LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ 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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