Name

strsv, dtrsv, ctrsv, ztrsv − Solver of a system of linear equations with a triangular matrix

FORMAT

{S,D,C,Z}TRSV (uplo, trans, diag, n, a, lda, x, incx)

Arguments

uplocharacter∗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. 

transcharacter∗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. 

diagcharacter∗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. 

ninteger∗4
On entry, the order of the matrix A; n >= 0.
On exit, n is unchanged. 

areal∗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. 

ldainteger∗4
On entry, the first dimension of array A; lda >= MAX(1,n).
On exit, lda is unchanged. 

xreal∗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. 

incxinteger∗4
On entry, the increment for the elements of X; incx must not equal zero.
On exit, incx is unchanged. 

Description

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. 

Example

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.