00001 SUBROUTINE ZSPSV( UPLO, N, NRHS, AP, IPIV, 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, LDB, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX*16 AP( * ), B( LDB, * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZSPSV computes the solution to a complex system of linear equations 00021 * A * X = B, 00022 * where A is an N-by-N symmetric matrix stored in packed format and X 00023 * and B are N-by-NRHS matrices. 00024 * 00025 * The diagonal pivoting method is used to factor A as 00026 * A = U * D * U**T, if UPLO = 'U', or 00027 * A = L * D * L**T, if UPLO = 'L', 00028 * where U (or L) is a product of permutation and unit upper (lower) 00029 * triangular matrices, D is symmetric and block diagonal with 1-by-1 00030 * and 2-by-2 diagonal blocks. The factored form of A is then used to 00031 * solve the system of equations A * X = B. 00032 * 00033 * Arguments 00034 * ========= 00035 * 00036 * UPLO (input) CHARACTER*1 00037 * = 'U': Upper triangle of A is stored; 00038 * = 'L': Lower triangle of A is stored. 00039 * 00040 * N (input) INTEGER 00041 * The number of linear equations, i.e., the order of the 00042 * matrix A. N >= 0. 00043 * 00044 * NRHS (input) INTEGER 00045 * The number of right hand sides, i.e., the number of columns 00046 * of the matrix B. NRHS >= 0. 00047 * 00048 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 00049 * On entry, the upper or lower triangle of the symmetric matrix 00050 * A, packed columnwise in a linear array. The j-th column of A 00051 * is stored in the array AP as follows: 00052 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00053 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00054 * See below for further details. 00055 * 00056 * On exit, the block diagonal matrix D and the multipliers used 00057 * to obtain the factor U or L from the factorization 00058 * A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as 00059 * a packed triangular matrix in the same storage format as A. 00060 * 00061 * IPIV (output) INTEGER array, dimension (N) 00062 * Details of the interchanges and the block structure of D, as 00063 * determined by ZSPTRF. If IPIV(k) > 0, then rows and columns 00064 * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 00065 * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, 00066 * then rows and columns k-1 and -IPIV(k) were interchanged and 00067 * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and 00068 * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and 00069 * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 00070 * diagonal block. 00071 * 00072 * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) 00073 * On entry, the N-by-NRHS right hand side matrix B. 00074 * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00075 * 00076 * LDB (input) INTEGER 00077 * The leading dimension of the array B. LDB >= max(1,N). 00078 * 00079 * INFO (output) INTEGER 00080 * = 0: successful exit 00081 * < 0: if INFO = -i, the i-th argument had an illegal value 00082 * > 0: if INFO = i, D(i,i) is exactly zero. The factorization 00083 * has been completed, but the block diagonal matrix D is 00084 * exactly singular, so the solution could not be 00085 * computed. 00086 * 00087 * Further Details 00088 * =============== 00089 * 00090 * The packed storage scheme is illustrated by the following example 00091 * when N = 4, UPLO = 'U': 00092 * 00093 * Two-dimensional storage of the symmetric matrix A: 00094 * 00095 * a11 a12 a13 a14 00096 * a22 a23 a24 00097 * a33 a34 (aij = aji) 00098 * a44 00099 * 00100 * Packed storage of the upper triangle of A: 00101 * 00102 * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] 00103 * 00104 * ===================================================================== 00105 * 00106 * .. External Functions .. 00107 LOGICAL LSAME 00108 EXTERNAL LSAME 00109 * .. 00110 * .. External Subroutines .. 00111 EXTERNAL XERBLA, ZSPTRF, ZSPTRS 00112 * .. 00113 * .. Intrinsic Functions .. 00114 INTRINSIC MAX 00115 * .. 00116 * .. Executable Statements .. 00117 * 00118 * Test the input parameters. 00119 * 00120 INFO = 0 00121 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00122 INFO = -1 00123 ELSE IF( N.LT.0 ) THEN 00124 INFO = -2 00125 ELSE IF( NRHS.LT.0 ) THEN 00126 INFO = -3 00127 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00128 INFO = -7 00129 END IF 00130 IF( INFO.NE.0 ) THEN 00131 CALL XERBLA( 'ZSPSV ', -INFO ) 00132 RETURN 00133 END IF 00134 * 00135 * Compute the factorization A = U*D*U' or A = L*D*L'. 00136 * 00137 CALL ZSPTRF( UPLO, N, AP, IPIV, INFO ) 00138 IF( INFO.EQ.0 ) THEN 00139 * 00140 * Solve the system A*X = B, overwriting B with X. 00141 * 00142 CALL ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) 00143 * 00144 END IF 00145 RETURN 00146 * 00147 * End of ZSPSV 00148 * 00149 END
1.7.2