org.netlib.lapack
Class SGGSVP
java.lang.Object
org.netlib.lapack.SGGSVP
public class SGGSVP
- extends java.lang.Object
SGGSVP is a simplified interface to the JLAPACK routine sggsvp.
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
* =======
*
* SGGSVP computes orthogonal matrices U, V and Q such that
*
* N-K-L K L
* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
* L ( 0 0 A23 )
* M-K-L ( 0 0 0 )
*
* N-K-L K L
* = K ( 0 A12 A13 ) if M-K-L < 0;
* M-K ( 0 0 A23 )
*
* N-K-L K L
* V'*B*Q = L ( 0 0 B13 )
* P-L ( 0 0 0 )
*
* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the
* transpose of Z.
*
* This decomposition is the preprocessing step for computing the
* Generalized Singular Value Decomposition (GSVD), see subroutine
* SGGSVD.
*
* Arguments
* =========
*
* JOBU (input) CHARACTER*1
* = 'U': Orthogonal matrix U is computed;
* = 'N': U is not computed.
*
* JOBV (input) CHARACTER*1
* = 'V': Orthogonal matrix V is computed;
* = 'N': V is not computed.
*
* JOBQ (input) CHARACTER*1
* = 'Q': Orthogonal matrix Q is computed;
* = 'N': Q is not computed.
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* P (input) INTEGER
* The number of rows of the matrix B. P >= 0.
*
* N (input) INTEGER
* The number of columns of the matrices A and B. N >= 0.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the M-by-N matrix A.
* On exit, A contains the triangular (or trapezoidal) matrix
* described in the Purpose section.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* B (input/output) REAL array, dimension (LDB,N)
* On entry, the P-by-N matrix B.
* On exit, B contains the triangular matrix described in
* the Purpose section.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,P).
*
* TOLA (input) REAL
* TOLB (input) REAL
* TOLA and TOLB are the thresholds to determine the effective
* numerical rank of matrix B and a subblock of A. Generally,
* they are set to
* TOLA = MAX(M,N)*norm(A)*MACHEPS,
* TOLB = MAX(P,N)*norm(B)*MACHEPS.
* The size of TOLA and TOLB may affect the size of backward
* errors of the decomposition.
*
* K (output) INTEGER
* L (output) INTEGER
* On exit, K and L specify the dimension of the subblocks
* described in Purpose.
* K + L = effective numerical rank of (A',B')'.
*
* U (output) REAL array, dimension (LDU,M)
* If JOBU = 'U', U contains the orthogonal matrix U.
* If JOBU = 'N', U is not referenced.
*
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= max(1,M) if
* JOBU = 'U'; LDU >= 1 otherwise.
*
* V (output) REAL array, dimension (LDV,M)
* If JOBV = 'V', V contains the orthogonal matrix V.
* If JOBV = 'N', V is not referenced.
*
* LDV (input) INTEGER
* The leading dimension of the array V. LDV >= max(1,P) if
* JOBV = 'V'; LDV >= 1 otherwise.
*
* Q (output) REAL array, dimension (LDQ,N)
* If JOBQ = 'Q', Q contains the orthogonal matrix Q.
* If JOBQ = 'N', Q is not referenced.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N) if
* JOBQ = 'Q'; LDQ >= 1 otherwise.
*
* IWORK (workspace) INTEGER array, dimension (N)
*
* TAU (workspace) REAL array, dimension (N)
*
* WORK (workspace) REAL array, dimension (max(3*N,M,P))
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value.
*
*
* Further Details
* ===============
*
* The subroutine uses LAPACK subroutine SGEQPF for the QR factorization
* with column pivoting to detect the effective numerical rank of the
* a matrix. It may be replaced by a better rank determination strategy.
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
SGGSVP(java.lang.String jobu,
java.lang.String jobv,
java.lang.String jobq,
int m,
int p,
int n,
float[][] a,
float[][] b,
float tola,
float tolb,
intW k,
intW l,
float[][] u,
float[][] v,
float[][] q,
int[] iwork,
float[] tau,
float[] work,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SGGSVP
public SGGSVP()
SGGSVP
public static void SGGSVP(java.lang.String jobu,
java.lang.String jobv,
java.lang.String jobq,
int m,
int p,
int n,
float[][] a,
float[][] b,
float tola,
float tolb,
intW k,
intW l,
float[][] u,
float[][] v,
float[][] q,
int[] iwork,
float[] tau,
float[] work,
intW info)