#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int ctptri_(char *uplo, char *diag, integer *n, complex *ap,
integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CTPTRI computes the inverse of a complex upper or lower triangular
matrix A stored in packed format.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangular matrix A, stored
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
Further Details
===============
A triangular matrix A can be transferred to packed storage using one
of the following program segments:
UPLO = 'U': UPLO = 'L':
JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer i__1, i__2;
complex q__1;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer j;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *,
complex *, complex *, integer *);
static logical upper;
static integer jc, jj;
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer jclast;
static logical nounit;
static complex ajj;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTPTRI", &i__1);
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
if (upper) {
jj = 0;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
jj += *info;
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
jj = jj + *n - *info + 1;
/* L20: */
}
}
*info = 0;
}
if (upper) {
/* Compute inverse of upper triangular matrix. */
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (nounit) {
i__2 = jc + j - 1;
c_div(&q__1, &c_b1, &ap[jc + j - 1]);
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = jc + j - 1;
q__1.r = -ap[i__2].r, q__1.i = -ap[i__2].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = 0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
ctpmv_("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], &
c__1);
i__2 = j - 1;
cscal_(&i__2, &ajj, &ap[jc], &c__1);
jc += j;
/* L30: */
}
} else {
/* Compute inverse of lower triangular matrix. */
jc = *n * (*n + 1) / 2;
for (j = *n; j >= 1; --j) {
if (nounit) {
i__1 = jc;
c_div(&q__1, &c_b1, &ap[jc]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = jc;
q__1.r = -ap[i__1].r, q__1.i = -ap[i__1].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = 0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
ctpmv_("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[
jc + 1], &c__1);
i__1 = *n - j;
cscal_(&i__1, &ajj, &ap[jc + 1], &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of CTPTRI */
} /* ctptri_ */