LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sgeql2()

subroutine sgeql2 ( integer  m,
integer  n,
real, dimension( lda, * )  a,
integer  lda,
real, dimension( * )  tau,
real, dimension( * )  work,
integer  info 
)

SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Download SGEQL2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SGEQL2 computes a QL factorization of a real m by n matrix A:
 A = Q * L.
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 lower triangle of the subarray
          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
          if m <= n, the elements on and below the (n-m)-th
          superdiagonal contain the m by n lower trapezoidal matrix L;
          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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
  A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 122 of file sgeql2.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( 'SGEQL2', -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(1:m-k+i-1,n-k+i)
174*
175 CALL slarfg( m-k+i, a( m-k+i, n-k+i ), a( 1, n-k+i ), 1,
176 $ tau( i ) )
177*
178* Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
179*
180 aii = a( m-k+i, n-k+i )
181 a( m-k+i, n-k+i ) = one
182 CALL slarf( 'Left', m-k+i, n-k+i-1, a( 1, n-k+i ), 1, tau( i ),
183 $ a, lda, work )
184 a( m-k+i, n-k+i ) = aii
185 10 CONTINUE
186 RETURN
187*
188* End of SGEQL2
189*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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
subroutine slarfg(n, alpha, x, incx, tau)
SLARFG generates an elementary reflector (Householder matrix).
Definition slarfg.f:106
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