Visible to Intel only — GUID: GUID-AAA9F2C6-3F0E-4937-9227-A1F02A54283B
Visible to Intel only — GUID: GUID-AAA9F2C6-3F0E-4937-9227-A1F02A54283B
?sysv
Computes the solution to the system of linear equations with a real or complex symmetric coefficient matrix A and multiple right-hand sides.
Syntax
call ssysv( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info )
call dsysv( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info )
call csysv( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info )
call zsysv( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info )
call sysv( a, b [,uplo] [,ipiv] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine solves for X the real or complex system of linear equations A*X = B, where A is an n-by-n symmetric matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.
The diagonal pivoting method is used to factor A as A = U*D*UT or A = L*D*LT, 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.
Input Parameters
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of A is stored: If uplo = 'U', the upper triangle of A is stored. If uplo = 'L', the lower triangle of A is stored. |
n |
INTEGER. The order of matrix A; n≥ 0. |
nrhs |
INTEGER. The number of right-hand sides; the number of columns in B; nrhs≥ 0. |
a, b, work |
REAL for ssysv DOUBLE PRECISION for dsysv COMPLEX for csysv DOUBLE COMPLEX for zsysv. Arrays: a(size lda by *), b(size ldb by *), work(*). The array a contains the upper or the lower triangular part of the symmetric matrix A (see uplo). The second dimension of a must be at least max(1, n). The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs). work is a workspace array, dimension at least max(1,lwork). |
lda |
INTEGER. The leading dimension of a; lda≥ max(1, n). |
ldb |
INTEGER. The leading dimension of b; ldb≥ max(1, n). |
lwork |
INTEGER. The size of the work array; lwork≥ 1. 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. See Application Notes below for details and for the suggested value of lwork. |
Output Parameters
a |
If info = 0, a is overwritten by the block-diagonal matrix D and the multipliers used to obtain the factor U (or L) from the factorization of A as computed by ?sytrf. |
b |
If info = 0, b is overwritten by the solution matrix X. |
ipiv |
INTEGER. Array, size at least max(1, n). Contains details of the interchanges and the block structure of D, as determined by ?sytrf. If ipiv(i) = k >0, then dii is a 1-by-1 diagonal block, and the i-th row and column of A was interchanged with the k-th row and column. If uplo = 'U' and ipiv(i) = ipiv(i-1) = -m < 0, then D has a 2-by-2 block in rows/columns i and i-1, and (i-1)-th row and column of A was interchanged with the m-th row and column. If uplo = 'L'and ipiv(i) = ipiv(i+1) = -m < 0, then D has a 2-by-2 block in rows/columns i and i+1, and (i+1)-th row and column of A was interchanged with the m-th row and column. |
work(1) |
If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs. |
info |
INTEGER. If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value. If info = i, dii is 0. The factorization has been completed, but D is exactly singular, so the solution could not be computed. |
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine sysv interface are as follows:
a |
Holds the matrix A of size (n,n). |
b |
Holds the matrix B of size (n,nrhs). |
ipiv |
Holds the vector of length n. |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |
Application Notes
For better performance, try using lwork = n*blocksize, where blocksize is a machine-dependent value (typically, 16 to 64) required for optimum performance of the blocked algorithm.
If you are in doubt how much workspace to supply, use a generous value of lwork for the first run or set lwork = -1.
If you choose the first option and set any of admissible lwork sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value (work(1)) for subsequent runs.
If you set lwork = -1, the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work). This operation is called a workspace query.
Note that if you set lwork to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.