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SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSSSSSYYYYMMMMVVVV, DDDDSSSSYYYYMMMMVVVV, CCCCSSSSYYYYMMMMVVVV, ZZZZSSSSYYYYMMMMVVVV - Multiplies a real or complex vector by a real or complex symmetric matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSSSSSYYYYMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ssssssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_a,,,, iiiinnnntttt _l_d_a,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _x,,,, ffffllllooooaaaatttt _b_e_t_a,,,, ffffllllooooaaaatttt *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDSSSSYYYYMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ddddssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_a,,,, iiiinnnntttt _l_d_a,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _x,,,, ddddoooouuuubbbblllleeee _b_e_t_a,,,, ddddoooouuuubbbblllleeee *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCSSSSYYYYMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _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 ccccssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,, iiiinnnntttt _x,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Double precision complex Fortran: CCCCAAAALLLLLLLL ZZZZSSSSYYYYMMMMVVVV ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _x,,,, _i_n_c_x,,,, _b_e_t_a,,,, _y,,,, _i_n_c_y)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _x,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx PPPPaaaaggggeeee 1111 SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) *_b_e_t_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _i_n_c_y))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyymmmmvvvv ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_x,,,, iiiinnnntttt _x,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_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 SSSSSSSSYYYYMMMMVVVV and DDDDSSSSYYYYMMMMVVVV multiplies a real vector by a real symmetric matrix. CCCCSSSSYYYYMMMMVVVV and ZZZZSSSSYYYYMMMMVVVV multiplies a complex vector by a complex symmetric matrix. 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 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 being supplied, as follows: _u_p_l_o= 'U' or 'u': only the upper triangular part of _A is being supplied. _u_p_l_o= 'L' or 'l': only the lower triangular part of _A is being PPPPaaaaggggeeee 2222 SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) supplied. For C/C++, a pointer to this character is passed. _n Integer. (input) Specifies the order of matrix _A. _n >= 0. _a_l_p_h_a Scalar alpha. (input) SSSSSSSSYYYYMMMMVVVV: Single precision. DDDDSSSSYYYYMMMMVVVV: Double precision. CCCCSSSSYYYYMMMMVVVV: Single precision complex. ZZZZSSSSYYYYMMMMVVVV: Double precision complex. For C/C++, a pointer to this scalar is passed when alpha is complex; otherwise, alpha is passed by value. _a Array of dimension (_l_d_a,_n). (input) SSSSSSSSYYYYMMMMVVVV: Single precision array. DDDDSSSSYYYYMMMMVVVV: Double precision array. CCCCSSSSYYYYMMMMVVVV: Single precision complex array. ZZZZSSSSYYYYMMMMVVVV: Double precision complex array. Before entry with _u_p_l_o = 'U' or 'u', the leading _n-by-_n upper triangular part of array _a must contain the upper triangular part of the symmetric matrix. The strictly lower triangular part of _a is not referenced. Before entry with _u_p_l_o = 'L' or 'l', the leading _n-by-_n lower triangular part of array _a must contain the lower triangular part of the symmetric matrix. The strictly upper triangular part of _a is not referenced. _l_d_a Integer. (input) Specifies the first dimension of _a as declared in the calling program. _l_d_a >= MMMMAAAAXXXX(1,_n). _x Array of dimension 1+(_n-1) * |_i_n_c_x|. (input) SSSSSSSSYYYYMMMMVVVV: Single precision array. DDDDSSSSYYYYMMMMVVVV: Double precision array. CCCCSSSSYYYYMMMMVVVV: Single precision complex array. ZZZZSSSSYYYYMMMMVVVV: Double precision complex array. Contains the 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) If _b_e_t_a is supplied as 0, _y need not be set on input. SSSSSSSSYYYYMMMMVVVV: Single precision. DDDDSSSSYYYYMMMMVVVV: Double precision. CCCCSSSSYYYYMMMMVVVV: Single precision complex. PPPPaaaaggggeeee 3333 SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) ZZZZSSSSYYYYMMMMVVVV: Double precision complex. 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) SSSSSSSSYYYYMMMMVVVV: Single precision array. DDDDSSSSYYYYMMMMVVVV: Double precision array. CCCCSSSSYYYYMMMMVVVV: Single precision complex array. ZZZZSSSSYYYYMMMMVVVV: Double precision complex array. Contains the 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 SSSSSSSSYYYYMMMMVVVV/DDDDSSSSYYYYMMMMVVVV is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS). CCCCSSSSYYYYMMMMVVVV/ZZZZSSSSYYYYMMMMVVVV 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)))) Array of dimensions (_m,_n) xxxx((((mmmm,,,,nnnn)))) Integer IIIINNNNTTTTEEEEGGGGEEEERRRR (IIIINNNNTTTTEEEEGGGGEEEERRRR****8888 for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision RRRREEEEAAAALLLL Double precision DDDDOOOOUUUUBBBBLLLLEEEE PPPPRRRREEEECCCCIIIISSSSIIIIOOOONNNN Single precision complex CCCCOOOOMMMMPPPPLLLLEEEEXXXX Double precision complex DDDDOOOOUUUUBBBBLLLLEEEE CCCCOOOOMMMMPPPPLLLLEEEEXXXX PPPPaaaaggggeeee 4444 SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) SSSSSSSSYYYYMMMMVVVV((((3333SSSS)))) C/C++: Array dimensioned _n xxxx[[[[_n]]]] Array of dimensions (_m,_n) xxxx[[[[mmmm****nnnn]]]] Integer iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision ffffllllooooaaaatttt Double precision ddddoooouuuubbbblllleeee Single precision complex ssssccccssssllll____ccccoooommmmpppplllleeeexxxx Double precision complex ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx C++ STL: Array dimensioned _n xxxx[[[[_n]]]] Array of dimensions (_m,_n) xxxx[[[[mmmm****nnnn]]]] 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), CCCCHHHHEEEEMMMMVVVV(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 
