org.netlib.lapack
Class Dlatrd
java.lang.Object
org.netlib.lapack.Dlatrd
public class Dlatrd
- 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
* =======
*
* DLATRD 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', DLATRD reduces the last NB rows and columns of a
* matrix, of which the upper triangle is supplied;
* if UPLO = 'L', DLATRD reduces the first NB rows and columns of a
* matrix, of which the lower triangle is supplied.
*
* This is an auxiliary routine called by DSYTRD.
*
* 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) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the symmetric matrix A. If UPLO = 'U', the leading
* n-by-n 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 n-by-n 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) DOUBLE PRECISION array, dimension (N-1)
* If UPLO = 'U', E(n-nb:n-1) 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) DOUBLE PRECISION array, dimension (N-1)
* The scalar factors of the elementary reflectors, stored in
* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
* See Further Details.
*
* W (output) DOUBLE PRECISION array, dimension (LDW,NB)
* The n-by-nb 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(n-1) . . . H(n-nb+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(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
* and tau in TAU(i-1).
*
* 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 n-by-nb matrix V
* which is needed, with W, to apply the transformation to the unreduced
* part of the matrix, using a symmetric rank-2k 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 |
dlatrd(java.lang.String uplo,
int n,
int nb,
double[] a,
int _a_offset,
int lda,
double[] e,
int _e_offset,
double[] tau,
int _tau_offset,
double[] w,
int _w_offset,
int ldw)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Dlatrd
public Dlatrd()
dlatrd
public static void dlatrd(java.lang.String uplo,
int n,
int nb,
double[] a,
int _a_offset,
int lda,
double[] e,
int _e_offset,
double[] tau,
int _tau_offset,
double[] w,
int _w_offset,
int ldw)