org.netlib.lapack
Class SGGQRF
java.lang.Object
org.netlib.lapack.SGGQRF
public class SGGQRF
 extends java.lang.Object
SGGQRF is a simplified interface to the JLAPACK routine sggqrf.
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
* =======
*
* SGGQRF computes a generalized QR factorization of an NbyM matrix A
* and an NbyP matrix B:
*
* A = Q*R, B = Q*T*Z,
*
* where Q is an NbyN orthogonal matrix, Z is a PbyP orthogonal
* matrix, and R and T assume one of the forms:
*
* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
* ( 0 ) NM N MN
* M
*
* where R11 is upper triangular, and
*
* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) NP,
* PN N ( T21 ) P
* P
*
* where T12 or T21 is upper triangular.
*
* In particular, if B is square and nonsingular, the GQR factorization
* of A and B implicitly gives the QR factorization of inv(B)*A:
*
* inv(B)*A = Z'*(inv(T)*R)
*
* where inv(B) denotes the inverse of the matrix B, and Z' denotes the
* transpose of the matrix Z.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of rows of the matrices A and B. N >= 0.
*
* M (input) INTEGER
* The number of columns of the matrix A. M >= 0.
*
* P (input) INTEGER
* The number of columns of the matrix B. P >= 0.
*
* A (input/output) REAL array, dimension (LDA,M)
* On entry, the NbyM matrix A.
* On exit, the elements on and above the diagonal of the array
* contain the min(N,M)byM upper trapezoidal matrix R (R is
* upper triangular if N >= M); the elements below the diagonal,
* with the array TAUA, represent the orthogonal matrix Q as a
* product of min(N,M) elementary reflectors (see Further
* Details).
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* TAUA (output) REAL array, dimension (min(N,M))
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix Q (see Further Details).
*
* B (input/output) REAL array, dimension (LDB,P)
* On entry, the NbyP matrix B.
* On exit, if N <= P, the upper triangle of the subarray
* B(1:N,PN+1:P) contains the NbyN upper triangular matrix T;
* if N > P, the elements on and above the (NP)th subdiagonal
* contain the NbyP upper trapezoidal matrix T; the remaining
* elements, with the array TAUB, represent the orthogonal
* matrix Z as a product of elementary reflectors (see Further
* Details).
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* TAUB (output) REAL array, dimension (min(N,P))
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix Z (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 dimension of the array WORK. LWORK >= max(1,N,M,P).
* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
* where NB1 is the optimal blocksize for the QR factorization
* of an NbyM matrix, NB2 is the optimal blocksize for the
* RQ factorization of an NbyP matrix, and NB3 is the optimal
* blocksize for a call of SORMQR.
*
* 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 ith argument had an illegal value.
*
* Further Details
* ===============
*
* The matrix Q is represented as a product of elementary reflectors
*
* Q = H(1) H(2) . . . H(k), where k = min(n,m).
*
* Each H(i) has the form
*
* H(i) = I  taua * v * v'
*
* where taua is a real scalar, and v is a real vector with
* v(1:i1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
* and taua in TAUA(i).
* To form Q explicitly, use LAPACK subroutine SORGQR.
* To use Q to update another matrix, use LAPACK subroutine SORMQR.
*
* The matrix Z is represented as a product of elementary reflectors
*
* Z = H(1) H(2) . . . H(k), where k = min(n,p).
*
* Each H(i) has the form
*
* H(i) = I  taub * v * v'
*
* where taub is a real scalar, and v is a real vector with
* v(pk+i+1:p) = 0 and v(pk+i) = 1; v(1:pk+i1) is stored on exit in
* B(nk+i,1:pk+i1), and taub in TAUB(i).
* To form Z explicitly, use LAPACK subroutine SORGRQ.
* To use Z to update another matrix, use LAPACK subroutine SORMRQ.
*
* =====================================================================
*
* .. Local Scalars ..
Method Summary 
static void 
SGGQRF(int n,
int m,
int p,
float[][] a,
float[] taua,
float[][] b,
float[] taub,
float[] work,
int lwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
SGGQRF
public SGGQRF()
SGGQRF
public static void SGGQRF(int n,
int m,
int p,
float[][] a,
float[] taua,
float[][] b,
float[] taub,
float[] work,
int lwork,
intW info)