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Diffstat (limited to '2.3-1/src/fortran/lapack/dgeqp3.f')
| -rw-r--r-- | 2.3-1/src/fortran/lapack/dgeqp3.f | 287 |
1 files changed, 287 insertions, 0 deletions
diff --git a/2.3-1/src/fortran/lapack/dgeqp3.f b/2.3-1/src/fortran/lapack/dgeqp3.f new file mode 100644 index 00000000..d6bc537d --- /dev/null +++ b/2.3-1/src/fortran/lapack/dgeqp3.f @@ -0,0 +1,287 @@ + SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, 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 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* DGEQP3 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) 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 trapezoidal 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(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) DOUBLE PRECISION array, dimension (min(M,N)) +* The scalar factors of the elementary reflectors. +* +* WORK (workspace/output) DOUBLE PRECISION 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 >= 3*N+1. +* For optimal performance LWORK >= 2*N+( 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. +* +* 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 DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA +* .. +* .. External Functions .. + INTEGER ILAENV + DOUBLE PRECISION DNRM2 + EXTERNAL ILAENV, DNRM2 +* .. +* .. 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 = 3*N + 1 + NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 ) + LWKOPT = 2*N + ( 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( 'DGEQP3', -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 DSWAP( 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 DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) + CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) + IWS = MAX( IWS, INT( WORK( 1 ) ) ) + IF( NA.LT.N ) THEN +*CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, +*CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) + CALL DORMQR( 'Left', '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, 'DGEQRF', ' ', 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, 'DGEQRF', ' ', SM, SN, -1, + $ -1 ) ) +* +* + IF( NX.LT.SMINMN ) THEN +* +* Determine if workspace is large enough for blocked code. +* + MINWS = 2*SN + ( 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-2*SN ) / ( SN+1 ) + NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', 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 + WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 ) + WORK( N+J ) = WORK( 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 DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, + $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ), + $ WORK( 2*N+1 ), WORK( 2*N+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 DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), + $ TAU( J ), WORK( J ), WORK( N+J ), + $ WORK( 2*N+1 ) ) +* + END IF +* + WORK( 1 ) = IWS + RETURN +* +* End of DGEQP3 +* + END |