00001 SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) 00002 * 00003 * -- LAPACK driver routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, LDA, LDB, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 REAL A( LDA, * ), B( LDB, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SPOSV computes the solution to a real system of linear equations 00020 * A * X = B, 00021 * where A is an N-by-N symmetric positive definite matrix and X and B 00022 * are N-by-NRHS matrices. 00023 * 00024 * The Cholesky decomposition is used to factor A as 00025 * A = U**T* U, if UPLO = 'U', or 00026 * A = L * L**T, if UPLO = 'L', 00027 * where U is an upper triangular matrix and L is a lower triangular 00028 * matrix. The factored form of A is then used to solve the system of 00029 * equations A * X = B. 00030 * 00031 * Arguments 00032 * ========= 00033 * 00034 * UPLO (input) CHARACTER*1 00035 * = 'U': Upper triangle of A is stored; 00036 * = 'L': Lower triangle of A is stored. 00037 * 00038 * N (input) INTEGER 00039 * The number of linear equations, i.e., the order of the 00040 * matrix A. N >= 0. 00041 * 00042 * NRHS (input) INTEGER 00043 * The number of right hand sides, i.e., the number of columns 00044 * of the matrix B. NRHS >= 0. 00045 * 00046 * A (input/output) REAL array, dimension (LDA,N) 00047 * On entry, the symmetric matrix A. If UPLO = 'U', the leading 00048 * N-by-N upper triangular part of A contains the upper 00049 * triangular part of the matrix A, and the strictly lower 00050 * triangular part of A is not referenced. If UPLO = 'L', the 00051 * leading N-by-N lower triangular part of A contains the lower 00052 * triangular part of the matrix A, and the strictly upper 00053 * triangular part of A is not referenced. 00054 * 00055 * On exit, if INFO = 0, the factor U or L from the Cholesky 00056 * factorization A = U**T*U or A = L*L**T. 00057 * 00058 * LDA (input) INTEGER 00059 * The leading dimension of the array A. LDA >= max(1,N). 00060 * 00061 * B (input/output) REAL array, dimension (LDB,NRHS) 00062 * On entry, the N-by-NRHS right hand side matrix B. 00063 * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00064 * 00065 * LDB (input) INTEGER 00066 * The leading dimension of the array B. LDB >= max(1,N). 00067 * 00068 * INFO (output) INTEGER 00069 * = 0: successful exit 00070 * < 0: if INFO = -i, the i-th argument had an illegal value 00071 * > 0: if INFO = i, the leading minor of order i of A is not 00072 * positive definite, so the factorization could not be 00073 * completed, and the solution has not been computed. 00074 * 00075 * ===================================================================== 00076 * 00077 * .. External Functions .. 00078 LOGICAL LSAME 00079 EXTERNAL LSAME 00080 * .. 00081 * .. External Subroutines .. 00082 EXTERNAL SPOTRF, SPOTRS, XERBLA 00083 * .. 00084 * .. Intrinsic Functions .. 00085 INTRINSIC MAX 00086 * .. 00087 * .. Executable Statements .. 00088 * 00089 * Test the input parameters. 00090 * 00091 INFO = 0 00092 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00093 INFO = -1 00094 ELSE IF( N.LT.0 ) THEN 00095 INFO = -2 00096 ELSE IF( NRHS.LT.0 ) THEN 00097 INFO = -3 00098 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00099 INFO = -5 00100 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00101 INFO = -7 00102 END IF 00103 IF( INFO.NE.0 ) THEN 00104 CALL XERBLA( 'SPOSV ', -INFO ) 00105 RETURN 00106 END IF 00107 * 00108 * Compute the Cholesky factorization A = U'*U or A = L*L'. 00109 * 00110 CALL SPOTRF( UPLO, N, A, LDA, INFO ) 00111 IF( INFO.EQ.0 ) THEN 00112 * 00113 * Solve the system A*X = B, overwriting B with X. 00114 * 00115 CALL SPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) 00116 * 00117 END IF 00118 RETURN 00119 * 00120 * End of SPOSV 00121 * 00122 END
1.7.2