HPL_dtrsv(3) HPL Library Functions HPL_dtrsv(3) NAME HPL_dtrsv - x := A^{-1} x. SYNOPSIS #include "hpl.h" void HPL_dtrsv( const enum HPL_ORDER ORDER, const enum HPL_UPLO UPLO, const enum HPL_TRANS TRANS, const enum HPL_DIAG DIAG, const int N, const double * A, const int LDA, double * X, const int INCX ); DESCRIPTION HPL_dtrsv solves one of the systems of equations A * x = b, or A^T * x = b, where b and x are n-element vectors and A is an n by n non-unit, or unit, upper or lower triangular matrix. No test for singularity or near-singularity is included in this rou- tine. Such tests must be performed before calling this routine. ARGUMENTS ORDER (local input) const enum HPL_ORDER On entry, ORDER specifies the storage format of the operands as follows: ORDER = HplRowMajor, ORDER = HplColumnMajor. UPLO (local input) const enum HPL_UPLO On entry, UPLO specifies whether the upper or lower tri- angular part of the array A is to be referenced. When UPLO==HplUpper, only the upper triangular part of A is to be ref- erenced, otherwise only the lower triangular part of A is to be referenced. TRANS (local input) const enum HPL_TRANS On entry, TRANS specifies the equations to be solved as fol- lows: TRANS==HplNoTrans A * x = b, TRANS==HplTrans A^T * x = b. DIAG (local input) const enum HPL_DIAG On entry, DIAG specifies whether A is unit triangular or not. When DIAG==HplUnit, A is assumed to be unit triangular, and other- wise, A is not assumed to be unit triangular. N (local input) const int On entry, N specifies the order of the matrix A. N must be at least zero. A (local input) const double * On entry, A points to an array of size equal to or greater than LDA * n. Before entry with UPLO==HplUpper, the leading n by n up- per triangular part of the array A must contain the upper triangu- lar matrix and the strictly lower triangular part of A is not referenced. When UPLO==HplLower on entry, the leading n by n lower triangular part of the array A must contain the lower trian- gular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG==HplUnit, the diagonal elements of A not referenced either, but are assumed to be unity. LDA (local input) const int On entry, LDA specifies the leading dimension of A as de- clared in the calling (sub) program. LDA must be at least MAX(1,n). X (local input/output) double * On entry, X is an incremented array of dimension at least ( 1 + ( n - 1 ) * abs( INCX ) ) that contains the vector x. Before en- try, the incremented array X must contain the n element right- hand side vector b. On exit, X is overwritten with the solution vector x. INCX (local input) const int On entry, INCX specifies the increment for the elements of X. INCX must not be zero. EXAMPLE #include "hpl.h" int main(int argc, char *argv[]) { double a[2*2], x[2]; a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0; x[0] = 2.0; x[1] = 1.0; HPL_dtrsv( HplColumnMajor, HplLower, HplNoTrans, HplNoUnit, a, 2, x, 1 ); printf("x=[%f,%f]\n", x[0], x[1]); exit(0); return(0); } SEE ALSO HPL_dger (3), HPL_dgemv (3). HPL 2.3 December 2, 2018 HPL_dtrsv(3)
NAME | SYNOPSIS | DESCRIPTION | ARGUMENTS | EXAMPLE | SEE ALSO
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