org.netlib.lapack
Class SGEBRD

java.lang.Object
  extended by org.netlib.lapack.SGEBRD

public class SGEBRD
extends java.lang.Object

SGEBRD is a simplified interface to the JLAPACK routine sgebrd.
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 * ======= * * SGEBRD reduces a general real M-by-N matrix A to upper or lower * bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. * * If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. * * Arguments * ========= * * M (input) INTEGER * The number of rows in the matrix A. M >= 0. * * N (input) INTEGER * The number of columns in the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the M-by-N general matrix to be reduced. * On exit, * if m >= n, the diagonal and the first superdiagonal are * overwritten with the upper bidiagonal matrix B; the * elements below the diagonal, with the array TAUQ, represent * the orthogonal matrix Q as a product of elementary * reflectors, and the elements above the first superdiagonal, * with the array TAUP, represent the orthogonal matrix P as * a product of elementary reflectors; * if m < n, the diagonal and the first subdiagonal are * overwritten with the lower bidiagonal matrix B; the * elements below the first subdiagonal, with the array TAUQ, * represent the orthogonal matrix Q as a product of * elementary reflectors, and the elements above the diagonal, * with the array TAUP, represent the orthogonal matrix P as * a product of elementary reflectors. * See Further Details. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * D (output) REAL array, dimension (min(M,N)) * The diagonal elements of the bidiagonal matrix B: * D(i) = A(i,i). * * E (output) REAL array, dimension (min(M,N)-1) * The off-diagonal elements of the bidiagonal matrix B: * if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; * if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. * * TAUQ (output) REAL array dimension (min(M,N)) * The scalar factors of the elementary reflectors which * represent the orthogonal matrix Q. See Further Details. * * TAUP (output) REAL array, dimension (min(M,N)) * The scalar factors of the elementary reflectors which * represent the orthogonal matrix P. See Further Details. * * WORK (workspace/output) REAL array, dimension (LWORK) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= max(1,M,N). * For optimum performance LWORK >= (M+N)*NB, where NB * is the optimal blocksize. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value. * * Further Details * =============== * * The matrices Q and P are represented as products of elementary * reflectors: * * If m >= n, * * Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) * * Each H(i) and G(i) has the form: * * H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' * * where tauq and taup are real scalars, and v and u are real vectors; * v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); * u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); * tauq is stored in TAUQ(i) and taup in TAUP(i). * * If m < n, * * Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) * * Each H(i) and G(i) has the form: * * H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' * * where tauq and taup are real scalars, and v and u are real vectors; * v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); * u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); * tauq is stored in TAUQ(i) and taup in TAUP(i). * * The contents of A on exit are illustrated by the following examples: * * m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): * * ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) * ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) * ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) * ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) * ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) * ( v1 v2 v3 v4 v5 ) * * where d and e denote diagonal and off-diagonal elements of B, vi * denotes an element of the vector defining H(i), and ui an element of * the vector defining G(i). * * ===================================================================== * * .. Parameters ..


Constructor Summary
SGEBRD()
           
 
Method Summary
static void SGEBRD(int m, int n, float[][] a, float[] d, float[] e, float[] tauq, float[] taup, float[] work, int lwork, intW info)
           
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

SGEBRD

public SGEBRD()
Method Detail

SGEBRD

public static void SGEBRD(int m,
                          int n,
                          float[][] a,
                          float[] d,
                          float[] e,
                          float[] tauq,
                          float[] taup,
                          float[] work,
                          int lwork,
                          intW info)