}
/// <summary>
/// find some eigenvalues and -vectors of symmetric (hermitian) matrix
/// </summary>
/// <param name="A">input matrix, Size [n x n], symmetric (hermitian for complex A) </param>
/// <param name="V">output: n eigenvectors as columns. Size [n x n]. If V is null on input, the eigenvectors will not be computed and V is not changed. </param>
/// <param name="rangeStart">specify the lowest limit for the range of eigenvalues to be queried.</param>
/// <param name="rangeEnd">specify the upper limit for the range of eigenvalues to be queried.</param>
/// <returns>diagonal matrix of size [n,n] with eigenvalues of A on the main diagonal.</returns>
/// <remarks><para>For computation the Lapack functions dsyevr, ssyevr, chesvr and zheesv are used. </para>
/// <para>Since A is symmetric, the eigenvalues will always be real. Therefore the return value will be of the same inner type as A.</para></remarks>
/// <exception cref="ILNumerics.Exceptions.ILArgumentException">if A is not square or <paramref name="rangeEnd"/> < <paramref name="rangeStart"/></exception>
public static /*!HC:HCCls1*/ ILArray<double> eigSymm (/*!HC:HCCls1*/ ILArray<double> A, ref /*!HC:HCCls1*/ ILArray<double> V, int rangeStart, int rangeEnd) {
if (A.IsEmpty) {
V = /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
return /*!HC:HCCls1*/ ILArray<double> .empty(A.Dimensions);
}
int n = A.Dimensions[0];
if (n != A.Dimensions[1])
throw new ILArgumentException("eigSymm: input matrix A must be square and symmetric/hermitian.");
/*!HC:HCCls1*/ ILArray<double> ret = null;
int m = 0,ldz = 0,info = 0;
if (rangeEnd < rangeStart || rangeStart < 1)
throw new ILArgumentException("eigSymm: invalid range of eigenvalues requested");
/*!HC:HCCls1*/ ILArray<double> tmpA = A.copyUpperTriangle(n);
/*!HC:HCClsReal*/ ILArray<double> w = new /*!HC:HCClsReal*/ ILArray<double> (new /*!HC:HCArrReal*/ double [n],1,n);
/*!HC:HCArr1*/ double [] z;
char jobz;
if (object.Equals(V,null)) {
z = new /*!HC:HCArr1*/ double [1];
jobz = 'N';
ldz = 1;
} else {
z = new /*!HC:HCArr1*/ double [n * n];
jobz = 'V';
ldz = n;
}
int [] isuppz = new int[2 * n];
/*!HC:lapack_???evr*/ Lapack.dsyevr (jobz,'I','U',n,tmpA.m_data,n,0,0,rangeStart,rangeEnd,0,ref m,w.m_data,z,ldz,isuppz,ref info);
ret = ILMath.diag(/*!HC:HCClsConv3*/ /**/ (w));
if (jobz == 'V') {
V = new /*!HC:HCCls1*/ ILArray<double> (z,n,n);
V = V[null,ILMath.vector(0,m-1)];
}
return ret;
}
