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STRSM(3S)							     STRSM(3S)

NAME
     STRSM, DTRSM, CTRSM, ZTRSM - Solves a real or complex triangular system
     of equations with multiple right-hand sides

SYNOPSIS
     Single precision

	  Fortran:

	       CALL STRSM (side, uplo, transa, diag, m, n, alpha, a, lda, b,
	       ldb)

	  C/C++:
	       #include <scsl_blas.h>
	       void strsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, float alpha, float *a, int lda, float *b, int
	       ldb);

     Double precision

	  Fortran:
	       CALL DTRSM (side, uplo, transa, diag, m, n, alpha, a, lda, b,
	       ldb)

	  C/C++:
	       #include <scsl_blas.h>
	       void dtrsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, double alpha, double *a, int lda, double *b, int
	       ldb);

     Single precision complex

	  Fortran:
	       CALL CTRSM (side, uplo, transa, diag, m, n, alpha, a, lda, b,
	       ldb)

	  C/C++:
	       #include <scsl_blas.h>
	       void ctrsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, scsl_complex *alpha, scsl_complex *a, int lda,
	       scsl_complex *b, int ldb);

	  C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void ctrsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, complex<float> *alpha, complex<float> *a, int
	       lda, complex<float> *b, int ldb);

     Double precision complex

									Page 1

STRSM(3S)							     STRSM(3S)

	  Fortran:
	       CALL ZTRSM (side, uplo, transa, diag, m, n, alpha, a, lda, b,
	       ldb)

	  C/C++:
	       #include <scsl_blas.h>
	       void ztrsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, scsl_zomplex *alpha, scsl_zomplex *a, int lda,
	       scsl_zomplex *b, int ldb);

	  C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void ztrsm (char *side, char *uplo, char *transA, char *diag,
	       int m, int n, complex<double> *alpha, complex<double> *a, int
	       lda, complex<double> *b, int ldb);

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, 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 -lscs_i8 option or the -lscs_i8_mp 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 int become long long and the <scsl_blas_i8.h> header
     file should be included.

DESCRIPTION
     STRSM and DTRSM solve a real triangular syste m of equations with
     multiple right-hand sides.

     CTRSM and ZTRSM solve a complex triangular system of equations with
     multiple right-hand sides.

     These routines solve one of the following matrix equations, using the
     operation associated with each:

	  op(A) X = alpha B

	  B <- alpha op(A-1)B

	  or

									Page 2

STRSM(3S)							     STRSM(3S)

	  X op(A) = alpha B

	  B <- alpha B op(A-1)

     where

     *	 alpha is a scalar

     *	 X and B are m-by-n matrices

     *	 A is either a unit or nonunit upper or lower triangular matrix

     *	 A-1 is the inverse of A

     *	 op(A) is one of the following:

	      op(A) = A

	      op(A) = AT

	      op(A) = AH (CTRSM	 and ZTRSM only)

     where AT is the transpose of A, and AH 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:

     side      Character.  (input)
	       Specifies whether op(A) appears on the left or right of X, as
	       follows:

	       side = 'L' or 'l':  op(A)*X = alpha*B

	       side = 'R' or 'r':  X*op(A) = alpha*B

	       For C/C++, a pointer to this character is passed.

     uplo      Character.  (input)
	       Specifies whether matrix A is an upper or lower triangular
	       matrix, as follows:

	       uplo = 'U' or 'u': A is an upper triangular matrix.
	       uplo = 'L' or 'l': A is a lower triangular matrix.

	       For C/C++, a pointer to this character is passed.

     transa    Character*1.  (input)
	       Specifies the form of op(A) to be used in the matrix
	       multiplication, as follows:

									Page 3

STRSM(3S)							     STRSM(3S)

	       transa = 'N' or 'n':  op(A) = A

	       transa = 'T' or 't':  op(A) = AT

	       transa = 'C' or 'c':  op(A) = AT (STRSM, DTRSM),

	       or op(A) = AH (CTRSM, ZTRSM)

	       For C/C++, a pointer to this character is passed.

     diag      Character.  (input)
	       Specifies whether A is unit triangular, as follows:

	       diag = 'U' or 'u': A is assumed to be unit triangular.
	       diag = '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.

     alpha     Scalar factor.  (input)
	       STRSM: Single precision.
	       DTRSM: Double precision.
	       CTRSM: Single precision complex.
	       ZTRSM: Double precision complex.
	       When alpha 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 (lda,k).  (input)
	       STRSM: Single precision array.
	       DTRSM: Double precision array.
	       CTRSM: Single precision complex array.
	       ZTRSM: Double precision complex array.
	       When side = 'L' or 'l', k is m; when side = 'R' or 'r', it is
	       n.
	       Contains the matrix A.

	       Before entry with uplo = '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 uplo = '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

									Page 4

STRSM(3S)							     STRSM(3S)

	       referenced.

	       When diag = 'U' or 'u', the diagonal elements of a are not
	       referenced, but they are assumed to be unity.

     lda       Integer.	 (input)
	       Specifies the first dimension of a as declared in the calling
	       program.

	       When side = 'L' or 'l', lda >= MAX(1,m).

	       When side = 'R' or 'r', lda >= MAX(1,n).

     b	       Array of dimension (ldb,n).  (input)
	       STRSM: Real array.
	       DTRSM: Double precision array.
	       CTRSM: Complex array.
	       ZTRSM: Double complex array.
	       Contains the matrix B.

	       Before entry, the leading m-by-n part of array b must contain
	       the right-hand side matrix B.  On exit, the solution matrix X
	       overwrites array b.

     ldb       Integer.	 (input)
	       Specifies the first dimension of b as declared in the calling
	       program.	 ldb >= MAX(1,m).

NOTES
     These routines are Level 3 Basic Linear Algebra Subprograms (Level 3
     BLAS).

   Data Types
     The following data types are described in this documentation:

	  Term Used			Data type

     Fortran:

	  Array dimensioned n		x(n)

	  Array of dimensions (m,n)	x(m,n)

	  Character			CHARACTER

	  Integer			INTEGER (INTEGER*8 for -lscs_i8[_mp])

	  Single precision		REAL

	  Double precision		DOUBLE PRECISION

									Page 5

STRSM(3S)							     STRSM(3S)

	  Single precision complex	COMPLEX

	  Double precision complex	DOUBLE COMPLEX

     C/C++:

	  Array dimensioned n		x[n]

	  Array of dimensions (m,n)	x[m*n]

	  Character			char

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	scsl_complex

	  Double precision complex	scsl_zomplex

     C++ STL:

	  Array dimensioned n		x[n]

	  Array of dimensions (m,n)	x[m*n]

	  Character			char

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	complex<float>

	  Double precision complex	complex<double>

     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., x[n][m] in C/C++ versus x(m,n) 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.

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS3(3S)

									Page 6

STRSM(3S)							     STRSM(3S)

     INTRO_CBLAS(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.

									Page 7

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