LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cgeqr2p()

subroutine cgeqr2p ( integer  M,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( * )  WORK,
integer  INFO 
)

CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Download CGEQR2P + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CGEQR2P computes a QR factorization of a complex 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 with nonnegative diagonal
    entries;
    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 COMPLEX 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 diagonal entries of R are
          real and nonnegative; the elements below the diagonal,
          with the array TAU, represent the unitary 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 COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[out]WORK
          WORK is COMPLEX 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**H

  where tau is a complex scalar, and v is a complex 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).

 See Lapack Working Note 203 for details

Definition at line 133 of file cgeqr2p.f.

134*
135* -- LAPACK computational routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 INTEGER INFO, LDA, M, N
141* ..
142* .. Array Arguments ..
143 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
144* ..
145*
146* =====================================================================
147*
148* .. Parameters ..
149 COMPLEX ONE
150 parameter( one = ( 1.0e+0, 0.0e+0 ) )
151* ..
152* .. Local Scalars ..
153 INTEGER I, K
154 COMPLEX ALPHA
155* ..
156* .. External Subroutines ..
157 EXTERNAL clarf, clarfgp, xerbla
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC conjg, max, min
161* ..
162* .. Executable Statements ..
163*
164* Test the input arguments
165*
166 info = 0
167 IF( m.LT.0 ) THEN
168 info = -1
169 ELSE IF( n.LT.0 ) THEN
170 info = -2
171 ELSE IF( lda.LT.max( 1, m ) ) THEN
172 info = -4
173 END IF
174 IF( info.NE.0 ) THEN
175 CALL xerbla( 'CGEQR2P', -info )
176 RETURN
177 END IF
178*
179 k = min( m, n )
180*
181 DO 10 i = 1, k
182*
183* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
184*
185 CALL clarfgp( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
186 $ tau( i ) )
187 IF( i.LT.n ) THEN
188*
189* Apply H(i)**H to A(i:m,i+1:n) from the left
190*
191 alpha = a( i, i )
192 a( i, i ) = one
193 CALL clarf( 'Left', m-i+1, n-i, a( i, i ), 1,
194 $ conjg( tau( i ) ), a( i, i+1 ), lda, work )
195 a( i, i ) = alpha
196 END IF
197 10 CONTINUE
198 RETURN
199*
200* End of CGEQR2P
201*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine clarfgp(N, ALPHA, X, INCX, TAU)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: clarfgp.f:104
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128
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