org.netlib.lapack
Class Slabrd
java.lang.Object
org.netlib.lapack.Slabrd
public class Slabrd
- extends java.lang.Object
Following is the description from the original
Fortran source. For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SLABRD reduces the first NB rows and columns of a real general
* m by n matrix A to upper or lower bidiagonal form by an orthogonal
* transformation Q' * A * P, and returns the matrices X and Y which
* are needed to apply the transformation to the unreduced part of A.
*
* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
* bidiagonal form.
*
* This is an auxiliary routine called by SGEBRD
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows in the matrix A.
*
* N (input) INTEGER
* The number of columns in the matrix A.
*
* NB (input) INTEGER
* The number of leading rows and columns of A to be reduced.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the m by n general matrix to be reduced.
* On exit, the first NB rows and columns of the matrix are
* overwritten; the rest of the array is unchanged.
* If m >= n, elements on and below the diagonal in the first NB
* columns, with the array TAUQ, represent the orthogonal
* matrix Q as a product of elementary reflectors; and
* elements above the diagonal in the first NB rows, with the
* array TAUP, represent the orthogonal matrix P as a product
* of elementary reflectors.
* If m < n, elements below the diagonal in the first NB
* columns, with the array TAUQ, represent the orthogonal
* matrix Q as a product of elementary reflectors, and
* elements on and above the diagonal in the first NB rows,
* 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 (NB)
* The diagonal elements of the first NB rows and columns of
* the reduced matrix. D(i) = A(i,i).
*
* E (output) REAL array, dimension (NB)
* The off-diagonal elements of the first NB rows and columns of
* the reduced matrix.
*
* TAUQ (output) REAL array dimension (NB)
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix Q. See Further Details.
*
* TAUP (output) REAL array, dimension (NB)
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix P. See Further Details.
*
* X (output) REAL array, dimension (LDX,NB)
* The m-by-nb matrix X required to update the unreduced part
* of A.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= M.
*
* Y (output) REAL array, dimension (LDY,NB)
* The n-by-nb matrix Y required to update the unreduced part
* of A.
*
* LDY (output) INTEGER
* The leading dimension of the array Y. LDY >= N.
*
* Further Details
* ===============
*
* The matrices Q and P are represented as products of elementary
* reflectors:
*
* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)
*
* 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.
*
* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in
* A(i:m,i); u(1:i) = 0, u(i+1) = 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).
*
* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in
* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in
* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
*
* The elements of the vectors v and u together form the m-by-nb matrix
* V and the nb-by-n matrix U' which are needed, with X and Y, to apply
* the transformation to the unreduced part of the matrix, using a block
* update of the form: A := A - V*Y' - X*U'.
*
* The contents of A on exit are illustrated by the following examples
* with nb = 2:
*
* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
*
* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 )
* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 )
* ( v1 v2 a a a ) ( v1 1 a a a a )
* ( v1 v2 a a a ) ( v1 v2 a a a a )
* ( v1 v2 a a a ) ( v1 v2 a a a a )
* ( v1 v2 a a a )
*
* where a denotes an element of the original matrix which is unchanged,
* vi denotes an element of the vector defining H(i), and ui an element
* of the vector defining G(i).
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
slabrd(int m,
int n,
int nb,
float[] a,
int _a_offset,
int lda,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
float[] tauq,
int _tauq_offset,
float[] taup,
int _taup_offset,
float[] x,
int _x_offset,
int ldx,
float[] y,
int _y_offset,
int ldy)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Slabrd
public Slabrd()
slabrd
public static void slabrd(int m,
int n,
int nb,
float[] a,
int _a_offset,
int lda,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
float[] tauq,
int _tauq_offset,
float[] taup,
int _taup_offset,
float[] x,
int _x_offset,
int ldx,
float[] y,
int _y_offset,
int ldy)