 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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

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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)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
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
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