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zggsvp.f(3) LAPACK zggsvp.f(3)

zggsvp.f -


subroutine zggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, INFO)
 
ZGGSVP

ZGGSVP
Purpose:
 ZGGSVP computes unitary matrices U, V and Q such that
N-K-L K L U**H*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**H*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**H,B**H)**H.
This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ZGGSVD.
Parameters:
JOBU
          JOBU is CHARACTER*1
          = 'U':  Unitary matrix U is computed;
          = 'N':  U is not computed.
JOBV
          JOBV is CHARACTER*1
          = 'V':  Unitary matrix V is computed;
          = 'N':  V is not computed.
JOBQ
          JOBQ is CHARACTER*1
          = 'Q':  Unitary matrix Q is computed;
          = 'N':  Q is not computed.
M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
P
          P is INTEGER
          The number of rows of the matrix B.  P >= 0.
N
          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.
A
          A is COMPLEX*16 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
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).
B
          B is COMPLEX*16 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
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,P).
TOLA
          TOLA is DOUBLE PRECISION
TOLB
          TOLB is DOUBLE PRECISION
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)*MAZHEPS, TOLB = MAX(P,N)*norm(B)*MAZHEPS. The size of TOLA and TOLB may affect the size of backward errors of the decomposition.
K
          K is INTEGER
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**H,B**H)**H.
U
          U is COMPLEX*16 array, dimension (LDU,M)
          If JOBU = 'U', U contains the unitary matrix U.
          If JOBU = 'N', U is not referenced.
LDU
          LDU is INTEGER
          The leading dimension of the array U. LDU >= max(1,M) if
          JOBU = 'U'; LDU >= 1 otherwise.
V
          V is COMPLEX*16 array, dimension (LDV,P)
          If JOBV = 'V', V contains the unitary matrix V.
          If JOBV = 'N', V is not referenced.
LDV
          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,P) if
          JOBV = 'V'; LDV >= 1 otherwise.
Q
          Q is COMPLEX*16 array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the unitary matrix Q.
          If JOBQ = 'N', Q is not referenced.
LDQ
          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= max(1,N) if
          JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK
          IWORK is INTEGER array, dimension (N)
RWORK
          RWORK is DOUBLE PRECISION array, dimension (2*N)
TAU
          TAU is COMPLEX*16 array, dimension (N)
WORK
          WORK is COMPLEX*16 array, dimension (max(3*N,M,P))
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
  The subroutine uses LAPACK subroutine ZGEQPF 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.
Definition at line 262 of file zggsvp.f.

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