*DECK QFORM
SUBROUTINE QFORM (M, N, Q, LDQ, WA)
C***BEGIN PROLOGUE QFORM
C***SUBSIDIARY
C***PURPOSE Subsidiary to SNSQ and SNSQE
C***LIBRARY SLATEC
C***TYPE SINGLE PRECISION (QFORM-S, DQFORM-D)
C***AUTHOR (UNKNOWN)
C***DESCRIPTION
C
C This subroutine proceeds from the computed QR factorization of
C an M by N matrix A to accumulate the M by M orthogonal matrix
C Q from its factored form.
C
C The subroutine statement is
C
C SUBROUTINE QFORM(M,N,Q,LDQ,WA)
C
C where
C
C M is a positive integer input variable set to the number
C of rows of A and the order of Q.
C
C N is a positive integer input variable set to the number
C of columns of A.
C
C Q is an M by M array. On input the full lower trapezoid in
C the first min(M,N) columns of Q contains the factored form.
C On output Q has been accumulated into a square matrix.
C
C LDQ is a positive integer input variable not less than M
C which specifies the leading dimension of the array Q.
C
C WA is a work array of length M.
C
C***SEE ALSO SNSQ, SNSQE
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 800301 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 900328 Added TYPE section. (WRB)
C***END PROLOGUE QFORM
INTEGER M,N,LDQ
REAL Q(LDQ,*),WA(*)
INTEGER I,J,JM1,K,L,MINMN,NP1
REAL ONE,SUM,TEMP,ZERO
SAVE ONE, ZERO
DATA ONE,ZERO /1.0E0,0.0E0/
C***FIRST EXECUTABLE STATEMENT QFORM
MINMN = MIN(M,N)
IF (MINMN .LT. 2) GO TO 30
DO 20 J = 2, MINMN
JM1 = J - 1
DO 10 I = 1, JM1
Q(I,J) = ZERO
10 CONTINUE
20 CONTINUE
30 CONTINUE
C
C INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX.
C
NP1 = N + 1
IF (M .LT. NP1) GO TO 60
DO 50 J = NP1, M
DO 40 I = 1, M
Q(I,J) = ZERO
40 CONTINUE
Q(J,J) = ONE
50 CONTINUE
60 CONTINUE
C
C ACCUMULATE Q FROM ITS FACTORED FORM.
C
DO 120 L = 1, MINMN
K = MINMN - L + 1
DO 70 I = K, M
WA(I) = Q(I,K)
Q(I,K) = ZERO
70 CONTINUE
Q(K,K) = ONE
IF (WA(K) .EQ. ZERO) GO TO 110
DO 100 J = K, M
SUM = ZERO
DO 80 I = K, M
SUM = SUM + Q(I,J)*WA(I)
80 CONTINUE
TEMP = SUM/WA(K)
DO 90 I = K, M
Q(I,J) = Q(I,J) - TEMP*WA(I)
90 CONTINUE
100 CONTINUE
110 CONTINUE
120 CONTINUE
RETURN
C
C LAST CARD OF SUBROUTINE QFORM.
C
END