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java.lang.Object | +----org.netlib.lapack.DHSEIN
DHSEIN is a simplified interface to the JLAPACK routine dhsein. This interface converts Java-style 2D row-major arrays into the 1D column-major linearized arrays expected by the lower level JLAPACK routines. Using this interface also allows you to omit offset and leading dimension arguments. However, because of these conversions, these routines will be slower than the low level ones. Following is the description from the original Fortran source. Contact seymour@cs.utk.edu with any questions.* .. * * Purpose * ======= * * DHSEIN uses inverse iteration to find specified right and/or left * eigenvectors of a real upper Hessenberg matrix H. * * The right eigenvector x and the left eigenvector y of the matrix H * corresponding to an eigenvalue w are defined by: * * H * x = w * x, y**h * H = w * y**h * * where y**h denotes the conjugate transpose of the vector y. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'R': compute right eigenvectors only; * = 'L': compute left eigenvectors only; * = 'B': compute both right and left eigenvectors. * * EIGSRC (input) CHARACTER*1 * Specifies the source of eigenvalues supplied in (WR,WI): * = 'Q': the eigenvalues were found using DHSEQR; thus, if * H has zero subdiagonal elements, and so is * block-triangular, then the j-th eigenvalue can be * assumed to be an eigenvalue of the block containing * the j-th row/column. This property allows DHSEIN to * perform inverse iteration on just one diagonal block. * = 'N': no assumptions are made on the correspondence * between eigenvalues and diagonal blocks. In this * case, DHSEIN must always perform inverse iteration * using the whole matrix H. * * INITV (input) CHARACTER*1 * = 'N': no initial vectors are supplied; * = 'U': user-supplied initial vectors are stored in the arrays * VL and/or VR. * * SELECT (input/output) LOGICAL array, dimension (N) * Specifies the eigenvectors to be computed. To select the * real eigenvector corresponding to a real eigenvalue WR(j), * SELECT(j) must be set to .TRUE.. To select the complex * eigenvector corresponding to a complex eigenvalue * (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), * either SELECT(j) or SELECT(j+1) or both must be set to * .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is * .FALSE.. * * N (input) INTEGER * The order of the matrix H. N >= 0. * * H (input) DOUBLE PRECISION array, dimension (LDH,N) * The upper Hessenberg matrix H. * * LDH (input) INTEGER * The leading dimension of the array H. LDH >= max(1,N). * * WR (input/output) DOUBLE PRECISION array, dimension (N) * WI (input) DOUBLE PRECISION array, dimension (N) * On entry, the real and imaginary parts of the eigenvalues of * H; a complex conjugate pair of eigenvalues must be stored in * consecutive elements of WR and WI. * On exit, WR may have been altered since close eigenvalues * are perturbed slightly in searching for independent * eigenvectors. * * VL (input/output) DOUBLE PRECISION array, dimension (LDVL,MM) * On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must * contain starting vectors for the inverse iteration for the * left eigenvectors; the starting vector for each eigenvector * must be in the same column(s) in which the eigenvector will * be stored. * On exit, if SIDE = 'L' or 'B', the left eigenvectors * specified by SELECT will be stored consecutively in the * columns of VL, in the same order as their eigenvalues. A * complex eigenvector corresponding to a complex eigenvalue is * stored in two consecutive columns, the first holding the real * part and the second the imaginary part. * If SIDE = 'R', VL is not referenced. * * LDVL (input) INTEGER * The leading dimension of the array VL. * LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. * * VR (input/output) DOUBLE PRECISION array, dimension (LDVR,MM) * On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must * contain starting vectors for the inverse iteration for the * right eigenvectors; the starting vector for each eigenvector * must be in the same column(s) in which the eigenvector will * be stored. * On exit, if SIDE = 'R' or 'B', the right eigenvectors * specified by SELECT will be stored consecutively in the * columns of VR, in the same order as their eigenvalues. A * complex eigenvector corresponding to a complex eigenvalue is * stored in two consecutive columns, the first holding the real * part and the second the imaginary part. * If SIDE = 'L', VR is not referenced. * * LDVR (input) INTEGER * The leading dimension of the array VR. * LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. * * MM (input) INTEGER * The number of columns in the arrays VL and/or VR. MM >= M. * * M (output) INTEGER * The number of columns in the arrays VL and/or VR required to * store the eigenvectors; each selected real eigenvector * occupies one column and each selected complex eigenvector * occupies two columns. * * WORK (workspace) DOUBLE PRECISION array, dimension ((N+2)*N) * * IFAILL (output) INTEGER array, dimension (MM) * If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left * eigenvector in the i-th column of VL (corresponding to the * eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the * eigenvector converged satisfactorily. If the i-th and (i+1)th * columns of VL hold a complex eigenvector, then IFAILL(i) and * IFAILL(i+1) are set to the same value. * If SIDE = 'R', IFAILL is not referenced. * * IFAILR (output) INTEGER array, dimension (MM) * If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right * eigenvector in the i-th column of VR (corresponding to the * eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the * eigenvector converged satisfactorily. If the i-th and (i+1)th * columns of VR hold a complex eigenvector, then IFAILR(i) and * IFAILR(i+1) are set to the same value. * If SIDE = 'L', IFAILR is not referenced. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i, i is the number of eigenvectors which * failed to converge; see IFAILL and IFAILR for further * details. * * Further Details * =============== * * Each eigenvector is normalized so that the element of largest * magnitude has magnitude 1; here the magnitude of a complex number * (x,y) is taken to be |x|+|y|. * * ===================================================================== * * .. Parameters ..
DHSEIN()
DHSEIN(String, String, String, boolean[], int, double[][], double[], double[], double[][], double[][], int, intW, double[], int[], int[], intW)
DHSEIN
public DHSEIN()
DHSEIN
public static void DHSEIN(String side,
String eigsrc,
String initv,
boolean select[],
int n,
double h[][],
double wr[],
double wi[],
double vl[][],
double vr[][],
int mm,
intW m,
double work[],
int ifaill[],
int ifailr[],
intW info)
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