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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +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-* This routine is deprecated and has been replaced by routine DGEQP3.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, DLARFG, 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 DLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
- ELSE
- CALL DLARFG( 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