org.netlib.lapack
Class STGSJA
java.lang.Object
org.netlib.lapack.STGSJA
public class STGSJA
 extends java.lang.Object
STGSJA is a simplified interface to the JLAPACK routine stgsja.
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
* =======
*
* STGSJA computes the generalized singular value decomposition (GSVD)
* of two real upper triangular (or trapezoidal) matrices A and B.
*
* On entry, it is assumed that matrices A and B have the following
* forms, which may be obtained by the preprocessing subroutine SGGSVP
* from a general MbyN matrix A and PbyN matrix B:
*
* NKL K L
* A = K ( 0 A12 A13 ) if MKL >= 0;
* L ( 0 0 A23 )
* MKL ( 0 0 0 )
*
* NKL K L
* A = K ( 0 A12 A13 ) if MKL < 0;
* MK ( 0 0 A23 )
*
* NKL K L
* B = L ( 0 0 B13 )
* PL ( 0 0 0 )
*
* where the KbyK matrix A12 and LbyL matrix B13 are nonsingular
* upper triangular; A23 is LbyL upper triangular if MKL >= 0,
* otherwise A23 is (MK)byL upper trapezoidal.
*
* On exit,
*
* U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R ),
*
* where U, V and Q are orthogonal matrices, Z' denotes the transpose
* of Z, R is a nonsingular upper triangular matrix, and D1 and D2 are
* ``diagonal'' matrices, which are of the following structures:
*
* If MKL >= 0,
*
* K L
* D1 = K ( I 0 )
* L ( 0 C )
* MKL ( 0 0 )
*
* K L
* D2 = L ( 0 S )
* PL ( 0 0 )
*
* NKL K L
* ( 0 R ) = K ( 0 R11 R12 ) K
* L ( 0 0 R22 ) L
*
* where
*
* C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
* S = diag( BETA(K+1), ... , BETA(K+L) ),
* C**2 + S**2 = I.
*
* R is stored in A(1:K+L,NKL+1:N) on exit.
*
* If MKL < 0,
*
* K MK K+LM
* D1 = K ( I 0 0 )
* MK ( 0 C 0 )
*
* K MK K+LM
* D2 = MK ( 0 S 0 )
* K+LM ( 0 0 I )
* PL ( 0 0 0 )
*
* NKL K MK K+LM
* ( 0 R ) = K ( 0 R11 R12 R13 )
* MK ( 0 0 R22 R23 )
* K+LM ( 0 0 0 R33 )
*
* where
* C = diag( ALPHA(K+1), ... , ALPHA(M) ),
* S = diag( BETA(K+1), ... , BETA(M) ),
* C**2 + S**2 = I.
*
* R = ( R11 R12 R13 ) is stored in A(1:M, NKL+1:N) and R33 is stored
* ( 0 R22 R23 )
* in B(MK+1:L,N+MKL+1:N) on exit.
*
* The computation of the orthogonal transformation matrices U, V or Q
* is optional. These matrices may either be formed explicitly, or they
* may be postmultiplied into input matrices U1, V1, or Q1.
*
* Arguments
* =========
*
* JOBU (input) CHARACTER*1
* = 'U': U must contain an orthogonal matrix U1 on entry, and
* the product U1*U is returned;
* = 'I': U is initialized to the unit matrix, and the
* orthogonal matrix U is returned;
* = 'N': U is not computed.
*
* JOBV (input) CHARACTER*1
* = 'V': V must contain an orthogonal matrix V1 on entry, and
* the product V1*V is returned;
* = 'I': V is initialized to the unit matrix, and the
* orthogonal matrix V is returned;
* = 'N': V is not computed.
*
* JOBQ (input) CHARACTER*1
* = 'Q': Q must contain an orthogonal matrix Q1 on entry, and
* the product Q1*Q is returned;
* = 'I': Q is initialized to the unit matrix, and the
* orthogonal matrix Q is returned;
* = '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.
*
* K (input) INTEGER
* L (input) INTEGER
* K and L specify the subblocks in the input matrices A and B:
* A23 = A(K+1:MIN(K+L,M),NL+1:N) and B13 = B(1:L,NL+1:N)
* of A and B, whose GSVD is going to be computed by STGSJA.
* See Further details.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the MbyN matrix A.
* On exit, A(NK+1:N,1:MIN(K+L,M) ) contains the triangular
* matrix R or part of R. See Purpose for details.
*
* 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 PbyN matrix B.
* On exit, if necessary, B(MK+1:L,N+MKL+1:N) contains
* a part of R. See Purpose for details.
*
* 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 convergence criteria for the Jacobi
* Kogbetliantz iteration procedure. Generally, they are the
* same as used in the preprocessing step, say
* TOLA = max(M,N)*norm(A)*MACHEPS,
* TOLB = max(P,N)*norm(B)*MACHEPS.
*
* ALPHA (output) REAL array, dimension (N)
* BETA (output) REAL array, dimension (N)
* On exit, ALPHA and BETA contain the generalized singular
* value pairs of A and B;
* ALPHA(1:K) = 1,
* BETA(1:K) = 0,
* and if MKL >= 0,
* ALPHA(K+1:K+L) = diag(C),
* BETA(K+1:K+L) = diag(S),
* or if MKL < 0,
* ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
* BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
* Furthermore, if K+L < N,
* ALPHA(K+L+1:N) = 0 and
* BETA(K+L+1:N) = 0.
*
* U (input/output) REAL array, dimension (LDU,M)
* On entry, if JOBU = 'U', U must contain a matrix U1 (usually
* the orthogonal matrix returned by SGGSVP).
* On exit,
* if JOBU = 'I', U contains the orthogonal matrix U;
* if JOBU = 'U', U contains the product U1*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 (input/output) REAL array, dimension (LDV,P)
* On entry, if JOBV = 'V', V must contain a matrix V1 (usually
* the orthogonal matrix returned by SGGSVP).
* On exit,
* if JOBV = 'I', V contains the orthogonal matrix V;
* if JOBV = 'V', V contains the product V1*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 (input/output) REAL array, dimension (LDQ,N)
* On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
* the orthogonal matrix returned by SGGSVP).
* On exit,
* if JOBQ = 'I', Q contains the orthogonal matrix Q;
* if JOBQ = 'Q', Q contains the product Q1*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.
*
* WORK (workspace) REAL array, dimension (2*N)
*
* NCYCLE (output) INTEGER
* The number of cycles required for convergence.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = i, the ith argument had an illegal value.
* = 1: the procedure does not converge after MAXIT cycles.
*
* Internal Parameters
* ===================
*
* MAXIT INTEGER
* MAXIT specifies the total loops that the iterative procedure
* may take. If after MAXIT cycles, the routine fails to
* converge, we return INFO = 1.
*
* Further Details
* ===============
*
* STGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
* min(L,MK)byL triangular (or trapezoidal) matrix A23 and LbyL
* matrix B13 to the form:
*
* U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
*
* where U1, V1 and Q1 are orthogonal matrix, and Z' is the transpose
* of Z. C1 and S1 are diagonal matrices satisfying
*
* C1**2 + S1**2 = I,
*
* and R1 is an LbyL nonsingular upper triangular matrix.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
STGSJA(java.lang.String jobu,
java.lang.String jobv,
java.lang.String jobq,
int m,
int p,
int n,
int k,
int l,
float[][] a,
float[][] b,
float tola,
float tolb,
float[] alpha,
float[] beta,
float[][] u,
float[][] v,
float[][] q,
float[] work,
intW ncycle,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
STGSJA
public STGSJA()
STGSJA
public static void STGSJA(java.lang.String jobu,
java.lang.String jobv,
java.lang.String jobq,
int m,
int p,
int n,
int k,
int l,
float[][] a,
float[][] b,
float tola,
float tolb,
float[] alpha,
float[] beta,
float[][] u,
float[][] v,
float[][] q,
float[] work,
intW ncycle,
intW info)