LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zgesv()

subroutine zgesv ( integer  N,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
complex*16, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

ZGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver)

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

Purpose:
 ZGESV computes the solution to a complex system of linear equations
    A * X = B,
 where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as
    A = P * L * U,
 where P is a permutation matrix, L is unit lower triangular, and U is
 upper triangular.  The factored form of A is then used to solve the
 system of equations A * X = B.
Parameters
[in]N
          N is INTEGER
          The number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in,out]A
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the N-by-N coefficient matrix A.
          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,N).
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i).
[in,out]B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS matrix of right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
                has been completed, but the factor U is exactly
                singular, so the solution could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 121 of file zgesv.f.

122 *
123 * -- LAPACK driver routine --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 *
127 * .. Scalar Arguments ..
128  INTEGER INFO, LDA, LDB, N, NRHS
129 * ..
130 * .. Array Arguments ..
131  INTEGER IPIV( * )
132  COMPLEX*16 A( LDA, * ), B( LDB, * )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. External Subroutines ..
138  EXTERNAL xerbla, zgetrf, zgetrs
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC max
142 * ..
143 * .. Executable Statements ..
144 *
145 * Test the input parameters.
146 *
147  info = 0
148  IF( n.LT.0 ) THEN
149  info = -1
150  ELSE IF( nrhs.LT.0 ) THEN
151  info = -2
152  ELSE IF( lda.LT.max( 1, n ) ) THEN
153  info = -4
154  ELSE IF( ldb.LT.max( 1, n ) ) THEN
155  info = -7
156  END IF
157  IF( info.NE.0 ) THEN
158  CALL xerbla( 'ZGESV ', -info )
159  RETURN
160  END IF
161 *
162 * Compute the LU factorization of A.
163 *
164  CALL zgetrf( n, n, a, lda, ipiv, info )
165  IF( info.EQ.0 ) THEN
166 *
167 * Solve the system A*X = B, overwriting B with X.
168 *
169  CALL zgetrs( 'No transpose', n, nrhs, a, lda, ipiv, b, ldb,
170  $ info )
171  END IF
172  RETURN
173 *
174 * End of ZGESV
175 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:121
subroutine zgetrf(M, N, A, LDA, IPIV, INFO)
ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
Definition: zgetrf.f:102
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