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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
- $ INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER INFO, LDA, LWORK, M, N
-* ..
-* .. Array Arguments ..
- INTEGER JPVT( * )
- DOUBLE PRECISION RWORK( * )
- COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* ZGEQP3 computes a QR factorization with column pivoting of a
-* matrix A: A*P = Q*R using Level 3 BLAS.
-*
-* 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 trapezoidal 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(J).ne.0, the J-th column of A is permuted
-* to the front of A*P (a leading column); if JPVT(J)=0,
-* the J-th column of A is a free column.
-* On exit, if JPVT(J)=K, then the J-th column of A*P was the
-* the K-th column of A.
-*
-* TAU (output) COMPLEX*16 array, dimension (min(M,N))
-* The scalar factors of the elementary reflectors.
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
-* On exit, if INFO=0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= N+1.
-* For optimal performance LWORK >= ( N+1 )*NB, where NB
-* is the optimal blocksize.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* 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(k), where k = min(m,n).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a real/complex scalar, and v is a real/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), and tau in TAU(i).
-*
-* Based on contributions by
-* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-* X. Sun, Computer Science Dept., Duke University, USA
-*
-* =====================================================================
-*
-* .. Parameters ..
- INTEGER INB, INBMIN, IXOVER
- PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
-* ..
-* .. Local Scalars ..
- LOGICAL LQUERY
- INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
- $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
-* ..
-* .. External Subroutines ..
- EXTERNAL XERBLA, ZGEQRF, ZLAQP2, ZLAQPS, ZSWAP, ZUNMQR
-* ..
-* .. External Functions ..
- INTEGER ILAENV
- DOUBLE PRECISION DZNRM2
- EXTERNAL ILAENV, DZNRM2
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC INT, MAX, MIN
-* ..
-* .. Executable Statements ..
-*
-* Test input arguments
-* ====================
-*
- INFO = 0
- LQUERY = ( LWORK.EQ.-1 )
- 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.EQ.0 ) THEN
- MINMN = MIN( M, N )
- IF( MINMN.EQ.0 ) THEN
- IWS = 1
- LWKOPT = 1
- ELSE
- IWS = N + 1
- NB = ILAENV( INB, 'ZGEQRF', ' ', M, N, -1, -1 )
- LWKOPT = ( N + 1 )*NB
- END IF
- WORK( 1 ) = LWKOPT
-*
- IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
- INFO = -8
- END IF
- END IF
-*
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'ZGEQP3', -INFO )
- RETURN
- ELSE IF( LQUERY ) THEN
- RETURN
- END IF
-*
-* Quick return if possible.
-*
- IF( MINMN.EQ.0 ) THEN
- RETURN
- END IF
-*
-* Move initial columns up front.
-*
- NFXD = 1
- DO 10 J = 1, N
- IF( JPVT( J ).NE.0 ) THEN
- IF( J.NE.NFXD ) THEN
- CALL ZSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
- JPVT( J ) = JPVT( NFXD )
- JPVT( NFXD ) = J
- ELSE
- JPVT( J ) = J
- END IF
- NFXD = NFXD + 1
- ELSE
- JPVT( J ) = J
- END IF
- 10 CONTINUE
- NFXD = NFXD - 1
-*
-* Factorize fixed columns
-* =======================
-*
-* Compute the QR factorization of fixed columns and update
-* remaining columns.
-*
- IF( NFXD.GT.0 ) THEN
- NA = MIN( M, NFXD )
-*CC CALL ZGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
- CALL ZGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
- IWS = MAX( IWS, INT( WORK( 1 ) ) )
- IF( NA.LT.N ) THEN
-*CC CALL ZUNM2R( 'Left', 'Conjugate Transpose', M, N-NA,
-*CC $ NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK,
-*CC $ INFO )
- CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, N-NA, NA, A,
- $ LDA, TAU, A( 1, NA+1 ), LDA, WORK, LWORK,
- $ INFO )
- IWS = MAX( IWS, INT( WORK( 1 ) ) )
- END IF
- END IF
-*
-* Factorize free columns
-* ======================
-*
- IF( NFXD.LT.MINMN ) THEN
-*
- SM = M - NFXD
- SN = N - NFXD
- SMINMN = MINMN - NFXD
-*
-* Determine the block size.
-*
- NB = ILAENV( INB, 'ZGEQRF', ' ', SM, SN, -1, -1 )
- NBMIN = 2
- NX = 0
-*
- IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
-*
-* Determine when to cross over from blocked to unblocked code.
-*
- NX = MAX( 0, ILAENV( IXOVER, 'ZGEQRF', ' ', SM, SN, -1,
- $ -1 ) )
-*
-*
- IF( NX.LT.SMINMN ) THEN
-*
-* Determine if workspace is large enough for blocked code.
-*
- MINWS = ( SN+1 )*NB
- IWS = MAX( IWS, MINWS )
- IF( LWORK.LT.MINWS ) THEN
-*
-* Not enough workspace to use optimal NB: Reduce NB and
-* determine the minimum value of NB.
-*
- NB = LWORK / ( SN+1 )
- NBMIN = MAX( 2, ILAENV( INBMIN, 'ZGEQRF', ' ', SM, SN,
- $ -1, -1 ) )
-*
-*
- END IF
- END IF
- END IF
-*
-* Initialize partial column norms. The first N elements of work
-* store the exact column norms.
-*
- DO 20 J = NFXD + 1, N
- RWORK( J ) = DZNRM2( SM, A( NFXD+1, J ), 1 )
- RWORK( N+J ) = RWORK( J )
- 20 CONTINUE
-*
- IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
- $ ( NX.LT.SMINMN ) ) THEN
-*
-* Use blocked code initially.
-*
- J = NFXD + 1
-*
-* Compute factorization: while loop.
-*
-*
- TOPBMN = MINMN - NX
- 30 CONTINUE
- IF( J.LE.TOPBMN ) THEN
- JB = MIN( NB, TOPBMN-J+1 )
-*
-* Factorize JB columns among columns J:N.
-*
- CALL ZLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
- $ JPVT( J ), TAU( J ), RWORK( J ),
- $ RWORK( N+J ), WORK( 1 ), WORK( JB+1 ),
- $ N-J+1 )
-*
- J = J + FJB
- GO TO 30
- END IF
- ELSE
- J = NFXD + 1
- END IF
-*
-* Use unblocked code to factor the last or only block.
-*
-*
- IF( J.LE.MINMN )
- $ CALL ZLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
- $ TAU( J ), RWORK( J ), RWORK( N+J ), WORK( 1 ) )
-*
- END IF
-*
- WORK( 1 ) = IWS
- RETURN
-*
-* End of ZGEQP3
-*
- END