LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  sggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO) 
SGGSVP 
subroutine sggsvp  (  character  JOBU, 
character  JOBV,  
character  JOBQ,  
integer  M,  
integer  P,  
integer  N,  
real, dimension( lda, * )  A,  
integer  LDA,  
real, dimension( ldb, * )  B,  
integer  LDB,  
real  TOLA,  
real  TOLB,  
integer  K,  
integer  L,  
real, dimension( ldu, * )  U,  
integer  LDU,  
real, dimension( ldv, * )  V,  
integer  LDV,  
real, dimension( ldq, * )  Q,  
integer  LDQ,  
integer, dimension( * )  IWORK,  
real, dimension( * )  TAU,  
real, dimension( * )  WORK,  
integer  INFO  
) 
SGGSVP
Download SGGSVP + dependencies [TGZ] [ZIP] [TXT]SGGSVP computes orthogonal matrices U, V and Q such that NKL K L U**T*A*Q = K ( 0 A12 A13 ) if MKL >= 0; L ( 0 0 A23 ) MKL ( 0 0 0 ) NKL K L = K ( 0 A12 A13 ) if MKL < 0; MK ( 0 0 A23 ) NKL K L V**T*B*Q = 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. K+L = the effective numerical rank of the (M+P)byN matrix (A**T,B**T)**T. This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine SGGSVD.
[in]  JOBU  JOBU is CHARACTER*1 = 'U': Orthogonal matrix U is computed; = 'N': U is not computed. 
[in]  JOBV  JOBV is CHARACTER*1 = 'V': Orthogonal matrix V is computed; = 'N': V is not computed. 
[in]  JOBQ  JOBQ is CHARACTER*1 = 'Q': Orthogonal matrix Q is computed; = 'N': Q is not computed. 
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  P  P is INTEGER The number of rows of the matrix B. P >= 0. 
[in]  N  N is INTEGER The number of columns of the matrices A and B. N >= 0. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[in,out]  B  B is REAL array, dimension (LDB,N) On entry, the PbyN matrix B. On exit, B contains the triangular matrix described in the Purpose section. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,P). 
[in]  TOLA  TOLA is REAL 
[in]  TOLB  TOLB is 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. 
[out]  K  K is INTEGER 
[out]  L  L is INTEGER On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (A**T,B**T)**T. 
[out]  U  U is REAL array, dimension (LDU,M) If JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced. 
[in]  LDU  LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise. 
[out]  V  V is REAL array, dimension (LDV,P) If JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced. 
[in]  LDV  LDV is INTEGER The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise. 
[out]  Q  Q is REAL array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced. 
[in]  LDQ  LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise. 
[out]  IWORK  IWORK is INTEGER array, dimension (N) 
[out]  TAU  TAU is REAL array, dimension (N) 
[out]  WORK  WORK is REAL array, dimension (max(3*N,M,P)) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. 
Definition at line 253 of file sggsvp.f.