Multiplies a real matrix by the real orthogonal matrix Q determined by ?sptrd.
lapack_int LAPACKE_sopmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const float* ap, const float* tau, float* c, lapack_int ldc);
lapack_int LAPACKE_dopmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const double* ap, const double* tau, double* c, lapack_int ldc);
The routine multiplies a real matrix C by Q or QT, where Q is the orthogonal matrix Q formed by sptrd when reducing a packed real symmetric matrix A to tridiagonal form: A = Q*T*QT. Use this routine after a call to ?sptrd.
Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, QT*C, C*Q, or C*QT (overwriting the result on C).
In the descriptions below, r denotes the order of Q:
If side = 'L', r = m; if side = 'R', r = n.
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
Must be either 'L' or 'R'.
If side = 'L', Q or QT is applied to C from the left.
If side = 'R', Q or QT is applied to C from the right.
Must be 'U' or 'L'.
Use the same uplo as supplied to ?sptrd.
Must be either 'N' or 'T'.
If trans = 'N', the routine multiplies C by Q.
If trans = 'T', the routine multiplies C by QT.
The number of rows in the matrix C (m≥ 0).
The number of columns in C (n≥ 0).
- ap, tau, c
ap and tau are the arrays returned by ?sptrd.
The dimension of ap must be at least max(1, r(r+1)/2).
The dimension of tau must be at least max(1, r-1).
c(size max(1, ldc*n) for column major layout and max(1, ldc*m) for row major layout) contains the matrix C.
The leading dimension of c; ldc≥ max(1, n) for column major layout and ldc≥ max(1, m) for row major layout .
Overwritten by the product Q*C, QT*C, C*Q, or C*QT (as specified by side and trans).
This function returns a value info.
If info=0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
The computed product differs from the exact product by a matrix E such that ||E||2 = O(ε) ||C||2, where ε is the machine precision.
The total number of floating-point operations is approximately 2*m2*n if side = 'L', or 2*n2*m if side = 'R'.
The complex counterpart of this routine is upmtr.