DSVDC(3F) DSVDC(3F)
DSVDC - DSVDC is a subroutine to reduce a double precision NxP matrix X
by orthogonal transformations U and V to diagonal form. The diagonal
elements S(I) are the singular values of X. The columns of U are the
corresponding left singular vectors, and the columns of V the right
singular vectors.
SUBROUTINE DSVDC(X,LDX,N,P,S,E,U,LDU,V,LDV,WORK,JOB,INFO)
On Entry
X DOUBLE PRECISION(LDX,P), where LDX .GE. N.
X contains the matrix whose singular value
decomposition is to be computed. X is
destroyed by DSVDC.
LDX INTEGER.
LDX is the leading dimension of the array X.
N INTEGER.
N is the number of columns of the matrix X.
P INTEGER.
P is the number of rows of the matrix X.
LDU INTEGER.
LDU is the leading dimension of the array U.
(See below).
LDV INTEGER.
LDV is the leading dimension of the array V.
(See below).
WORK DOUBLE PRECISION(N).
WORK is a scratch array.
JOB INTEGER.
JOB controls the computation of the singular
vectors. It has the decimal expansion AB
with the following meaning
A .EQ. 0 do not compute the left singular
vectors.
A .EQ. 1 return the N left singular vectors
in U.
A .GE. 2 return the first MIN(N,P) singular
vectors in U.
B .EQ. 0 do not compute the right singular
vectors.
B .EQ. 1 return the right singular vectors
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DSVDC(3F) DSVDC(3F)
in V. On Return
S DOUBLE PRECISION(MM), where MM=MIN(N+1,P).
The first MIN(N,P) entries of S contain the
singular values of X arranged in descending
order of magnitude.
E DOUBLE PRECISION(P).
E ordinarily contains zeros. However see the
discussion of INFO for exceptions.
U DOUBLE PRECISION(LDU,K), where LDU .GE. N.
If JOBA .EQ. 1, then K .EQ. N.
If JOBA .GE. 2, then K .EQ. MIN(N,P).
U contains the matrix of right singular vectors.
U is not referenced if JOBA .EQ. 0. If N .LE. P
or if JOBA .EQ. 2, then U may be identified with X
in the subroutine call.
V DOUBLE PRECISION(LDV,P), where LDV .GE. P.
V contains the matrix of right singular vectors.
V is not referenced if JOB .EQ. 0. If P .LE. N,
then V may be identified with X in the
subroutine call.
INFO INTEGER.
The singular values (and their corresponding
singular vectors) S(INFO+1),S(INFO+2),...,S(M)
are correct (here M=MIN(N,P)). Thus if
INFO .EQ. 0, all the singular values and their
vectors are correct. In any event, the matrix
B = TRANS(U)*X*V is the bidiagonal matrix
with the elements of S on its diagonal and the
elements of E on its super-diagonal (TRANS(U)
is the transpose of U). Thus the singular
values of X and B are the same. LINPACK. This version dated 03/19/79
. G. W. Stewart, University of Maryland, Argonne National Lab.
DSVDC uses the following functions and subprograms. External DROT BLAS
DAXPY,DDOT,DSCAL,DSWAP,DNRM2,DROTG Fortran DABS,DMAX1,MAX0,MIN0,MOD,DSQRT
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