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SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSSSSSYYYYMMMMMMMM, DDDDSSSSYYYYMMMMMMMM, CCCCSSSSYYYYMMMMMMMM, ZZZZSSSSYYYYMMMMMMMM - Multiplies a real or complex general matrix by a real or complex symmetric matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSSSSSYYYYMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b,,,, _b_e_t_a,,,, _c,,,, _l_d_c)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ssssssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_a,,,, iiiinnnntttt _l_d_a,,,, ffffllllooooaaaatttt *_b,,,, iiiinnnntttt _l_d_b,,,, ffffllllooooaaaatttt _b_e_t_a,,,, ffffllllooooaaaatttt *_c,,,, iiiinnnntttt _l_d_c))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDSSSSYYYYMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b,,,, _b_e_t_a,,,, _c,,,, _l_d_c)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ddddssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_a,,,, iiiinnnntttt _l_d_a,,,, ddddoooouuuubbbblllleeee *_b,,,, iiiinnnntttt _l_d_b,,,, ddddoooouuuubbbblllleeee _b_e_t_a,,,, ddddoooouuuubbbblllleeee *_c,,,, iiiinnnntttt _l_d_c))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCSSSSYYYYMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b,,,, _b_e_t_a,,,, _c,,,, _l_d_c)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_b,,,, iiiinnnntttt _l_d_b,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_b_e_t_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_c,,,, iiiinnnntttt _l_d_c))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_b,,,, iiiinnnntttt _l_d_b,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_c,,,, iiiinnnntttt _l_d_c))));;;; Double precision complex PPPPaaaaggggeeee 1111 SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) Fortran: CCCCAAAALLLLLLLL ZZZZSSSSYYYYMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b,,,, _b_e_t_a,,,, _c,,,, _l_d_c)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_b,,,, iiiinnnntttt _l_d_b,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_b_e_t_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_c,,,, iiiinnnntttt _l_d_c))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyymmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_b,,,, iiiinnnntttt _l_d_b,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_b_e_t_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_c,,,, iiiinnnntttt _l_d_c))));;;; 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 SSSSSSSSYYYYMMMMMMMM and DDDDSSSSYYYYMMMMMMMM multiply a real general matrix by a real symmetric matrix. CCCCSSSSYYYYMMMMMMMM and ZZZZSSSSYYYYMMMMMMMM multiply a complex general matrix by a complex symmetric matrix. These routines perform one of the following matrix-matrix operations: _C <- _a_l_p_h_a _A_B + _b_e_t_a _C or _C <- _a_l_p_h_a _B_A + _b_e_t_a _C PPPPaaaaggggeeee 2222 SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) where _a_l_p_h_a and _b_e_t_a are scalars, _A is a symmetric matrix, and _B and _C are _m-by-_n matrices. 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: _s_i_d_e Character. (input) Specifies whether the symmetric matrix _A appears on the left or right in the operation, as follows: _s_i_d_e = 'L' or 'l': _C <- _a_l_p_h_a _A_B + _b_e_t_a _C _s_i_d_e = 'R' or 'r'; _C <- _a_l_p_h_a _B_A + _b_e_t_a _C For C/C++, a pointer to this character is passed. _u_p_l_o Character. (input) Specifies whether the upper or lower triangular part of the symmetric matrix _A is referenced, as follows: _u_p_l_o = 'U' or 'u': only the upper triangular part of the symmetric matrix is referenced. _u_p_l_o = 'L' or 'l': only the lower triangular part of the symmetric matrix is referenced. For C/C++, a pointer to this character is passed. _m Integer. (input) Specifies the number of rows in matrix _C. _m must be >= 0. _n Integer. (input) Specifies the number of columns in matrix _C. _n must be >= 0. _a_l_p_h_a Scalar factor. (input) SSSSSSSSYYYYMMMMMMMM: Single precision. DDDDSSSSYYYYMMMMMMMM: Double precision. CCCCSSSSYYYYMMMMMMMM: Single precision complex. ZZZZSSSSYYYYMMMMMMMM: 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,_k_a). (input) SSSSSSSSYYYYMMMMMMMM: Single precision array. DDDDSSSSYYYYMMMMMMMM: Double precision array. CCCCSSSSYYYYMMMMMMMM: Single precision complex array. ZZZZSSSSYYYYMMMMMMMM: Double precision complex array. When _s_i_d_e = 'L' or 'l', _k_a is _m; otherwise, it is _n. Contains the matrix _A. PPPPaaaaggggeeee 3333 SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) Before entry with _s_i_d_e = 'L' or 'l', the _m-by-_m part of array _a must contain the symmetric matrix _A, such that: * If _u_p_l_o = 'U' or 'u', the leading _m-by-_m 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. * If _u_p_l_o = 'L' or 'l', the leading _m-by-_m 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. Before entry with _s_i_d_e = 'R' or 'r', the _n-by-_n part of array _a must contain the symmetric matrix _A, such that: * If _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. * If _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. When _s_i_d_e = 'L' or 'l', _l_d_a >= MMMMAAAAXXXX(1,_m); otherwise, _l_d_a >= MMMMAAAAXXXX(1,_n). _b Array of dimension (_l_d_b,_n). (input) SSSSSSSSYYYYMMMMMMMM: Single precision array. DDDDSSSSYYYYMMMMMMMM: Double precision array. CCCCSSSSYYYYMMMMMMMM: Single precision complex array. ZZZZSSSSYYYYMMMMMMMM: Double precision complex array. Contains the matrix _B. Before entry, the leading _m-by-_n part of array _b must contain matrix _B. _l_d_b Integer. (input) Specifies the first dimension of _b as declared in the calling program. _l_d_b >= MMMMAAAAXXXX(1,_m). _b_e_t_a Scalar factor. (input) SSSSSSSSYYYYMMMMMMMM: Single precision. DDDDSSSSYYYYMMMMMMMM: Double precision. CCCCSSSSYYYYMMMMMMMM: Single precision complex. ZZZZSSSSYYYYMMMMMMMM: Double precision complex. When _b_e_t_a is supplied as 0, _c need not be set on input. PPPPaaaaggggeeee 4444 SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) For C/C++, a pointer to this scalar is passed when beta is complex; otherwise, beta is passed by value. _c Array of dimension (_l_d_c,_n). (input and output) SSSSSSSSYYYYMMMMMMMM: Single precision array. DDDDSSSSYYYYMMMMMMMM: Double precision array. CCCCSSSSYYYYMMMMMMMM: Single precision complex array. ZZZZSSSSYYYYMMMMMMMM: Double precision complex array. Contains the matrix _C. Before entry, the leading _m-by-_n part of array _c must contain matrix _C, except when _b_e_t_a is 0; in which case, _c need not be set. On exit, the _m-by-_n updated matrix overwrites array _c. _l_d_c Integer. (input) Specifies the first dimension of _c as declared in the calling program. _l_d_c >= MMMMAAAAXXXX(1,_m). NNNNOOOOTTTTEEEESSSS These routines are Level 3 Basic Linear Algebra Subprograms (Level 3 BLAS). 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)))) 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]]]] PPPPaaaaggggeeee 5555 SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) SSSSSSSSYYYYMMMMMMMM((((3333SSSS)))) Array of dimensions (_m,_n) xxxx[[[[mmmm****nnnn]]]] Character *Cchar 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]]]] 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____BBBBLLLLAAAASSSS3333(3S) CCCCHHHHEEEEMMMMMMMM(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 6666 
