1ZCGESV(1) LAPACK PROTOTYPE driver routine (version 3.2) ZCGESV(1)
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6 ZCGESV - computes the solution to a complex system of linear equations
7 A * X = B,
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10 SUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
11 + SWORK, RWORK, ITER, INFO )
13 INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
15 INTEGER IPIV( * )
17 DOUBLE PRECISION RWORK( * )
19 COMPLEX SWORK( * )
21 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( N, * ),
23 + X( LDX, * )
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27 ZCGESV computes the solution to a complex system of linear equations
28 A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS
29 matrices. ZCGESV first attempts to factorize the matrix in COMPLEX and
30 use this factorization within an iterative refinement procedure to pro‐
31 duce a solution with COMPLEX*16 normwise backward error quality (see
32 below). If the approach fails the method switches to a COMPLEX*16 fac‐
33 torization and solve.
34 The iterative refinement is not going to be a winning strategy if the
35 ratio COMPLEX performance over COMPLEX*16 performance is too small. A
36 reasonable strategy should take the number of right-hand sides and the
37 size of the matrix into account. This might be done with a call to
38 ILAENV in the future. Up to now, we always try iterative refinement.
39 The iterative refinement process is stopped if
40 ITER > ITERMAX
41 or for all the RHS we have:
42 RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
43 where
44 o ITER is the number of the current iteration in the iterative
45 refinement process
46 o RNRM is the infinity-norm of the residual
47 o XNRM is the infinity-norm of the solution
48 o ANRM is the infinity-operator-norm of the matrix A
49 o EPS is the machine epsilon returned by DLAMCH('Epsilon') The
50 value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
51 respectively.
52
54 N (input) INTEGER
55 The number of linear equations, i.e., the order of the matrix
56 A. N >= 0.
57 NRHS (input) INTEGER
59 The number of right hand sides, i.e., the number of columns of
60 the matrix B. NRHS >= 0.
61 A (input or input/ouptut) COMPLEX*16 array,
63 dimension (LDA,N) On entry, the N-by-N coefficient matrix A.
64 On exit, if iterative refinement has been successfully used
65 (INFO.EQ.0 and ITER.GE.0, see description below), then A is
66 unchanged, if double precision factorization has been used
67 (INFO.EQ.0 and ITER.LT.0, see description below), then the
68 array A contains the factors L and U from the factorization A =
69 P*L*U; the unit diagonal elements of L are not stored.
70 LDA (input) INTEGER
72 The leading dimension of the array A. LDA >= max(1,N).
73 IPIV (output) INTEGER array, dimension (N)
75 The pivot indices that define the permutation matrix P; row i
76 of the matrix was interchanged with row IPIV(i). Corresponds
77 either to the single precision factorization (if INFO.EQ.0 and
78 ITER.GE.0) or the double precision factorization (if INFO.EQ.0
79 and ITER.LT.0).
80 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
82 The N-by-NRHS right hand side matrix B.
83 LDB (input) INTEGER
85 The leading dimension of the array B. LDB >= max(1,N).
86 X (output) COMPLEX*16 array, dimension (LDX,NRHS)
88 If INFO = 0, the N-by-NRHS solution matrix X.
89 LDX (input) INTEGER
91 The leading dimension of the array X. LDX >= max(1,N).
92 WORK (workspace) COMPLEX*16 array, dimension (N*NRHS)
94 This array is used to hold the residual vectors.
95 SWORK (workspace) COMPLEX array, dimension (N*(N+NRHS))
97 This array is used to use the single precision matrix and the
98 right-hand sides or solutions in single precision.
99 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
101 ITER (output) INTEGER
103 < 0: iterative refinement has failed, COMPLEX*16 factorization
104 has been performed -1 : the routine fell back to full precision
105 for implementation- or machine-specific reasons -2 : narrowing
106 the precision induced an overflow, the routine fell back to
107 full precision -3 : failure of CGETRF
108 -31: stop the iterative refinement after the 30th iterations >
109 0: iterative refinement has been sucessfully used. Returns the
110 number of iterations
111 INFO (output) INTEGER
113 = 0: successful exit
114 < 0: if INFO = -i, the i-th argument had an illegal value
115 > 0: if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
116 zero. The factorization has been completed, but the factor U
117 is exactly singular, so the solution could not be computed.
118 =========
119 LAPACK PROTOTYPE driver routine (Nvoevresmiboenr 32.020)8 ZCGESV(1)