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SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSSSSSPPPPMMMMVVVV, DDDDSSSSPPPPMMMMVVVV, CCCCSSSSPPPPMMMMVVVV, ZZZZSSSSPPPPMMMMVVVV - Multiplies a real or complex symmetric packed matrix by a real or complex vector SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSSSSSPPPPMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a_p,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ssssssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_a_p,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _i_n_c_x,,,, ffffllllooooaaaatttt _b_e_t_a,,,, ffffllllooooaaaatttt *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDSSSSPPPPMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a_p,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ddddssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_a_p,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _i_n_c_x,,,, ddddoooouuuubbbblllleeee _b_e_t_a,,,, ddddoooouuuubbbblllleeee *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCSSSSPPPPMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a_p,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_p,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _i_n_c_x,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_b_e_t_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _i_n_c_y))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_p,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,, iiiinnnntttt _i_n_c_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Double precision complex Fortran: CCCCAAAALLLLLLLL ZZZZSSSSPPPPMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a_p,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_p,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _i_n_c_x,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx PPPPaaaaggggeeee 1111 SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) *_b_e_t_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _i_n_c_y))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssppppmmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_p,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,, iiiinnnntttt _i_n_c_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_y,,,, iiiinnnntttt _i_n_c_y))));;;; IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN These routines are part of the SCSL Scientific Library and can be loaded using either the ----llllssssccccssss or the ----llllssssccccssss____mmmmpppp option. The ----llllssssccccssss____mmmmpppp option directs the linker to use the multi-processor version of the library. When linking to SCSL with ----llllssssccccssss or ----llllssssccccssss____mmmmpppp, the default integer size is 4 bytes (32 bits). Another version of SCSL is available in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using the ----llllssssccccssss____iiii8888 option or the ----llllssssccccssss____iiii8888____mmmmpppp option. A program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. The C and C++ prototypes shown above are appropriate for the 4-byte integer version of SCSL. When using the 8-byte integer version, the variables of type iiiinnnntttt become lllloooonnnngggg lllloooonnnngggg and the <<<<ssssccccssssllll____bbbbllllaaaassss____iiii8888....hhhh>>>> header file should be included. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN These routines perform the following matrix-vector operation: _y <-_a_l_p_h_a _A_x + _b_e_t_a _y where _a_l_p_h_a and _b_e_t_a are scalars, _x and _y are _n-element vectors, and _A is an _n-by-_n symmetric packed matrix. See the NOTES section of this man page for information about the interpretation of the data types described in the following arguments. These routines have the following arguments: _u_p_l_o Character. (input) Specifies whether the upper or lower triangular part of matrix _A is packed into the array argument _a_p, as follows: _u_p_l_o= 'U' or 'u': the upper triangular part of _A is being supplied in the argument _a_p. _u_p_l_o= 'L' or 'l': the lower triangular part of _A is being supplied in the argument _a_p. For C/C++, a pointer to this character is passed. PPPPaaaaggggeeee 2222 SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) _n Integer. (input) Specifies the order of matrix _A. _n >= 0. _a_l_p_h_a Scalar alpha. (input) SSSSSSSSPPPPMMMMVVVV: Single precision. DDDDSSSSPPPPMMMMVVVV: Double precision. CCCCSSSSPPPPMMMMVVVV: Single precision complex. ZZZZSSSSPPPPMMMMVVVV: Double precision complex. For C/C++, a pointer to this scalar is passed when alpha is complex; otherwise, alpha is passed by value. _a_p Array of dimension (_n(_n+1))/2 (input) SSSSSSSSPPPPMMMMVVVV: Single precision array. DDDDSSSSPPPPMMMMVVVV: Double precision array. CCCCSSSSPPPPMMMMVVVV: Single precision complex array. ZZZZSSSSPPPPMMMMVVVV: Double precision complex array. Before entry with _u_p_l_o = 'U' or 'u', array _a_p must contain the upper triangular part of the symmetric matrix packed sequentially, column-by-column, so that _a_p(1) contains _A(1,1), _a_p(2) contains _A(1,2), _a_p(3) contains _A(2,2), and so on. Before entry with _u_p_l_o = 'L' or 'l', array _a_p must contain the lower triangular part of the symmetric matrix packed sequentially, column-by-column, so that _a_p(1) contains _A(1,1), _a_p(2) contains _A(2,1), _a_p(3) contains _A(3,1), and so on. _x Array of dimension 1+(_n-1) * |_i_n_c_x|. (input) SSSSSSSSPPPPMMMMVVVV: Single precision array. DDDDSSSSPPPPMMMMVVVV: Double precision array. CCCCSSSSPPPPMMMMVVVV: Single precision omplex array. ZZZZSSSSPPPPMMMMVVVV: Double precision complex array. Contains vector _x. _i_n_c_x Integer. (input) Specifies the increment for the elements of _x. _i_n_c_x must not be 0. _b_e_t_a Scalar beta. (input) SSSSSSSSPPPPMMMMVVVV: Single precision. DDDDSSSSPPPPMMMMVVVV: Double precision. CCCCSSSSPPPPMMMMVVVV: Single precision complex. ZZZZSSSSPPPPMMMMVVVV: Double precision complex. If _b_e_t_a is supplied as 0, _y need not be set on input. For C/C++, a pointer to this scalar is passed when beta is complex; otherwise, beta is passed by value. _y Array of dimension 1+(_n-1) * |_i_n_c_y|. (input and output) SSSSSSSSPPPPMMMMVVVV: Single precision array. DDDDSSSSPPPPMMMMVVVV: Double precision array. PPPPaaaaggggeeee 3333 SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) CCCCSSSSPPPPMMMMVVVV: Single precision complex array. ZZZZSSSSPPPPMMMMVVVV: Double precision complex array. Contains vector _y. On exit, the updated vector overwrites array _y. _i_n_c_y Integer. (input) Specifies the increment for the elements of _y. _i_n_c_y must not be 0. NNNNOOOOTTTTEEEESSSS SSSSSSSSPPPPMMMMVVVV/DDDDSSSSPPPPMMMMVVVV is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS). CCCCSSSSPPPPMMMMVVVV/ZZZZSSSSPPPPMMMMVVVV is an extension to Level 2 BLAS. When working backward (_i_n_c_x < 0 or _i_n_c_y < 0), each routine starts at the end of the vector and moves backward, as follows: _x(1-_i_n_c_x * (_n-1)), _x(1-_i_n_c_x * (_n-2)) , ..., _x(1) _y(1-_i_n_c_y * (_n-1)), _y(1-_i_n_c_y * (_n-2)) , ..., _y(1) DDDDaaaattttaaaa TTTTyyyyppppeeeessss The following data types are described in this documentation: TTTTeeeerrrrmmmm UUUUsssseeeedddd DDDDaaaattttaaaa ttttyyyyppppeeee Fortran: Array dimensioned _n xxxx((((nnnn)))) Character CCCCHHHHAAAARRRRAAAACCCCTTTTEEEERRRR Integer IIIINNNNTTTTEEEEGGGGEEEERRRR (IIIINNNNTTTTEEEEGGGGEEEERRRR****8888 for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision RRRREEEEAAAALLLL Double precision DDDDOOOOUUUUBBBBLLLLEEEE PPPPRRRREEEECCCCIIIISSSSIIIIOOOONNNN Single precision complex CCCCOOOOMMMMPPPPLLLLEEEEXXXX Double precision complex DDDDOOOOUUUUBBBBLLLLEEEE CCCCOOOOMMMMPPPPLLLLEEEEXXXX C/C++: Array dimensioned _n xxxx[[[[_n]]]] Character cccchhhhaaaarrrr Integer iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) PPPPaaaaggggeeee 4444 SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) SSSSSSSSPPPPMMMMVVVV((((3333SSSS)))) Single precision ffffllllooooaaaatttt Double precision ddddoooouuuubbbblllleeee Single precision complex ssssccccssssllll____ccccoooommmmpppplllleeeexxxx Double precision complex ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx C++ STL: Array dimensioned _n xxxx[[[[_n]]]] Character cccchhhhaaaarrrr Integer iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision ffffllllooooaaaatttt Double precision ddddoooouuuubbbblllleeee Single precision complex ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> Double precision complex ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> Note that you can explicitly declare multidimensional C/C++ arrays provided that the array dimensions are swapped with respect to the Fortran declaration (e.g., xxxx[[[[nnnn]]]][[[[mmmm]]]] in C/C++ versus xxxx((((mmmm,,,,nnnn)))) in Fortran). To avoid a compiler type mismatch error in C++ (or a compiler warning message in C), however, the array should be cast to a pointer of the appropriate type when passed as an argument to a SCSL routine. SSSSEEEEEEEE AAAALLLLSSSSOOOO IIIINNNNTTTTRRRROOOO____SSSSCCCCSSSSLLLL(3S), IIIINNNNTTTTRRRROOOO____BBBBLLLLAAAASSSS2222(3S), CCCCHHHHPPPPMMMMVVVV(3S) IIIINNNNTTTTRRRROOOO____CCCCBBBBLLLLAAAASSSS(3S) for information about using the C interface to Fortran 77 Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic Linear Algebra Subprograms Technical Forum. PPPPaaaaggggeeee 5555 
