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authorjason <jason@8a072113-8704-0410-8d35-dd094bca7971>2008-10-28 01:38:50 +0000
committerjason <jason@8a072113-8704-0410-8d35-dd094bca7971>2008-10-28 01:38:50 +0000
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+ SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
+*
+* -- LAPACK deprecated driver routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+ INTEGER JPVT( * )
+ DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+* Purpose
+* =======
+*
+* This routine is deprecated and has been replaced by routine DGEQP3.
+*
+* DGEQPF computes a QR factorization with column pivoting of a
+* real M-by-N matrix A: A*P = Q*R.
+*
+* Arguments
+* =========
+*
+* M (input) INTEGER
+* The number of rows of the matrix A. M >= 0.
+*
+* N (input) INTEGER
+* The number of columns of the matrix A. N >= 0
+*
+* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
+* On entry, the M-by-N matrix A.
+* On exit, the upper triangle of the array contains the
+* min(M,N)-by-N upper triangular matrix R; the elements
+* below the diagonal, together with the array TAU,
+* represent the orthogonal matrix Q as a product of
+* min(m,n) elementary reflectors.
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(1,M).
+*
+* JPVT (input/output) INTEGER array, dimension (N)
+* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
+* to the front of A*P (a leading column); if JPVT(i) = 0,
+* the i-th column of A is a free column.
+* On exit, if JPVT(i) = k, then the i-th column of A*P
+* was the k-th column of A.
+*
+* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
+* The scalar factors of the elementary reflectors.
+*
+* WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
+*
+* INFO (output) INTEGER
+* = 0: successful exit
+* < 0: if INFO = -i, the i-th argument had an illegal value
+*
+* Further Details
+* ===============
+*
+* The matrix Q is represented as a product of elementary reflectors
+*
+* Q = H(1) H(2) . . . H(n)
+*
+* Each H(i) has the form
+*
+* H = I - tau * v * v'
+*
+* where tau is a real scalar, and v is a real vector with
+* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
+*
+* The matrix P is represented in jpvt as follows: If
+* jpvt(j) = i
+* then the jth column of P is the ith canonical unit vector.
+*
+* Partial column norm updating strategy modified by
+* Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
+* University of Zagreb, Croatia.
+* June 2006.
+* For more details see LAPACK Working Note 176.
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, ITEMP, J, MA, MN, PVT
+ DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
+* ..
+* .. External Subroutines ..
+ EXTERNAL DGEQR2, DLARF, DLARFP, DORM2R, DSWAP, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN, SQRT
+* ..
+* .. External Functions ..
+ INTEGER IDAMAX
+ DOUBLE PRECISION DLAMCH, DNRM2
+ EXTERNAL IDAMAX, DLAMCH, DNRM2
+* ..
+* .. Executable Statements ..
+*
+* Test the input arguments
+*
+ INFO = 0
+ IF( M.LT.0 ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+ INFO = -4
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DGEQPF', -INFO )
+ RETURN
+ END IF
+*
+ MN = MIN( M, N )
+ TOL3Z = SQRT(DLAMCH('Epsilon'))
+*
+* Move initial columns up front
+*
+ ITEMP = 1
+ DO 10 I = 1, N
+ IF( JPVT( I ).NE.0 ) THEN
+ IF( I.NE.ITEMP ) THEN
+ CALL DSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
+ JPVT( I ) = JPVT( ITEMP )
+ JPVT( ITEMP ) = I
+ ELSE
+ JPVT( I ) = I
+ END IF
+ ITEMP = ITEMP + 1
+ ELSE
+ JPVT( I ) = I
+ END IF
+ 10 CONTINUE
+ ITEMP = ITEMP - 1
+*
+* Compute the QR factorization and update remaining columns
+*
+ IF( ITEMP.GT.0 ) THEN
+ MA = MIN( ITEMP, M )
+ CALL DGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
+ IF( MA.LT.N ) THEN
+ CALL DORM2R( 'Left', 'Transpose', M, N-MA, MA, A, LDA, TAU,
+ $ A( 1, MA+1 ), LDA, WORK, INFO )
+ END IF
+ END IF
+*
+ IF( ITEMP.LT.MN ) THEN
+*
+* Initialize partial column norms. The first n elements of
+* work store the exact column norms.
+*
+ DO 20 I = ITEMP + 1, N
+ WORK( I ) = DNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
+ WORK( N+I ) = WORK( I )
+ 20 CONTINUE
+*
+* Compute factorization
+*
+ DO 40 I = ITEMP + 1, MN
+*
+* Determine ith pivot column and swap if necessary
+*
+ PVT = ( I-1 ) + IDAMAX( N-I+1, WORK( I ), 1 )
+*
+ IF( PVT.NE.I ) THEN
+ CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
+ ITEMP = JPVT( PVT )
+ JPVT( PVT ) = JPVT( I )
+ JPVT( I ) = ITEMP
+ WORK( PVT ) = WORK( I )
+ WORK( N+PVT ) = WORK( N+I )
+ END IF
+*
+* Generate elementary reflector H(i)
+*
+ IF( I.LT.M ) THEN
+ CALL DLARFP( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
+ ELSE
+ CALL DLARFP( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
+ END IF
+*
+ IF( I.LT.N ) THEN
+*
+* Apply H(i) to A(i:m,i+1:n) from the left
+*
+ AII = A( I, I )
+ A( I, I ) = ONE
+ CALL DLARF( 'LEFT', M-I+1, N-I, A( I, I ), 1, TAU( I ),
+ $ A( I, I+1 ), LDA, WORK( 2*N+1 ) )
+ A( I, I ) = AII
+ END IF
+*
+* Update partial column norms
+*
+ DO 30 J = I + 1, N
+ IF( WORK( J ).NE.ZERO ) THEN
+*
+* NOTE: The following 4 lines follow from the analysis in
+* Lapack Working Note 176.
+*
+ TEMP = ABS( A( I, J ) ) / WORK( J )
+ TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
+ TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2
+ IF( TEMP2 .LE. TOL3Z ) THEN
+ IF( M-I.GT.0 ) THEN
+ WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 )
+ WORK( N+J ) = WORK( J )
+ ELSE
+ WORK( J ) = ZERO
+ WORK( N+J ) = ZERO
+ END IF
+ ELSE
+ WORK( J ) = WORK( J )*SQRT( TEMP )
+ END IF
+ END IF
+ 30 CONTINUE
+*
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of DGEQPF
+*
+ END