LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dgeqr2()

subroutine dgeqr2 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
integer  INFO 
)

DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Download DGEQR2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DGEQR2 computes a QR factorization of a real m-by-n matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a m-by-m orthogonal matrix;
    R is an upper-triangular n-by-n matrix;
    0 is a (m-n)-by-n zero matrix, if m > n.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in,out]A
          A is DOUBLE PRECISION 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).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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**T

  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).

Definition at line 129 of file dgeqr2.f.

130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  INTEGER INFO, LDA, M, N
137 * ..
138 * .. Array Arguments ..
139  DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION ONE
146  parameter( one = 1.0d+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER I, K
150  DOUBLE PRECISION AII
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL dlarf, dlarfg, xerbla
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC max, min
157 * ..
158 * .. Executable Statements ..
159 *
160 * Test the input arguments
161 *
162  info = 0
163  IF( m.LT.0 ) THEN
164  info = -1
165  ELSE IF( n.LT.0 ) THEN
166  info = -2
167  ELSE IF( lda.LT.max( 1, m ) ) THEN
168  info = -4
169  END IF
170  IF( info.NE.0 ) THEN
171  CALL xerbla( 'DGEQR2', -info )
172  RETURN
173  END IF
174 *
175  k = min( m, n )
176 *
177  DO 10 i = 1, k
178 *
179 * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
180 *
181  CALL dlarfg( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
182  $ tau( i ) )
183  IF( i.LT.n ) THEN
184 *
185 * Apply H(i) to A(i:m,i+1:n) from the left
186 *
187  aii = a( i, i )
188  a( i, i ) = one
189  CALL dlarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
190  $ a( i, i+1 ), lda, work )
191  a( i, i ) = aii
192  END IF
193  10 CONTINUE
194  RETURN
195 *
196 * End of DGEQR2
197 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:124
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).
Definition: dlarfg.f:106
Here is the call graph for this function:
Here is the caller graph for this function: