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SSSSSSSSYYYYRRRR((((3333SSSS)))) SSSSSSSSYYYYRRRR((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSSSSSYYYYRRRR, DDDDSSSSYYYYRRRR, CCCCSSSSYYYYRRRR, ZZZZSSSSYYYYRRRR - Performs symmetric rank 1 update of a real or complex symmetric matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSSSSSYYYYRRRR ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _x,,,, _i_n_c_x,,,, _a,,,, _l_d_a)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ssssssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _i_n_c_x,,,, ffffllllooooaaaatttt *_a,,,, iiiinnnntttt _l_d_a))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDSSSSYYYYRRRR ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _x,,,, _i_n_c_x,,,, _a,,,, _l_d_a)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ddddssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _i_n_c_x,,,, ddddoooouuuubbbblllleeee *_a,,,, iiiinnnntttt _l_d_a))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCSSSSYYYYRRRR ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _x,,,, _i_n_c_x,,,, _a,,,, _l_d_a)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _i_n_c_x,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,, iiiinnnntttt _i_n_c_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a,,,, iiiinnnntttt _l_d_a))));;;; Double precision complex Fortran: CCCCAAAALLLLLLLL ZZZZSSSSYYYYRRRR ((((_u_p_l_o,,,, _n,,,, _a_l_p_h_a,,,, _x,,,, _i_n_c_x,,,, _a,,,, _l_d_a)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _i_n_c_x,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a))));;;; PPPPaaaaggggeeee 1111 SSSSSSSSYYYYRRRR((((3333SSSS)))) SSSSSSSSYYYYRRRR((((3333SSSS)))) C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzssssyyyyrrrr ((((cccchhhhaaaarrrr *_u_p_l_o,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_x,,,, iiiinnnntttt _i_n_c_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a,,,, iiiinnnntttt _l_d_a))));;;; 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 symmetric rank 1 operation: _A <- _a_l_p_h_a _x_x_T + _A where _x_T is the transpose of _x, _a_l_p_h_a is a real or complex scalar, _x is an _n-element vector, 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 array _a is referenced, as follows: _u_p_l_o= 'U' or 'u': only the upper triangular part of _a is referenced. _u_p_l_o= 'L' or 'l': only the lower triangular part of _a is referenced. For C/C++, a pointer to this character is passed. _n Integer. (input) Specifies the order of matrix _A. _n >= 0. PPPPaaaaggggeeee 2222 SSSSSSSSYYYYRRRR((((3333SSSS)))) SSSSSSSSYYYYRRRR((((3333SSSS)))) _a_l_p_h_a Scalar alpha. (input) SSSSSSSSYYYYRRRR: Single precision. DDDDSSSSYYYYRRRR: Double precision. CCCCSSSSYYYYRRRR: Single precision complex. ZZZZSSSSYYYYRRRR: Double precision complex. For C/C++, a pointer to this scalar is passed when alpha is complex; otherwise, alpha is passed by value. _x Array of dimension 1+(_n-1) * |_i_n_c_x|. (input) SSSSSSSSYYYYRRRR: Single precision array. DDDDSSSSYYYYRRRR: Double precision array. CCCCSSSSYYYYRRRR: Single precision complex array. ZZZZSSSSYYYYRRRR: 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. _a Array of dimension (_l_d_a,_n). (input and output) SSSSSSSSYYYYRRRR: Single precision array. DDDDSSSSYYYYRRRR: Double precision array. CCCCSSSSYYYYRRRR: Single precision complex array. ZZZZSSSSYYYYRRRR: 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. On exit, the upper triangular part of the updated matrix overwrites the upper triangular part of array _a. 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. On exit, the lower triangular part of the updated matrix overwrites the lower triangular part of array _a. _l_d_a Integer. (input) Specifies the first dimension of _a as declared in the calling program. _l_d_a >= MMMMAAAAXXXX(1,_n). NNNNOOOOTTTTEEEESSSS SSSSSSSSYYYYRRRR/DDDDSSSSYYYYRRRR is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS). CCCCSSSSYYYYRRRR/ZZZZSSSSYYYYRRRR is an extension to Level 2 BLAS. When working backward (_i_n_c_x < 0), each routine starts at the end of the vector and moves backward, as follows: PPPPaaaaggggeeee 3333 SSSSSSSSYYYYRRRR((((3333SSSS)))) SSSSSSSSYYYYRRRR((((3333SSSS)))) _x(1-_i_n_c_x * (_n-1)), _x(1-_i_n_c_x * (_n-2)), ..., _x(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)))) 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]]]] 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]]]] PPPPaaaaggggeeee 4444 SSSSSSSSYYYYRRRR((((3333SSSS)))) SSSSSSSSYYYYRRRR((((3333SSSS)))) 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), CCCCHHHHEEEERRRR(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 
