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Technical Reference: Base Operating System and Extensions , Volume 2
Solves system of
equations.
BLAS Library
(libblas.a)
SUBROUTINE STRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
REAL A(LDA,*), X(*)
SUBROUTINE DTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
DOUBLE PRECISION A(LDA,*), X(*)
SUBROUTINE CTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)
SUBROUTINE ZTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX*16 A(LDA,*), X(*)
The STRSV,
DTRSV, CTRSV, or ZTRSV subroutine solves one
of the systems of equations:
A * x = b
OR
A' * x =
b
where b and x are N
element vectors and A is an N by N unit, or
nonunit, upper or lower triangular matrix.
UPLO
 On entry, UPLO specifies whether the matrix 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.
Unchanged on exit.

TRANS
 On entry, TRANS specifies the equations to be solved as
follows:
 TRANS = 'N'
or 'n'
 A * x = b
 TRANS = 'T'
or 't'
 A' * x = b
 TRANS = 'C'
or 'c'
 A' * x = b
Unchanged on exit.

DIAG
 On entry, DIAG specifies whether or not 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.
Unchanged on exit.

N
 On entry, N specifies the order of the matrix
A; N must be at least 0; unchanged on
exit.

A
 An array of dimension ( LDA, N ); on entry
with UPLO = 'U' or 'u', the leading
N by N upper triangular part of the array A
must contain the upper triangular matrix and the strictly lower triangular
part of A is not referenced. On entry with UPLO =
'L' or 'l', the leading N by N lower
triangular part of the array A must contain the lower triangular
matrix and the strictly upper triangular part of A is not
referenced. When DIAG = 'U' or 'u', the
diagonal elements of A are not referenced, but are assumed to be
unity; unchanged on exit.

LDA
 On entry, LDA specifies the first dimension of A as
declared in the calling (sub) program; LDA must be at least
max( 1, N ); unchanged on exit.

X
 A vector of dimension at least (1 + (N1) *
abs(INCX) ); on entry, the incremented array X must
contain the N element righthand side vector b; on exit,
X is overwritten with the solution vector x.

INCX
 On entry, INCX specifies the increment for the elements of
X; INCX must not be 0; unchanged on
exit.

No test for singularity or
nearsingularity is included in this routine. Such tests must be
performed before calling this routine.
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