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SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSGGGGEEEEMMMMVVVV, DDDDGGGGEEEEMMMMVVVV, CCCCGGGGEEEEMMMMVVVV, ZZZZGGGGEEEEMMMMVVVV - Multiplies a real or complex vector by a real or complex general matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSGGGGEEEEMMMMVVVV ((((_t_r_a_n_s,,,, _m,,,, _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 ssssggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_a,,,, iiiinnnntttt _l_d_a,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _i_n_c_x,,,, ffffllllooooaaaatttt _b_e_t_a,,,, ffffllllooooaaaatttt *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDGGGGEEEEMMMMVVVV ((((_t_r_a_n_s,,,, _m,,,, _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 ddddggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_a,,,, iiiinnnntttt _l_d_a,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _i_n_c_x,,,, ddddoooouuuubbbblllleeee _b_e_t_a,,,, ddddoooouuuubbbblllleeee *_y,,,, iiiinnnntttt _i_n_c_y))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCGGGGEEEEMMMMVVVV ((((_t_r_a_n_s,,,, _m,,,, _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 ccccggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, 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 ccccggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, 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 ZZZZGGGGEEEEMMMMVVVV ((((_t_r_a_n_s,,,, _m,,,, _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 zzzzggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a_l_p_h_a,,,, PPPPaaaaggggeeee 1111 SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_a,,,, iiiinnnntttt _l_d_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _i_n_c_x,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_b_e_t_a,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _i_n_c_y))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzggggeeeemmmmvvvv ((((cccchhhhaaaarrrr *_t_r_a_n_s,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a_l_p_h_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_a,,,, iiiinnnntttt _l_d_a,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_x,,,, iiiinnnntttt _i_n_c_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 SSSSGGGGEEEEMMMMVVVV and DDDDGGGGEEEEMMMMVVVV multiply a real vector by a real general matrix. CCCCGGGGEEEEMMMMVVVV and ZZZZGGGGEEEEMMMMVVVV multiply a complex vector by a complex general matrix. These routines perform one of the following matrix-vector operations: _y <- _a_l_p_h_a _A_x + _b_e_t_a _y _y <- _a_l_p_h_a _A_T_x + _b_e_t_a _y _y <- _a_l_p_h_a _A_H_x + _b_e_t_a _y where * _a_l_p_h_a and _b_e_t_a are scalars, * _x and _y are vectors * _A is an _m-by-_n general matrix * _A_T is the transpose of _A PPPPaaaaggggeeee 2222 SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) * _A_H is the conjugate transpose of _A 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: _t_r_a_n_s Character. (input) Specifies the operation to be performed: _t_r_a_n_s = 'N' or 'n': _y <- _a_l_p_h_a _A_x + _b_e_t_a _y _t_r_a_n_s = 'T' or 't': _y <- _a_l_p_h_a _A_T_x + _b_e_t_a _y _t_r_a_n_s = 'C' or 'c': _y <- _a_l_p_h_a _A_T_x + _b_e_t_a _y (SSSSGGGGEEEEMMMMVVVV, DDDDGGGGEEEEMMMMVVVV), or _y <- _a_l_p_h_a _A_H_x + _b_e_t_a _y (CCCCGGGGEEEEMMMMVVVV, ZZZZGGGGEEEEMMMMVVVV) For C/C++, a pointer to this character is passed. _m Integer. (input) Specifies the number of rows in matrix _A. _m >= 0. _n Integer. (input) Specifies the number of columns in matrix _A. _n >= 0. _a_l_p_h_a Scalar alpha. (input) SSSSGGGGEEEEMMMMVVVV: Single precision. DDDDGGGGEEEEMMMMVVVV: Double precision. CCCCGGGGEEEEMMMMVVVV: Single precision complex. ZZZZGGGGEEEEMMMMVVVV: 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) SSSSGGGGEEEEMMMMVVVV: Single precision array. DDDDGGGGEEEEMMMMVVVV: Double precision array. CCCCGGGGEEEEMMMMVVVV: Single precision complex array. ZZZZGGGGEEEEMMMMVVVV: Double precision complex array. Before entry, the leading _m-by-_n part of array _a must contain the matrix of coefficients. _l_d_a Integer. (input) Specifies the first dimension of _a as declared in the calling program. _l_d_a >= MMMMAAAAXXXX(1,_m). _x Array of dimension 1+(_k_x-1) * |_i_n_c_x|. (input) SSSSGGGGEEEEMMMMVVVV: Single precision array. DDDDGGGGEEEEMMMMVVVV: Double precision array. CCCCGGGGEEEEMMMMVVVV: Single precision complex array. ZZZZGGGGEEEEMMMMVVVV: Double precision complex array. PPPPaaaaggggeeee 3333 SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) Contains the vector _x. When _t_r_a_n_s = 'N' or 'n', _k_x is _n; otherwise, it is _m. _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) SSSSGGGGEEEEMMMMVVVV: Single precision. DDDDGGGGEEEEMMMMVVVV: Double precision. CCCCGGGGEEEEMMMMVVVV: Single precision complex. ZZZZGGGGEEEEMMMMVVVV: Double precision complex. When _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+(_k_y-1) * |_i_n_c_y|. (input and output) SSSSGGGGEEEEMMMMVVVV: Single precision array. DDDDGGGGEEEEMMMMVVVV: Double precision array. CCCCGGGGEEEEMMMMVVVV: Single precision complex array. ZZZZGGGGEEEEMMMMVVVV: Double precision complex array. Contains the vector _y. When _t_r_a_n_s = 'N' or 'n', _k_y is _m; otherwise, it is _n. When _b_e_t_a is supplied as 0, _y need not be set on input. 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 SSSSGGGGEEEEMMMMVVVV, DDDDGGGGEEEEMMMMVVVV and CCCCGGGGEEEEMMMMVVVV, ZZZZGGGGEEEEMMMMVVVV are Level 2 Basic Linear Algebra Subprograms (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)))) PPPPaaaaggggeeee 4444 SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) 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]]]] 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>>>> PPPPaaaaggggeeee 5555 SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) SSSSGGGGEEEEMMMMVVVV((((3333SSSS)))) 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) 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 
