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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, 00002 $ LWORK, INFO ) 00003 * 00004 * -- LAPACK driver routine (version 3.3.1) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * -- April 2011 -- 00008 * @precisions normal z -> s d c 00009 * 00010 * .. Scalar Arguments .. 00011 CHARACTER UPLO 00012 INTEGER INFO, LDA, LDB, LWORK, N, NRHS 00013 * .. 00014 * .. Array Arguments .. 00015 INTEGER IPIV( * ) 00016 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * ZSYSV computes the solution to a complex system of linear equations 00023 * A * X = B, 00024 * where A is an N-by-N symmetric matrix and X and B are N-by-NRHS 00025 * matrices. 00026 * 00027 * The diagonal pivoting method is used to factor A as 00028 * A = U * D * U**T, if UPLO = 'U', or 00029 * A = L * D * L**T, if UPLO = 'L', 00030 * where U (or L) is a product of permutation and unit upper (lower) 00031 * triangular matrices, and D is symmetric and block diagonal with 00032 * 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then 00033 * used to solve the system of equations A * X = B. 00034 * 00035 * Arguments 00036 * ========= 00037 * 00038 * UPLO (input) CHARACTER*1 00039 * = 'U': Upper triangle of A is stored; 00040 * = 'L': Lower triangle of A is stored. 00041 * 00042 * N (input) INTEGER 00043 * The number of linear equations, i.e., the order of the 00044 * matrix A. N >= 0. 00045 * 00046 * NRHS (input) INTEGER 00047 * The number of right hand sides, i.e., the number of columns 00048 * of the matrix B. NRHS >= 0. 00049 * 00050 * A (input/output) COMPLEX*16 array, dimension (LDA,N) 00051 * On entry, the symmetric matrix A. If UPLO = 'U', the leading 00052 * N-by-N upper triangular part of A contains the upper 00053 * triangular part of the matrix A, and the strictly lower 00054 * triangular part of A is not referenced. If UPLO = 'L', the 00055 * leading N-by-N lower triangular part of A contains the lower 00056 * triangular part of the matrix A, and the strictly upper 00057 * triangular part of A is not referenced. 00058 * 00059 * On exit, if INFO = 0, the block diagonal matrix D and the 00060 * multipliers used to obtain the factor U or L from the 00061 * factorization A = U*D*U**T or A = L*D*L**T as computed by 00062 * ZSYTRF. 00063 * 00064 * LDA (input) INTEGER 00065 * The leading dimension of the array A. LDA >= max(1,N). 00066 * 00067 * IPIV (output) INTEGER array, dimension (N) 00068 * Details of the interchanges and the block structure of D, as 00069 * determined by ZSYTRF. If IPIV(k) > 0, then rows and columns 00070 * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 00071 * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, 00072 * then rows and columns k-1 and -IPIV(k) were interchanged and 00073 * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and 00074 * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and 00075 * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 00076 * diagonal block. 00077 * 00078 * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) 00079 * On entry, the N-by-NRHS right hand side matrix B. 00080 * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00081 * 00082 * LDB (input) INTEGER 00083 * The leading dimension of the array B. LDB >= max(1,N). 00084 * 00085 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00086 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00087 * 00088 * LWORK (input) INTEGER 00089 * The length of WORK. LWORK >= 1, and for best performance 00090 * LWORK >= max(1,N*NB), where NB is the optimal blocksize for 00091 * ZSYTRF. 00092 * for LWORK < N, TRS will be done with Level BLAS 2 00093 * for LWORK >= N, TRS will be done with Level BLAS 3 00094 * 00095 * If LWORK = -1, then a workspace query is assumed; the routine 00096 * only calculates the optimal size of the WORK array, returns 00097 * this value as the first entry of the WORK array, and no error 00098 * message related to LWORK is issued by XERBLA. 00099 * 00100 * INFO (output) INTEGER 00101 * = 0: successful exit 00102 * < 0: if INFO = -i, the i-th argument had an illegal value 00103 * > 0: if INFO = i, D(i,i) is exactly zero. The factorization 00104 * has been completed, but the block diagonal matrix D is 00105 * exactly singular, so the solution could not be computed. 00106 * 00107 * ===================================================================== 00108 * 00109 * .. Local Scalars .. 00110 LOGICAL LQUERY 00111 INTEGER LWKOPT, NB 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 INTEGER ILAENV 00116 EXTERNAL LSAME, ILAENV 00117 * .. 00118 * .. External Subroutines .. 00119 EXTERNAL XERBLA, ZSYTRF, ZSYTRS, ZSYTRS2 00120 * .. 00121 * .. Intrinsic Functions .. 00122 INTRINSIC MAX 00123 * .. 00124 * .. Executable Statements .. 00125 * 00126 * Test the input parameters. 00127 * 00128 INFO = 0 00129 LQUERY = ( LWORK.EQ.-1 ) 00130 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00131 INFO = -1 00132 ELSE IF( N.LT.0 ) THEN 00133 INFO = -2 00134 ELSE IF( NRHS.LT.0 ) THEN 00135 INFO = -3 00136 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00137 INFO = -5 00138 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00139 INFO = -8 00140 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN 00141 INFO = -10 00142 END IF 00143 * 00144 IF( INFO.EQ.0 ) THEN 00145 IF( N.EQ.0 ) THEN 00146 LWKOPT = 1 00147 ELSE 00148 CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, -1, INFO ) 00149 LWKOPT = WORK(1) 00150 END IF 00151 WORK( 1 ) = LWKOPT 00152 END IF 00153 * 00154 IF( INFO.NE.0 ) THEN 00155 CALL XERBLA( 'ZSYSV ', -INFO ) 00156 RETURN 00157 ELSE IF( LQUERY ) THEN 00158 RETURN 00159 END IF 00160 * 00161 * Compute the factorization A = U*D*U**T or A = L*D*L**T. 00162 * 00163 CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) 00164 IF( INFO.EQ.0 ) THEN 00165 * 00166 * Solve the system A*X = B, overwriting B with X. 00167 * 00168 IF ( LWORK.LT.N ) THEN 00169 * 00170 * Solve with TRS ( Use Level BLAS 2) 00171 * 00172 CALL ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) 00173 * 00174 ELSE 00175 * 00176 * Solve with TRS2 ( Use Level BLAS 3) 00177 * 00178 CALL ZSYTRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO ) 00179 * 00180 END IF 00181 * 00182 END IF 00183 * 00184 WORK( 1 ) = LWKOPT 00185 * 00186 RETURN 00187 * 00188 * End of ZSYSV 00189 * 00190 END
1.7.3 
