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SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSSSSSYYYYRRRR2222KKKK, DDDDSSSSYYYYRRRR2222KKKK, CCCCSSSSYYYYRRRR2222KKKK, ZZZZSSSSYYYYRRRR2222KKKK - Performs symmetric rank 2_k update of a real or complex symmetric matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSSSSSYYYYRRRR2222KKKK ((((_u_p_l_o,,,, _t_r_a_n_s,,,, _n,,,, _k,,,, _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 ssssssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, 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 DDDDSSSSYYYYRRRR2222KKKK ((((_u_p_l_o,,,, _t_r_a_n_s,,,, _n,,,, _k,,,, _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 ddddssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, 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 CCCCSSSSYYYYRRRR2222KKKK ((((_u_p_l_o,,,, _t_r_a_n_s,,,, _n,,,, _k,,,, _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 ccccssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, 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>>>> vvvvooooiiiidddd ccccssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_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 Fortran: CCCCAAAALLLLLLLL ZZZZSSSSYYYYRRRR2222KKKK ((((_u_p_l_o,,,, _t_r_a_n_s,,,, _n,,,, _k,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b,,,, _b_e_t_a,,,, _c,,,, _l_d_c)))) PPPPaaaaggggeeee 1111 SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, 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>>>> vvvvooooiiiidddd zzzzssssyyyyrrrr2222kkkk ((((cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _n,,,, iiiinnnntttt _k,,,, 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 SSSSSSSSYYYYRRRR2222KKKK and DDDDSSSSYYYYRRRR2222KKKK performs a symmetric rank 2_k update of a real symmetric matrix. CCCCSSSSYYYYRRRR2222KKKK and ZZZZSSSSYYYYRRRR2222KKKK performs a symmetric rank 2_k update of a complex symmetric matrix. These routines perform one of the following symmetric rank 2_k operations: _C <- _a_l_p_h_a _A_B_T + _a_l_p_h_a _B_A_T + _b_e_t_a _C or _C <- _a_l_p_h_a _A_T_B + _a_l_p_h_a _B_T_A + _b_e_t_a _C where * _a_l_p_h_a and _b_e_t_a are scalars PPPPaaaaggggeeee 2222 SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) * _C is an _n-by-_n symmetric matrix * _A and _B are _n-by-_k matrices in the first operation listed previously and _k-by-_n matrices in the second * _A_T and _B_T are transposes of _A and _B, respectively 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 array _c is referenced, as follows: _u_p_l_o = 'U' or 'u': only the upper triangular part of _c is referenced. _u_p_l_o = 'L' or 'l': only the lower triangular part of _c is referenced. For C/C++, a pointer to this character is passed. _t_r_a_n_s Character. (input) Specifies the operation to be performed, as follows: _t_r_a_n_s = 'N' or 'n': _C <- _a_l_p_h_a _A_B_T + _a_l_p_h_a _B_A_T + _b_e_t_a _C _t_r_a_n_s = 'T' or 't': _C <- _a_l_p_h_a _A_T_B + _a_l_p_h_a _B_T_A + _b_e_t_a _C For C/C++, a pointer to this character is passed. _n Integer. (input) Specifies the order of matrix _C. _n must be >= 0. _k Integer. (input) On entry with _t_r_a_n_s = 'N' or 'n', _k specifies the number of columns of matrices _A and _B. On entry with _t_r_a_n_s = 'T' or 't', _k specifies the number of rows of matrices _A and _B. _k must be >= 0. _a_l_p_h_a Scalar factor. (input) SSSSSSSSYYYYRRRR2222KKKK: Single precision. DDDDSSSSYYYYRRRR2222KKKK: Double precision. CCCCSSSSYYYYRRRR2222KKKK: Single precision complex. ZZZZSSSSYYYYRRRR2222KKKK: Double precision complex. PPPPaaaaggggeeee 3333 SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) 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) SSSSSSSSYYYYRRRR2222KKKK: Single precision array. DDDDSSSSYYYYRRRR2222KKKK: Double precision array. CCCCSSSSYYYYRRRR2222KKKK: Single precision complex array. ZZZZSSSSYYYYRRRR2222KKKK: Double precision complex array. When _t_r_a_n_s = 'N' or 'n', _k_a is _k; otherwise, it is _n. Contains the matrix _A. Before entry with _t_r_a_n_s = 'N' or 'n', the leading _n-by-_k part of array _a must contain matrix _A; otherwise, the leading _k-by-_n part of array _a must contain matrix _A. _l_d_a Integer. (input) Specifies the first dimension of _a as declared in the calling program. If _t_r_a_n_s = 'N' or 'n', _l_d_a >= MMMMAAAAXXXX(1,_n); otherwise, _l_d_a >= MMMMAAAAXXXX(1,_k). _b Array of dimension (_l_d_b,_k_b). (input) SSSSSSSSYYYYRRRR2222KKKK: Single precision array. DDDDSSSSYYYYRRRR2222KKKK: Double precision array. CCCCSSSSYYYYRRRR2222KKKK: Single precision complex array. ZZZZSSSSYYYYRRRR2222KKKK: Double precision complex array. When _t_r_a_n_s = 'N' or 'n', _k_b is _k; otherwise, it is _n. Contains the matrix _B. Before entry with _t_r_a_n_s = 'N' or 'n', the leading _n-by-_k part of array _b must contain matrix _B; otherwise, the leading _k-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. If _t_r_a_n_s = 'N' or 'n', _l_d_b >= MMMMAAAAXXXX(1,_n); otherwise, _l_d_b >= MMMMAAAAXXXX(1,_k). _b_e_t_a Scalar factor. (input) SSSSSSSSYYYYRRRR2222KKKK: Single precision. DDDDSSSSYYYYRRRR2222KKKK: Double precision. CCCCSSSSYYYYRRRR2222KKKK: Single precision complex. ZZZZSSSSYYYYRRRR2222KKKK: Double precision complex. 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) SSSSSSSSYYYYRRRR2222KKKK: Single precision array. DDDDSSSSYYYYRRRR2222KKKK: Double precision array. CCCCSSSSYYYYRRRR2222KKKK: Single precision complex array. ZZZZSSSSYYYYRRRR2222KKKK: Double precision complex array. PPPPaaaaggggeeee 4444 SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) Contains the matrix _C. Before entry with _u_p_l_o = 'U' or 'u', the leading _n-by-_n upper triangular part of array _c must contain the upper triangular part of the symmetric matrix. The strictly lower triangular part of _c is not referenced. On exit, the upper triangular part of the updated matrix overwrites the upper triangular part of array _c. Before entry with _u_p_l_o = 'L' or 'l', the leading _n-by-_n lower triangular part of array _c must contain the lower triangular part of the symmetric matrix. The strictly upper triangular part of _c is not referenced. On exit, the lower triangular part of the updated matrix overwrites the lower triangular part of array _c. _l_d_c Integer. (input) Specifies the first dimension of _c as declared in the calling program. _l_d_c >= MMMMAAAAXXXX(1,_n). 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++: PPPPaaaaggggeeee 5555 SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) SSSSSSSSYYYYRRRR2222KKKK((((3333SSSS)))) 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 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), CCCCHHHHEEEERRRR2222KKKK(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 
