#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; /* Subroutine */ int csysv_(char *uplo, integer *n, integer *nrhs, complex *a, integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ integer nb; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int csytrf_(char *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); integer lwkopt; logical lquery; extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CSYSV computes the solution to a complex system of linear equations */ /* A * X = B, */ /* where A is an N-by-N symmetric matrix and X and B are N-by-NRHS */ /* matrices. */ /* The diagonal pivoting method is used to factor A as */ /* A = U * D * U**T, if UPLO = 'U', or */ /* A = L * D * L**T, if UPLO = 'L', */ /* where U (or L) is a product of permutation and unit upper (lower) */ /* triangular matrices, and D is symmetric and block diagonal with */ /* 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then */ /* used to solve the system of equations A * X = B. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrix B. NRHS >= 0. */ /* A (input/output) COMPLEX array, dimension (LDA,N) */ /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ /* N-by-N upper triangular part of A contains the upper */ /* triangular part of the matrix A, and the strictly lower */ /* triangular part of A is not referenced. If UPLO = 'L', the */ /* leading N-by-N lower triangular part of A contains the lower */ /* triangular part of the matrix A, and the strictly upper */ /* triangular part of A is not referenced. */ /* On exit, if INFO = 0, the block diagonal matrix D and the */ /* multipliers used to obtain the factor U or L from the */ /* factorization A = U*D*U**T or A = L*D*L**T as computed by */ /* CSYTRF. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* IPIV (output) INTEGER array, dimension (N) */ /* Details of the interchanges and the block structure of D, as */ /* determined by CSYTRF. If IPIV(k) > 0, then rows and columns */ /* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 */ /* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, */ /* then rows and columns k-1 and -IPIV(k) were interchanged and */ /* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and */ /* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and */ /* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 */ /* diagonal block. */ /* B (input/output) COMPLEX array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS right hand side matrix B. */ /* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The length of WORK. LWORK >= 1, and for best performance */ /* LWORK >= max(1,N*NB), where NB is the optimal blocksize for */ /* CSYTRF. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal size of the WORK array, returns */ /* this value as the first entry of the WORK array, and no error */ /* message related to LWORK is issued by XERBLA. */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */ /* has been completed, but the block diagonal matrix D is */ /* exactly singular, so the solution could not be computed. */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --work; /* Function Body */ *info = 0; lquery = *lwork == -1; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else if (*ldb < max(1,*n)) { *info = -8; } else if (*lwork < 1 && ! lquery) { *info = -10; } if (*info == 0) { if (*n == 0) { lwkopt = 1; } else { nb = ilaenv_(&c__1, "CSYTRF", uplo, n, &c_n1, &c_n1, &c_n1); lwkopt = *n * nb; } work[1].r = (real) lwkopt, work[1].i = 0.f; } if (*info != 0) { i__1 = -(*info); xerbla_("CSYSV ", &i__1); return 0; } else if (lquery) { return 0; } /* Compute the factorization A = U*D*U' or A = L*D*L'. */ csytrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], lwork, info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ csytrs_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb, info); } work[1].r = (real) lwkopt, work[1].i = 0.f; return 0; /* End of CSYSV */ } /* csysv_ */