subroutine cunbdb4 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
CUNBDB4
CUNBDB4
Purpose:
CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny matrix X with orthonomal columns: [ B11 ] [ X11 ] [ P1 | ] [ 0 ] [-----] = [---------] [-----] Q1**T . [ X21 ] [ | P2 ] [ B21 ] [ 0 ] X11 is P-by-Q, and X21 is (M-P)-by-Q. M-Q must be no larger than P, M-P, or Q. Routines CUNBDB1, CUNBDB2, and CUNBDB3 handle cases in which M-Q is not the minimum dimension. The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), and (M-Q)-by-(M-Q), respectively. They are represented implicitly by Householder vectors. B11 and B12 are (M-Q)-by-(M-Q) bidiagonal matrices represented implicitly by angles THETA, PHI.
Parameters:
M is INTEGER The number of rows X11 plus the number of rows in X21.
P
P is INTEGER The number of rows in X11. 0 <= P <= M.
Q
Q is INTEGER The number of columns in X11 and X21. 0 <= Q <= M and M-Q <= min(P,M-P,Q).
X11
X11 is COMPLEX array, dimension (LDX11,Q) On entry, the top block of the matrix X to be reduced. On exit, the columns of tril(X11) specify reflectors for P1 and the rows of triu(X11,1) specify reflectors for Q1.
LDX11
LDX11 is INTEGER The leading dimension of X11. LDX11 >= P.
X21
X21 is COMPLEX array, dimension (LDX21,Q) On entry, the bottom block of the matrix X to be reduced. On exit, the columns of tril(X21) specify reflectors for P2.
LDX21
LDX21 is INTEGER The leading dimension of X21. LDX21 >= M-P.
THETA
THETA is REAL array, dimension (Q) The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.
PHI
PHI is REAL array, dimension (Q-1) The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.
TAUP1
TAUP1 is COMPLEX array, dimension (P) The scalar factors of the elementary reflectors that define P1.
TAUP2
TAUP2 is COMPLEX array, dimension (M-P) The scalar factors of the elementary reflectors that define P2.
TAUQ1
TAUQ1 is COMPLEX array, dimension (Q) The scalar factors of the elementary reflectors that define Q1.
PHANTOM
PHANTOM is COMPLEX array, dimension (M) The routine computes an M-by-1 column vector Y that is orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and Y(P+1:M), respectively.
WORK
WORK is COMPLEX array, dimension (LWORK)
LWORK
LWORK is INTEGER The dimension of the array WORK. LWORK >= M-Q. 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
INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Further Details:
The upper-bidiagonal blocks B11, B21 are represented implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry in each bidiagonal band is a product of a sine or cosine of a THETA with a sine or cosine of a PHI. See [1] or CUNCSD for details.
P1, P2, and Q1 are represented as products of elementary reflectors. See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR and CUNGLQ.
References:
Definition at line 215 of file cunbdb4.f.
Generated automatically by Doxygen for LAPACK from the source code.