LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zgetrs()

 subroutine zgetrs ( character trans, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info )

ZGETRS

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

Purpose:
``` ZGETRS solves a system of linear equations
A * X = B,  A**T * X = B,  or  A**H * X = B
with a general N-by-N matrix A using the LU factorization computed
by ZGETRF.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose)``` [in] N ``` N is INTEGER 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] A ``` A is COMPLEX*16 array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from ZGETRF; for 1<=i<=N, 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 right hand side matrix B. On exit, the 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```

Definition at line 120 of file zgetrs.f.

121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER TRANS
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* .. Parameters ..
138 COMPLEX*16 ONE
139 parameter( one = ( 1.0d+0, 0.0d+0 ) )
140* ..
141* .. Local Scalars ..
142 LOGICAL NOTRAN
143* ..
144* .. External Functions ..
145 LOGICAL LSAME
146 EXTERNAL lsame
147* ..
148* .. External Subroutines ..
149 EXTERNAL xerbla, zlaswp, ztrsm
150* ..
151* .. Intrinsic Functions ..
152 INTRINSIC max
153* ..
154* .. Executable Statements ..
155*
156* Test the input parameters.
157*
158 info = 0
159 notran = lsame( trans, 'N' )
160 IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
161 \$ lsame( trans, 'C' ) ) THEN
162 info = -1
163 ELSE IF( n.LT.0 ) THEN
164 info = -2
165 ELSE IF( nrhs.LT.0 ) THEN
166 info = -3
167 ELSE IF( lda.LT.max( 1, n ) ) THEN
168 info = -5
169 ELSE IF( ldb.LT.max( 1, n ) ) THEN
170 info = -8
171 END IF
172 IF( info.NE.0 ) THEN
173 CALL xerbla( 'ZGETRS', -info )
174 RETURN
175 END IF
176*
177* Quick return if possible
178*
179 IF( n.EQ.0 .OR. nrhs.EQ.0 )
180 \$ RETURN
181*
182 IF( notran ) THEN
183*
184* Solve A * X = B.
185*
186* Apply row interchanges to the right hand sides.
187*
188 CALL zlaswp( nrhs, b, ldb, 1, n, ipiv, 1 )
189*
190* Solve L*X = B, overwriting B with X.
191*
192 CALL ztrsm( 'Left', 'Lower', 'No transpose', 'Unit', n, nrhs,
193 \$ one, a, lda, b, ldb )
194*
195* Solve U*X = B, overwriting B with X.
196*
197 CALL ztrsm( 'Left', 'Upper', 'No transpose', 'Non-unit', n,
198 \$ nrhs, one, a, lda, b, ldb )
199 ELSE
200*
201* Solve A**T * X = B or A**H * X = B.
202*
203* Solve U**T *X = B or U**H *X = B, overwriting B with X.
204*
205 CALL ztrsm( 'Left', 'Upper', trans, 'Non-unit', n, nrhs, one,
206 \$ a, lda, b, ldb )
207*
208* Solve L**T *X = B, or L**H *X = B overwriting B with X.
209*
210 CALL ztrsm( 'Left', 'Lower', trans, 'Unit', n, nrhs, one, a,
211 \$ lda, b, ldb )
212*
213* Apply row interchanges to the solution vectors.
214*
215 CALL zlaswp( nrhs, b, ldb, 1, n, ipiv, -1 )
216 END IF
217*
218 RETURN
219*
220* End of ZGETRS
221*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zlaswp(n, a, lda, k1, k2, ipiv, incx)
ZLASWP performs a series of row interchanges on a general rectangular matrix.
Definition zlaswp.f:115
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180
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