CQRDC(3F)							     CQRDC(3F)

NAME    [Toc]    [Back]

     CQRDC   - CQRDC 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 users	option.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE CQRDC(X,LDX,N,P,QRAUX,JPVT,WORK,JOB)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     X COMPLEX(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.  JVPT    INTEGER(P).
	JVPT 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 JVPT(K).
	If JVPT(K) .GT.	0, then	X(K) is	an initial
	column.
	If JVPT(K) .EQ.	0, then	X(K) is	a free column.
	If JVPT(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.  JVPT is not referenced if
	JOB .EQ. 0.

     WORK COMPLEX(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

     X X contains in its upper triangle	the upper



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CQRDC(3F)							     CQRDC(3F)



	triangular matrix R of the QR factorization.
	Below its diagonal X contains information from
	which the unitary 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 JVPT.

     QRAUX COMPLEX(P).
	QRAUX contains further information required to recover
	the unitary part of the	decomposition.	JVPT	JVPT(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 .  Stewart,	G. W., University of Maryland, Argonne
     National Lab.

     CQRDC uses	the following functions	and subprograms. BLAS
     CAXPY,CDOTC,CSCAL,CSWAP,SCNRM2 Fortran
     ABS,AIMAG,AMAX1,CABS,CMPLX,CSQRT,MIN0,REAL


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