SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, $ LWORK, INFO ) * * -- LAPACK driver routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LDB, LWORK, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * Purpose * ======= * * ZHESV computes the solution to a complex system of linear equations * A * X = B, * where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS * matrices. * * The diagonal pivoting method is used to factor A as * A = U * D * U**H, if UPLO = 'U', or * A = L * D * L**H, if UPLO = 'L', * where U (or L) is a product of permutation and unit upper (lower) * triangular matrices, and D is Hermitian 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*16 array, dimension (LDA,N) * On entry, the Hermitian 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**H or A = L*D*L**H as computed by * ZHETRF. * * 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 ZHETRF. 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*16 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*16 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 * ZHETRF. * * 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 .. LOGICAL LQUERY INTEGER LWKOPT, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHETRF, ZHETRS * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN INFO = -10 END IF * IF( INFO.EQ.0 ) THEN IF( N.EQ.0 ) THEN LWKOPT = 1 ELSE NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 ) LWKOPT = N*NB END IF WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHESV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Compute the factorization A = U*D*U' or A = L*D*L'. * CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * END IF * WORK( 1 ) = LWKOPT * RETURN * * End of ZHESV * END