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SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
* * -- LAPACK deprecated computational routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER JPVT( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * This routine is deprecated and has been replaced by routine ZGEQP3. * * ZGEQPF computes a QR factorization with column pivoting of a * complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N)) * The scalar factors of the elementary reflectors. * * WORK (workspace) COMPLEX*16 array, dimension (N) * * RWORK (workspace) DOUBLE PRECISION array, dimension (2*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**H * * where tau is a complex scalar, and v is a complex 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. * -- April 2011 -- * 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 TEMP, TEMP2, TOL3Z COMPLEX*16 AII * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEQR2, ZLARF, ZLARFG, ZSWAP, ZUNM2R * .. * .. Intrinsic Functions .. INTRINSIC ABS, DCMPLX, DCONJG, MAX, MIN, SQRT * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DZNRM2 EXTERNAL IDAMAX, DLAMCH, DZNRM2 * .. * .. 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( 'ZGEQPF', -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 ZSWAP( 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 ZGEQR2( M, MA, A, LDA, TAU, WORK, INFO ) IF( MA.LT.N ) THEN CALL ZUNM2R( 'Left', 'Conjugate 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 RWORK( I ) = DZNRM2( M-ITEMP, A( ITEMP+1, I ), 1 ) RWORK( N+I ) = RWORK( 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, RWORK( I ), 1 ) * IF( PVT.NE.I ) THEN CALL ZSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) ITEMP = JPVT( PVT ) JPVT( PVT ) = JPVT( I ) JPVT( I ) = ITEMP RWORK( PVT ) = RWORK( I ) RWORK( N+PVT ) = RWORK( N+I ) END IF * * Generate elementary reflector H(i) * AII = A( I, I ) CALL ZLARFG( M-I+1, AII, A( MIN( I+1, M ), I ), 1, $ TAU( I ) ) A( I, I ) = AII * 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 ) = DCMPLX( ONE ) CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK ) A( I, I ) = AII END IF * * Update partial column norms * DO 30 J = I + 1, N IF( RWORK( J ).NE.ZERO ) THEN * * NOTE: The following 4 lines follow from the analysis in * Lapack Working Note 176. * TEMP = ABS( A( I, J ) ) / RWORK( J ) TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) ) TEMP2 = TEMP*( RWORK( J ) / RWORK( N+J ) )**2 IF( TEMP2 .LE. TOL3Z ) THEN IF( M-I.GT.0 ) THEN RWORK( J ) = DZNRM2( M-I, A( I+1, J ), 1 ) RWORK( N+J ) = RWORK( J ) ELSE RWORK( J ) = ZERO RWORK( N+J ) = ZERO END IF ELSE RWORK( J ) = RWORK( J )*SQRT( TEMP ) END IF END IF 30 CONTINUE * 40 CONTINUE END IF RETURN * * End of ZGEQPF * END |