DQRDC(3F)DQRDC(3F)NAMEDQRDC - DQRDC uses Householder transformations to compute the QR
factorization of an N by P matrix X. Column pivoting based on the 2-
norms of the reduced columns may be performed at the user's option.
SYNOPSYS
SUBROUTINE DQRDC(X,LDX,N,P,QRAUX,JPVT,WORK,JOB)
DESCRIPTION
On Entry
X DOUBLE PRECISION(LDX,P), where LDX .GE. N.
X contains the matrix whose decomposition is to be
computed.
LDX INTEGER.
LDX is the leading dimension of the array X.
N INTEGER.
N is the number of rows of the matrix X.
P INTEGER.
P is the number of columns of the matrix X.
JPVT INTEGER(P).
JPVT contains integers that control the selection
of the pivot columns. The K-th column X(K) of X
is placed in one of three classes according to the
value of JPVT(K).
If JPVT(K) .GT. 0, then X(K) is an initial
column.
If JPVT(K) .EQ. 0, then X(K) is a free column.
If JPVT(K) .LT. 0, then X(K) is a final column.
Before the decomposition is computed, initial columns
are moved to the beginning of the array X and final
columns to the end. Both initial and final columns
are frozen in place during the computation and only
free columns are moved. At the K-th stage of the
reduction, if X(K) is occupied by a free column
it is interchanged with the free column of largest
reduced norm. JPVT is not referenced if
JOB .EQ. 0.
WORK DOUBLE PRECISION(P).
WORK is a work array. WORK is not referenced if
JOB .EQ. 0.
JOB INTEGER.
JOB is an integer that initiates column pivoting.
If JOB .EQ. 0, no pivoting is done.
If JOB .NE. 0, pivoting is done. On Return
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DQRDC(3F)DQRDC(3F)
X X contains in its upper triangle the upper
triangular matrix R of the QR factorization.
Below its diagonal X contains information from
which the orthogonal part of the decomposition
can be recovered. Note that if pivoting has
been requested, the decomposition is not that
of the original matrix X but that of X
with its columns permuted as described by JPVT.
QRAUX DOUBLE PRECISION(P).
QRAUX contains further information required to recover
the orthogonal part of the decomposition.
JPVT JPVT(K) contains the index of the column of the
original matrix that has been interchanged into
the K-th column, if pivoting was requested. LINPACK. This version
dated 08/14/78 . G. W. Stewart, University of Maryland, Argonne National
Lab.
DQRDC uses the following functions and subprograms. BLAS
DAXPY,DDOT,DSCAL,DSWAP,DNRM2 Fortran DABS,DMAX1,MIN0,DSQRT
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