Texas Instruments voyage 200 User Manual - Page 856
PxlVert, The resulting Q and R
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PxlVert CATALOG PxlVert col [, drawMode] Draws a vertical line down the screen at pixel position col. If drawMode = 1, draws the line (default). If drawMode = 0, turns off the line. If drawMode = -1, turns a line that is on to off or off to on (inverts pixels along the line). Note: Regraphing erases all drawn items. See also LineVert. PxlVert 50,1 ¸ QR MATH/Matrix menu QR matrix, qMatName, rMatName[ , tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified MatNames. The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, tol is ignored. • If you use ¥ ¸ or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic. The floating-point number (9.) in m1 causes results to be calculated in floating-point form. [1,2,3;4,5,6;7,8,9.]!m1 ¸ 14 2 5 3 6 7 8 9. QR m1,qm,rm ¸ Done qm ¸ ..142932...... .904... .301... .ë4.0881...6... .861... ë.301... .408... rm ¸ 80..124... 9.601... .904... 111..800798...... 0. 0. 0. • If tol is omitted or not used, the default tolerance is calculated as: 5Eë 14 ù max(dim(matrix)) ù rowNorm(matrix) [m,n;o,p]!m1 ¸ [ ] m n o p The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram-Schmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix. QR m1,qm,rm ¸ Done qm ¸ m ë sign(møpì nøo)øo m2 + o2 m2 + o2 o møsign(møpì nøo) m2 + o2 m2 + o2 rm ¸ m2 + o2 0 møn+oøp m2 + o2 |møpì nøo| m2 + o2 858 Appendix A: Functions and Instructions
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