Move LAPACK trunk into position.

1 files changed, 121 insertions, 0 deletions

diff --git a/SRC/sgeqr2.f b/SRC/sgeqr2.f
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+      SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO )
+*
+*  -- LAPACK routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LDA, M, N
+*     ..
+*     .. Array Arguments ..
+      REAL               A( LDA, * ), TAU( * ), WORK( * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  SGEQR2 computes a QR factorization of a real m by n matrix A:
+*  A = 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) REAL array, dimension (LDA,N)
+*          On entry, the m by n matrix A.
+*          On exit, the elements on and above the diagonal of the array
+*          contain the min(m,n) by n upper trapezoidal matrix R (R is
+*          upper triangular if m >= n); the elements below the diagonal,
+*          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) REAL array, dimension (min(M,N))
+*          The scalar factors of the elementary reflectors (see Further
+*          Details).
+*
+*  WORK    (workspace) REAL array, dimension (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 scalar, and v is a real 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).
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ONE
+      PARAMETER          ( ONE = 1.0E+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, K
+      REAL               AII
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SLARF, SLARFP, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX, MIN
+*     ..
+*     .. 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( 'SGEQR2', -INFO )
+         RETURN
+      END IF
+*
+      K = MIN( M, N )
+*
+      DO 10 I = 1, K
+*
+*        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
+*
+         CALL SLARFP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
+     $                TAU( I ) )
+         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 ) = ONE
+            CALL SLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
+     $                  A( I, I+1 ), LDA, WORK )
+            A( I, I ) = AII
+         END IF
+   10 CONTINUE
+      RETURN
+*
+*     End of SGEQR2
+*
+      END