{S,D,C,Z}TRSV (uplo, trans, diag, n, a, lda, x, incx)
uplo character*1 On entry, specifies whether the matrix A is an upper- or lower-triangular matrix: If uplo = 'U' or 'u', A is an upper-triangular matrix. If uplo = 'L' or On exit, uplo is unchanged. trans character*1 On entry, specifies the system to be solved: If trans = 'N' or 'n', the system is Ax = b. If trans = 'T' or 't', the system is transp(A)*x = b. If trans = 'C' or 'c', the system is conjug_transp(A)*x = b. On exit, trans is unchanged. diag character*1 On entry, specifies whether the matrix A is unit- triangular: If diag = 'U' or 'u', A is a unit-triangular matrix. If diag = 'N' or 'n', A is not a unit-triangular matrix. On exit, diag is unchanged. n integer*4 On entry, the order of the matrix A; n >= 0. On exit, n is unchanged. a real*4 | real*8 | complex*8 | complex*16 On entry, a two-dimensional array with dimensions lda by n. When uplo specifies the upper portion of the matrix, the leading n by n part of the array contains the upper-triangular part of the matrix, and the lower-triangular part of array A is not referenced. When uplo specifies the lower portion of the matrix, the leading n by n part of the array contains the lower-triangular part of the matrix, and the upper-triangular part of array A is not referenced. If diag is equal to 'U' or 'u', the diagonal elements of A are also not referenced, but are assumed to be unity. On exit, a is unchanged. lda integer*4 On entry, the first dimension of array A; lda >= MAX(1,n). On exit, lda is unchanged. x real*4 | real*8 | complex*8 | complex*16 On entry, a one-dimensional array X of length at least (1+(n-1)*|incx|). Array X contains the vector b. On exit, x is overwritten with the solution vector x. incx integer*4 On entry, the increment for the elements of X; incx must not equal zero. On exit, incx is unchanged.
The _TRSV subprograms solve one of the following systems of linear equations for x: Ax = b or transp(A)*x = b . In addition to these operations, the CTRSV and ZTRSV subprograms solve the following systems of linear equation: conjug_transp(A)*x = b . b and x are vectors with n elements and A is an n by n, unit or non-unit, upper- or lower-triangular matrix. The _TRSV routines do not perform checks for singularity or near singularity of the triangular matrix. The requirements for such a test depend on the application. If necessary, perform the test in your application program before calling this routine.
REAL*8 A(100,40), X(40) INCX = 1 N = 40 LDA = 100 CALL DTRSV('L','N','U',N,A,LDA,X,INCX) This FORTRAN code solves the system Ax=b where A is a lower-triangular matrix of order 40, with a unit diagonal. The right hand side b is originally stored in the vector x.