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java.lang.Object | +----org.netlib.lapack.DGEHRD
DGEHRD is a simplified interface to the JLAPACK routine dgehrd. 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 * ======= * * DGEHRD reduces a real general matrix A to upper Hessenberg form H by * an orthogonal similarity transformation: Q' * A * Q = H . * * Arguments * ========= * * N (input) INTEGER * The order of the matrix A. N >= 0. * * ILO (input) INTEGER * IHI (input) INTEGER * It is assumed that A is already upper triangular in rows * and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally * set by a previous call to DGEBAL; otherwise they should be * set to 1 and N respectively. See Further Details. * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the N-by-N general matrix to be reduced. * On exit, the upper triangle and the first subdiagonal of A * are overwritten with the upper Hessenberg matrix H, and the * elements below the first subdiagonal, with the array TAU, * represent the orthogonal matrix Q as a product of elementary * reflectors. See Further Details. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * TAU (output) DOUBLE PRECISION array, dimension (N-1) * The scalar factors of the elementary reflectors (see Further * Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to * zero. * * WORK (workspace/output) DOUBLE PRECISION 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,N). * For optimum performance LWORK >= N*NB, where NB is the * optimal blocksize. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value. * * Further Details * =============== * * The matrix Q is represented as a product of (ihi-ilo) elementary * reflectors * * Q = H(ilo) H(ilo+1) . . . H(ihi-1). * * Each H(i) has the form * * H(i) = I - tau * v * v' * * where tau is a real scalar, and v is a real vector with * v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on * exit in A(i+2:ihi,i), and tau in TAU(i). * * The contents of A are illustrated by the following example, with * n = 7, ilo = 2 and ihi = 6: * * on entry, on exit, * * ( a a a a a a a ) ( a a h h h h a ) * ( a a a a a a ) ( a h h h h a ) * ( a a a a a a ) ( h h h h h h ) * ( a a a a a a ) ( v2 h h h h h ) * ( a a a a a a ) ( v2 v3 h h h h ) * ( a a a a a a ) ( v2 v3 v4 h h h ) * ( a ) ( a ) * * where a denotes an element of the original matrix A, h denotes a * modified element of the upper Hessenberg matrix H, and vi denotes an * element of the vector defining H(i). * * ===================================================================== * * .. Parameters ..
DGEHRD()
DGEHRD(int, int, int, double[][], double[], double[], int, intW)
DGEHRD
public DGEHRD()
DGEHRD
public static void DGEHRD(int n,
int ilo,
int ihi,
double a[][],
double tau[],
double work[],
int lwork,
intW info)
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