Annotation of rpl/lapack/lapack/zhesv.f, revision 1.9
1.1 bertrand 1: SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
2: $ LWORK, INFO )
3: *
1.9 ! bertrand 4: * -- LAPACK driver routine (version 3.3.1) --
1.1 bertrand 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 7: * -- April 2011 --
! 8: * @precisions normal z -> c
1.1 bertrand 9: *
10: * .. Scalar Arguments ..
11: CHARACTER UPLO
12: INTEGER INFO, LDA, LDB, LWORK, N, NRHS
13: * ..
14: * .. Array Arguments ..
15: INTEGER IPIV( * )
16: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZHESV computes the solution to a complex system of linear equations
23: * A * X = B,
24: * where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
25: * matrices.
26: *
27: * The diagonal pivoting method is used to factor A as
28: * A = U * D * U**H, if UPLO = 'U', or
29: * A = L * D * L**H, if UPLO = 'L',
30: * where U (or L) is a product of permutation and unit upper (lower)
31: * triangular matrices, and D is Hermitian and block diagonal with
32: * 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
33: * used to solve the system of equations A * X = B.
34: *
35: * Arguments
36: * =========
37: *
38: * UPLO (input) CHARACTER*1
39: * = 'U': Upper triangle of A is stored;
40: * = 'L': Lower triangle of A is stored.
41: *
42: * N (input) INTEGER
43: * The number of linear equations, i.e., the order of the
44: * matrix A. N >= 0.
45: *
46: * NRHS (input) INTEGER
47: * The number of right hand sides, i.e., the number of columns
48: * of the matrix B. NRHS >= 0.
49: *
50: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
51: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
52: * N-by-N upper triangular part of A contains the upper
53: * triangular part of the matrix A, and the strictly lower
54: * triangular part of A is not referenced. If UPLO = 'L', the
55: * leading N-by-N lower triangular part of A contains the lower
56: * triangular part of the matrix A, and the strictly upper
57: * triangular part of A is not referenced.
58: *
59: * On exit, if INFO = 0, the block diagonal matrix D and the
60: * multipliers used to obtain the factor U or L from the
61: * factorization A = U*D*U**H or A = L*D*L**H as computed by
62: * ZHETRF.
63: *
64: * LDA (input) INTEGER
65: * The leading dimension of the array A. LDA >= max(1,N).
66: *
67: * IPIV (output) INTEGER array, dimension (N)
68: * Details of the interchanges and the block structure of D, as
69: * determined by ZHETRF. If IPIV(k) > 0, then rows and columns
70: * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
71: * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
72: * then rows and columns k-1 and -IPIV(k) were interchanged and
73: * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
74: * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
75: * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
76: * diagonal block.
77: *
78: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
79: * On entry, the N-by-NRHS right hand side matrix B.
80: * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
81: *
82: * LDB (input) INTEGER
83: * The leading dimension of the array B. LDB >= max(1,N).
84: *
85: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
86: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
87: *
88: * LWORK (input) INTEGER
89: * The length of WORK. LWORK >= 1, and for best performance
90: * LWORK >= max(1,N*NB), where NB is the optimal blocksize for
91: * ZHETRF.
1.9 ! bertrand 92: * for LWORK < N, TRS will be done with Level BLAS 2
! 93: * for LWORK >= N, TRS will be done with Level BLAS 3
1.1 bertrand 94: *
95: * If LWORK = -1, then a workspace query is assumed; the routine
96: * only calculates the optimal size of the WORK array, returns
97: * this value as the first entry of the WORK array, and no error
98: * message related to LWORK is issued by XERBLA.
99: *
100: * INFO (output) INTEGER
101: * = 0: successful exit
102: * < 0: if INFO = -i, the i-th argument had an illegal value
103: * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
104: * has been completed, but the block diagonal matrix D is
105: * exactly singular, so the solution could not be computed.
106: *
107: * =====================================================================
108: *
109: * .. Local Scalars ..
110: LOGICAL LQUERY
111: INTEGER LWKOPT, NB
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: INTEGER ILAENV
116: EXTERNAL LSAME, ILAENV
117: * ..
118: * .. External Subroutines ..
1.9 ! bertrand 119: EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
1.1 bertrand 120: * ..
121: * .. Intrinsic Functions ..
122: INTRINSIC MAX
123: * ..
124: * .. Executable Statements ..
125: *
126: * Test the input parameters.
127: *
128: INFO = 0
129: LQUERY = ( LWORK.EQ.-1 )
130: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
131: INFO = -1
132: ELSE IF( N.LT.0 ) THEN
133: INFO = -2
134: ELSE IF( NRHS.LT.0 ) THEN
135: INFO = -3
136: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
137: INFO = -5
138: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
139: INFO = -8
140: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
141: INFO = -10
142: END IF
143: *
144: IF( INFO.EQ.0 ) THEN
145: IF( N.EQ.0 ) THEN
146: LWKOPT = 1
147: ELSE
148: NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
149: LWKOPT = N*NB
150: END IF
151: WORK( 1 ) = LWKOPT
152: END IF
153: *
154: IF( INFO.NE.0 ) THEN
155: CALL XERBLA( 'ZHESV ', -INFO )
156: RETURN
157: ELSE IF( LQUERY ) THEN
158: RETURN
159: END IF
160: *
1.9 ! bertrand 161: * Compute the factorization A = U*D*U**H or A = L*D*L**H.
1.1 bertrand 162: *
163: CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
164: IF( INFO.EQ.0 ) THEN
165: *
166: * Solve the system A*X = B, overwriting B with X.
167: *
1.9 ! bertrand 168: IF ( LWORK.LT.N ) THEN
! 169: *
! 170: * Solve with TRS ( Use Level BLAS 2)
! 171: *
! 172: CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
! 173: *
! 174: ELSE
! 175: *
! 176: * Solve with TRS2 ( Use Level BLAS 3)
! 177: *
! 178: CALL ZHETRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO )
! 179: *
! 180: END IF
1.1 bertrand 181: *
182: END IF
183: *
184: WORK( 1 ) = LWKOPT
185: *
186: RETURN
187: *
188: * End of ZHESV
189: *
190: END
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