LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zgetf2()

subroutine zgetf2 ( integer  M,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
integer  INFO 
)

ZGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).

Download ZGETF2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZGETF2 computes an LU factorization of a general m-by-n matrix A
 using partial pivoting with row interchanges.

 The factorization has the form
    A = P * L * U
 where P is a permutation matrix, L is lower triangular with unit
 diagonal elements (lower trapezoidal if m > n), and U is upper
 triangular (upper trapezoidal if m < n).

 This is the right-looking Level 2 BLAS version of the algorithm.
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*16 array, dimension (LDA,N)
          On entry, the m by n matrix to be factored.
          On exit, the factors L and U from the factorization
          A = P*L*U; the unit diagonal elements of L are not stored.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]IPIV
          IPIV is INTEGER array, dimension (min(M,N))
          The pivot indices; for 1 <= i <= min(M,N), row i of the
          matrix was interchanged with row IPIV(i).
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, U(k,k) is exactly zero. The factorization
               has been completed, but the factor U is exactly
               singular, and division by zero will occur if it is used
               to solve a system of equations.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 107 of file zgetf2.f.

108 *
109 * -- LAPACK computational routine --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 *
113 * .. Scalar Arguments ..
114  INTEGER INFO, LDA, M, N
115 * ..
116 * .. Array Arguments ..
117  INTEGER IPIV( * )
118  COMPLEX*16 A( LDA, * )
119 * ..
120 *
121 * =====================================================================
122 *
123 * .. Parameters ..
124  COMPLEX*16 ONE, ZERO
125  parameter( one = ( 1.0d+0, 0.0d+0 ),
126  $ zero = ( 0.0d+0, 0.0d+0 ) )
127 * ..
128 * .. Local Scalars ..
129  DOUBLE PRECISION SFMIN
130  INTEGER I, J, JP
131 * ..
132 * .. External Functions ..
133  DOUBLE PRECISION DLAMCH
134  INTEGER IZAMAX
135  EXTERNAL dlamch, izamax
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL xerbla, zgeru, zscal, zswap
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC max, min
142 * ..
143 * .. Executable Statements ..
144 *
145 * Test the input parameters.
146 *
147  info = 0
148  IF( m.LT.0 ) THEN
149  info = -1
150  ELSE IF( n.LT.0 ) THEN
151  info = -2
152  ELSE IF( lda.LT.max( 1, m ) ) THEN
153  info = -4
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'ZGETF2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( m.EQ.0 .OR. n.EQ.0 )
163  $ RETURN
164 *
165 * Compute machine safe minimum
166 *
167  sfmin = dlamch('S')
168 *
169  DO 10 j = 1, min( m, n )
170 *
171 * Find pivot and test for singularity.
172 *
173  jp = j - 1 + izamax( m-j+1, a( j, j ), 1 )
174  ipiv( j ) = jp
175  IF( a( jp, j ).NE.zero ) THEN
176 *
177 * Apply the interchange to columns 1:N.
178 *
179  IF( jp.NE.j )
180  $ CALL zswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
181 *
182 * Compute elements J+1:M of J-th column.
183 *
184  IF( j.LT.m ) THEN
185  IF( abs(a( j, j )) .GE. sfmin ) THEN
186  CALL zscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
187  ELSE
188  DO 20 i = 1, m-j
189  a( j+i, j ) = a( j+i, j ) / a( j, j )
190  20 CONTINUE
191  END IF
192  END IF
193 *
194  ELSE IF( info.EQ.0 ) THEN
195 *
196  info = j
197  END IF
198 *
199  IF( j.LT.min( m, n ) ) THEN
200 *
201 * Update trailing submatrix.
202 *
203  CALL zgeru( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ),
204  $ lda, a( j+1, j+1 ), lda )
205  END IF
206  10 CONTINUE
207  RETURN
208 *
209 * End of ZGETF2
210 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:130
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