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SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSTTTTRRRRMMMMMMMM, DDDDTTTTRRRRMMMMMMMM, CCCCTTTTRRRRMMMMMMMM, ZZZZTTTTRRRRMMMMMMMM - Multiplies a real or complex general matrix by a real or complex triangular matrix SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision Fortran: CCCCAAAALLLLLLLL SSSSTTTTRRRRMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _t_r_a_n_s_a,,,, _d_i_a_g,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ssssttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _a_l_p_h_a,,,, ffffllllooooaaaatttt *_a,,,, iiiinnnntttt _l_d_a,,,, ffffllllooooaaaatttt *_b,,,, iiiinnnntttt _l_d_b))));;;; Double precision Fortran: CCCCAAAALLLLLLLL DDDDTTTTRRRRMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _t_r_a_n_s_a,,,, _d_i_a_g,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ddddttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, iiiinnnntttt _m,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _a_l_p_h_a,,,, ddddoooouuuubbbblllleeee *_a,,,, iiiinnnntttt _l_d_a,,,, ddddoooouuuubbbblllleeee *_b,,,, iiiinnnntttt _l_d_b))));;;; Single precision complex Fortran: CCCCAAAALLLLLLLL CCCCTTTTRRRRMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _t_r_a_n_s_a,,,, _d_i_a_g,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, 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))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd ccccttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, 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))));;;; Double precision complex PPPPaaaaggggeeee 1111 SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) Fortran: CCCCAAAALLLLLLLL ZZZZTTTTRRRRMMMMMMMM ((((_s_i_d_e,,,, _u_p_l_o,,,, _t_r_a_n_s_a,,,, _d_i_a_g,,,, _m,,,, _n,,,, _a_l_p_h_a,,,, _a,,,, _l_d_a,,,, _b,,,, _l_d_b)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, 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))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____bbbbllllaaaassss....hhhh>>>> vvvvooooiiiidddd zzzzttttrrrrmmmmmmmm ((((cccchhhhaaaarrrr *_s_i_d_e,,,, cccchhhhaaaarrrr *_u_p_l_o,,,, cccchhhhaaaarrrr *_t_r_a_n_s_A,,,, cccchhhhaaaarrrr *_d_i_a_g,,,, 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))));;;; 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 SSSSTTTTRRRRMMMMMMMM and DDDDTTTTRRRRMMMMMMMM multiply a real general matrix by a real triangular matrix. CCCCTTTTRRRRMMMMMMMM and ZZZZTTTTRRRRMMMMMMMM multiply a complex general matrix by a complex triangular matrix. These routines perform one of the matrix-matrix operations: _B <- _a_l_p_h_a _o_p(_A)_B or _B <- _a_l_p_h_a _B _o_p(_A) PPPPaaaaggggeeee 2222 SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) where _a_l_p_h_a is a scalar; _B is an _m-by-_n matrix; _A is either a unit or nonunit upper or lower triangular matrix, and _o_p(_A) is one of the following: * _o_p(_A) = _A * _o_p(_A) = _A_T * _o_p(_A) = _A_H (CCCCTTTTRRRRMMMMMMMM and ZZZZTTTTRRRRMMMMMMMM only) where * _A_T is the transpose of _A * _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: _s_i_d_e Character. (input) Specifies whether _o_p(_A) multiplies _B from the left or right, as follows: _s_i_d_e = 'L' or 'l': _B <- _a_l_p_h_a _o_p(_A)_B _s_i_d_e = 'R' or 'r': _B <- _a_l_p_h_a _B _o_p(_A) For C/C++, a pointer to this character is passed. _u_p_l_o Character. (input) Specifies whether matrix _A is an upper or lower triangular matrix, as follows: _u_p_l_o = 'U' or 'u': _A is an upper triangular matrix. _u_p_l_o = 'L' or 'l': _A is a lower triangular matrix. For C/C++, a pointer to this character is passed. _t_r_a_n_s_a Character. (input) Specifies the form of _o_p(_A) to be used in the matrix multiplication, as follows: _t_r_a_n_s_a = 'N' or 'n': _o_p(_A) = _A _t_r_a_n_s_a = 'T' or 't', _o_p(_A) = _A_T _t_r_a_n_s_a = 'C' or 'c': _o_p(_A) = _A_T (SSSSTTTTRRRRMMMMMMMM, DDDDTTTTRRRRMMMMMMMM), PPPPaaaaggggeeee 3333 SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) or _o_p(_A) = _A_H (CCCCTTTTRRRRMMMMMMMM, ZZZZTTTTRRRRMMMMMMMM) For C/C++, a pointer to this character is passed. _d_i_a_g Character*1. (input) Specifies whether _A is unit triangular, as follows: _d_i_a_g = 'U' or 'u': _A is assumed to be unit triangular. _d_i_a_g = 'N' or 'n': _A is not assumed to be unit triangular. For C/C++, a pointer to this character is passed. _m Integer. (input) Specifies the number of rows in _B. _m must be >= 0. _n Integer. (input) Specifies the number of columns in _B. _n must be >= 0. _a_l_p_h_a Scalar factor. (input) SSSSTTTTRRRRMMMMMMMM: Single precision. DDDDTTTTRRRRMMMMMMMM: Double precision. CCCCTTTTRRRRMMMMMMMM: Single precision complex. ZZZZTTTTRRRRMMMMMMMM: Double precision complex. When _a_l_p_h_a is 0, _a is not referenced and _b need not be set before entry. 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). (input) SSSSTTTTRRRRMMMMMMMM: Single precision array. DDDDTTTTRRRRMMMMMMMM: Double precision array. CCCCTTTTRRRRMMMMMMMM: Single precision complex array. ZZZZTTTTRRRRMMMMMMMM: Double precision complex array. When _s_i_d_e = 'L' or 'l', _k is _m; when _s_i_d_e = 'R' or 'r', _k is _n. Contains the matrix _A. Before entry with _u_p_l_o = 'U' or 'u', the leading _k-by-_k upper triangular part of array _a must contain the upper triangular matrix. The strictly lower triangular part of _a is not referenced. Before entry with _u_p_l_o = 'L' or 'l', the leading _k-by-_k lower triangular part of array _a must contain the lower triangular matrix. The strictly upper triangular part of _a is not referenced. When _d_i_a_g = 'U' or 'u', the diagonal elements of _a are not referenced, but they are assumed to be unity. PPPPaaaaggggeeee 4444 SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) _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). When _s_i_d_e = 'R' or 'r', _l_d_a >= MMMMAAAAXXXX(1,_n). _b Array of dimension (_l_d_b,_n). (input and output) SSSSTTTTRRRRMMMMMMMM: Single precision array. DDDDTTTTRRRRMMMMMMMM: Double precision array. CCCCTTTTRRRRMMMMMMMM: Single precision complex array. ZZZZTTTTRRRRMMMMMMMM: Double precision complex array. Contains the matrix _B. Before entry, the leading _m-by-_n part of array _b must contain matrix _B. On exit, the transformed matrix overwrites array _b. _l_d_b Integer. (input) Specifies the first dimension of _b as declared in the calling program. _l_d_b >= 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++: PPPPaaaaggggeeee 5555 SSSSTTTTRRRRMMMMMMMM((((3333SSSS)))) SSSSTTTTRRRRMMMMMMMM((((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) 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 
