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Diffstat (limited to 'src/lib/lapack/dgeqlf.f')
| -rw-r--r-- | src/lib/lapack/dgeqlf.f | 213 |
1 files changed, 0 insertions, 213 deletions
diff --git a/src/lib/lapack/dgeqlf.f b/src/lib/lapack/dgeqlf.f deleted file mode 100644 index ec293574..00000000 --- a/src/lib/lapack/dgeqlf.f +++ /dev/null @@ -1,213 +0,0 @@ - SUBROUTINE DGEQLF( 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 .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* DGEQLF computes a QL factorization of a real M-by-N matrix A: -* A = Q * L. -* -* 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, -* if m >= n, the lower triangle of the subarray -* A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; -* if m <= n, the elements on and below the (n-m)-th -* superdiagonal contain the M-by-N lower trapezoidal matrix L; -* the remaining elements, with the array TAU, represent the -* orthogonal matrix Q as a product of elementary reflectors -* (see Further Details). -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors (see Further -* Details). -* -* 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 >= max(1,N). -* For optimum performance LWORK >= N*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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in -* A(1:m-k+i-1,n-k+i), 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 DGEQL2, DLARFB, DLARFT, 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 - END IF -* - IF( INFO.EQ.0 ) THEN - K = MIN( M, N ) - IF( K.EQ.0 ) THEN - LWKOPT = 1 - ELSE - NB = ILAENV( 1, 'DGEQLF', ' ', M, N, -1, -1 ) - LWKOPT = N*NB - END IF - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -7 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGEQLF', -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 = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DGEQLF', ' ', M, N, -1, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - 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, 'DGEQLF', ' ', 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 columns 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 QL factorization of the current block -* A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) -* - CALL DGEQL2( M-K+I+IB-1, IB, A( 1, N-K+I ), LDA, TAU( I ), - $ WORK, IINFO ) - IF( N-K+I.GT.1 ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i+ib-1) . . . H(i+1) H(i) -* - CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, - $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left -* - CALL DLARFB( 'Left', 'Transpose', 'Backward', - $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, - $ A( 1, N-K+I ), 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 DGEQL2( MU, NU, A, LDA, TAU, WORK, IINFO ) -* - WORK( 1 ) = IWS - RETURN -* -* End of DGEQLF -* - END |