org.netlib.lapack
Class SLATRD
java.lang.Object
org.netlib.lapack.SLATRD
public class SLATRD
 extends java.lang.Object
SLATRD is a simplified interface to the JLAPACK routine slatrd.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor 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
* =======
*
* SLATRD reduces NB rows and columns of a real symmetric matrix A to
* symmetric tridiagonal form by an orthogonal similarity
* transformation Q' * A * Q, and returns the matrices V and W which are
* needed to apply the transformation to the unreduced part of A.
*
* If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
* matrix, of which the upper triangle is supplied;
* if UPLO = 'L', SLATRD reduces the first NB rows and columns of a
* matrix, of which the lower triangle is supplied.
*
* This is an auxiliary routine called by SSYTRD.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the matrix A.
*
* NB (input) INTEGER
* The number of rows and columns to be reduced.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the symmetric matrix A. If UPLO = 'U', the leading
* nbyn upper triangular part of A contains the upper
* triangular part of the matrix A, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading nbyn lower triangular part of A contains the lower
* triangular part of the matrix A, and the strictly upper
* triangular part of A is not referenced.
* On exit:
* if UPLO = 'U', the last NB columns have been reduced to
* tridiagonal form, with the diagonal elements overwriting
* the diagonal elements of A; the elements above the diagonal
* with the array TAU, represent the orthogonal matrix Q as a
* product of elementary reflectors;
* if UPLO = 'L', the first NB columns have been reduced to
* tridiagonal form, with the diagonal elements overwriting
* the diagonal elements of A; the elements below the diagonal
* 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 >= (1,N).
*
* E (output) REAL array, dimension (N1)
* If UPLO = 'U', E(nnb:n1) contains the superdiagonal
* elements of the last NB columns of the reduced matrix;
* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
* the first NB columns of the reduced matrix.
*
* TAU (output) REAL array, dimension (N1)
* The scalar factors of the elementary reflectors, stored in
* TAU(nnb:n1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
* See Further Details.
*
* W (output) REAL array, dimension (LDW,NB)
* The nbynb matrix W required to update the unreduced part
* of A.
*
* LDW (input) INTEGER
* The leading dimension of the array W. LDW >= max(1,N).
*
* Further Details
* ===============
*
* If UPLO = 'U', the matrix Q is represented as a product of elementary
* reflectors
*
* Q = H(n) H(n1) . . . H(nnb+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(i:n) = 0 and v(i1) = 1; v(1:i1) is stored on exit in A(1:i1,i),
* and tau in TAU(i1).
*
* If UPLO = 'L', the matrix Q is represented as a product of elementary
* reflectors
*
* Q = H(1) H(2) . . . H(nb).
*
* 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 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
* and tau in TAU(i).
*
* The elements of the vectors v together form the nbynb matrix V
* which is needed, with W, to apply the transformation to the unreduced
* part of the matrix, using a symmetric rank2k update of the form:
* A := A  V*W'  W*V'.
*
* The contents of A on exit are illustrated by the following examples
* with n = 5 and nb = 2:
*
* if UPLO = 'U': if UPLO = 'L':
*
* ( a a a v4 v5 ) ( d )
* ( a a v4 v5 ) ( 1 d )
* ( a 1 v5 ) ( v1 1 a )
* ( d 1 ) ( v1 v2 a a )
* ( d ) ( v1 v2 a a a )
*
* where d denotes a diagonal element of the reduced matrix, a denotes
* an element of the original matrix that is unchanged, and vi denotes
* an element of the vector defining H(i).
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
SLATRD(java.lang.String uplo,
int n,
int nb,
float[][] a,
float[] e,
float[] tau,
float[][] w)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
SLATRD
public SLATRD()
SLATRD
public static void SLATRD(java.lang.String uplo,
int n,
int nb,
float[][] a,
float[] e,
float[] tau,
float[][] w)