LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgerq2()

subroutine sgerq2 ( integer  M,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  TAU,
real, dimension( * )  WORK,
integer  INFO 
)

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Download SGERQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SGERQ2 computes an RQ factorization of a real m by n matrix A:
 A = R * Q.
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 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 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 REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[out]WORK
          WORK is REAL array, dimension (M)
[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(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).

Definition at line 122 of file sgerq2.f.

123 *
124 * -- LAPACK computational routine --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 *
128 * .. Scalar Arguments ..
129  INTEGER INFO, LDA, M, N
130 * ..
131 * .. Array Arguments ..
132  REAL A( LDA, * ), TAU( * ), WORK( * )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  REAL ONE
139  parameter( one = 1.0e+0 )
140 * ..
141 * .. Local Scalars ..
142  INTEGER I, K
143  REAL AII
144 * ..
145 * .. External Subroutines ..
146  EXTERNAL slarf, slarfg, xerbla
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC max, min
150 * ..
151 * .. Executable Statements ..
152 *
153 * Test the input arguments
154 *
155  info = 0
156  IF( m.LT.0 ) THEN
157  info = -1
158  ELSE IF( n.LT.0 ) THEN
159  info = -2
160  ELSE IF( lda.LT.max( 1, m ) ) THEN
161  info = -4
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'SGERQ2', -info )
165  RETURN
166  END IF
167 *
168  k = min( m, n )
169 *
170  DO 10 i = k, 1, -1
171 *
172 * Generate elementary reflector H(i) to annihilate
173 * A(m-k+i,1:n-k+i-1)
174 *
175  CALL slarfg( n-k+i, a( m-k+i, n-k+i ), a( m-k+i, 1 ), lda,
176  $ tau( i ) )
177 *
178 * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
179 *
180  aii = a( m-k+i, n-k+i )
181  a( m-k+i, n-k+i ) = one
182  CALL slarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
183  $ tau( i ), a, lda, work )
184  a( m-k+i, n-k+i ) = aii
185  10 CONTINUE
186  RETURN
187 *
188 * End of SGERQ2
189 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
Here is the call graph for this function:
Here is the caller graph for this function: