 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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.

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
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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