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Diffstat (limited to 'SRC/sgerqf.f')
| -rw-r--r-- | SRC/sgerqf.f | 216 |
1 files changed, 216 insertions, 0 deletions
diff --git a/SRC/sgerqf.f b/SRC/sgerqf.f new file mode 100644 index 00000000..fb9b7a2d --- /dev/null +++ b/SRC/sgerqf.f @@ -0,0 +1,216 @@ + SUBROUTINE SGERQF( M, N, A, LDA, 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 .. + REAL A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* SGERQF computes an RQ factorization of a real M-by-N matrix A: +* A = R * Q. +* +* 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, +* if m <= n, the upper triangle of the subarray +* A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; +* if m >= n, the elements on and above the (m-n)-th subdiagonal +* contain the M-by-N upper trapezoidal matrix R; +* the remaining elements, with the array TAU, represent the +* orthogonal matrix Q as a product of min(m,n) elementary +* reflectors (see Further Details). +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* TAU (output) REAL array, dimension (min(M,N)) +* The scalar factors of the elementary reflectors (see Further +* Details). +* +* WORK (workspace/output) REAL 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 >= max(1,M). +* For optimum performance LWORK >= M*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 scalar, and v is a real vector with +* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in +* A(m-k+i,1:n-k+i-1), and tau in TAU(i). +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT, + $ MU, NB, NBMIN, NU, NX +* .. +* .. External Subroutines .. + EXTERNAL SGERQ2, SLARFB, SLARFT, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + INTEGER ILAENV + EXTERNAL ILAENV +* .. +* .. Executable Statements .. +* +* Test the 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 + ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN + INFO = -7 + END IF +* + IF( INFO.EQ.0 ) THEN + K = MIN( M, N ) + IF( K.EQ.0 ) THEN + LWKOPT = 1 + ELSE + NB = ILAENV( 1, 'SGERQF', ' ', M, N, -1, -1 ) + LWKOPT = M*NB + WORK( 1 ) = LWKOPT + END IF + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN + INFO = -7 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SGERQF', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( K.EQ.0 ) THEN + RETURN + END IF +* + NBMIN = 2 + NX = 1 + IWS = M + IF( NB.GT.1 .AND. NB.LT.K ) THEN +* +* Determine when to cross over from blocked to unblocked code. +* + NX = MAX( 0, ILAENV( 3, 'SGERQF', ' ', M, N, -1, -1 ) ) + IF( NX.LT.K ) THEN +* +* Determine if workspace is large enough for blocked code. +* + LDWORK = M + IWS = LDWORK*NB + IF( LWORK.LT.IWS ) THEN +* +* Not enough workspace to use optimal NB: reduce NB and +* determine the minimum value of NB. +* + NB = LWORK / LDWORK + NBMIN = MAX( 2, ILAENV( 2, 'SGERQF', ' ', M, N, -1, + $ -1 ) ) + END IF + END IF + END IF +* + IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN +* +* Use blocked code initially. +* The last kk rows are handled by the block method. +* + KI = ( ( K-NX-1 ) / NB )*NB + KK = MIN( K, KI+NB ) +* + DO 10 I = K - KK + KI + 1, K - KK + 1, -NB + IB = MIN( K-I+1, NB ) +* +* Compute the RQ factorization of the current block +* A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) +* + CALL SGERQ2( IB, N-K+I+IB-1, A( M-K+I, 1 ), LDA, TAU( I ), + $ WORK, IINFO ) + IF( M-K+I.GT.1 ) THEN +* +* Form the triangular factor of the block reflector +* H = H(i+ib-1) . . . H(i+1) H(i) +* + CALL SLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, + $ A( M-K+I, 1 ), LDA, TAU( I ), WORK, LDWORK ) +* +* Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right +* + CALL SLARFB( 'Right', 'No transpose', 'Backward', + $ 'Rowwise', M-K+I-1, N-K+I+IB-1, IB, + $ A( M-K+I, 1 ), LDA, WORK, LDWORK, A, LDA, + $ WORK( IB+1 ), LDWORK ) + END IF + 10 CONTINUE + MU = M - K + I + NB - 1 + NU = N - K + I + NB - 1 + ELSE + MU = M + NU = N + END IF +* +* Use unblocked code to factor the last or only block +* + IF( MU.GT.0 .AND. NU.GT.0 ) + $ CALL SGERQ2( MU, NU, A, LDA, TAU, WORK, IINFO ) +* + WORK( 1 ) = IWS + RETURN +* +* End of SGERQF +* + END |