232 lines
6.8 KiB
FortranFixed
232 lines
6.8 KiB
FortranFixed
SUBROUTINE SGEQPF( 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( * )
|
|
REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* This routine is deprecated and has been replaced by routine SGEQP3.
|
|
*
|
|
* SGEQPF 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) REAL 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) REAL array, dimension (min(M,N))
|
|
* The scalar factors of the elementary reflectors.
|
|
*
|
|
* WORK (workspace) REAL 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 ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, ITEMP, J, MA, MN, PVT
|
|
REAL AII, TEMP, TEMP2, TOL3Z
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SGEQR2, SLARF, SLARFP, SORM2R, SSWAP, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX, MIN, SQRT
|
|
* ..
|
|
* .. External Functions ..
|
|
INTEGER ISAMAX
|
|
REAL SLAMCH, SNRM2
|
|
EXTERNAL ISAMAX, SLAMCH, SNRM2
|
|
* ..
|
|
* .. 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( 'SGEQPF', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
MN = MIN( M, N )
|
|
TOL3Z = SQRT(SLAMCH('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 SSWAP( 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 SGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
|
|
IF( MA.LT.N ) THEN
|
|
CALL SORM2R( '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 ) = SNRM2( 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 ) + ISAMAX( N-I+1, WORK( I ), 1 )
|
|
*
|
|
IF( PVT.NE.I ) THEN
|
|
CALL SSWAP( 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 SLARFP( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
|
|
ELSE
|
|
CALL SLARFP( 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 SLARF( '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 ) = SNRM2( 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 SGEQPF
|
|
*
|
|
END
|