1 SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
2 $ LWORK, INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 * @precisions normal z -> c
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.
92 * for LWORK < N, TRS will be done with Level BLAS 2
93 * for LWORK >= N, TRS will be done with Level BLAS 3
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 ..
119 EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
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 *
161 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
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 *
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
181 *
182 END IF
183 *
184 WORK( 1 ) = LWKOPT
185 *
186 RETURN
187 *
188 * End of ZHESV
189 *
190 END
2 $ LWORK, INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 * @precisions normal z -> c
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.
92 * for LWORK < N, TRS will be done with Level BLAS 2
93 * for LWORK >= N, TRS will be done with Level BLAS 3
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 ..
119 EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
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 *
161 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
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 *
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
181 *
182 END IF
183 *
184 WORK( 1 ) = LWKOPT
185 *
186 RETURN
187 *
188 * End of ZHESV
189 *
190 END