#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int cgtts2_(integer *itrans, integer *n, integer *nrhs,
complex *dl, complex *d__, complex *du, complex *du2, integer *ipiv,
complex *b, integer *ldb)
{
/* -- LAPACK auxiliary routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
CGTTS2 solves one of the systems of equations
A * X = B, A**T * X = B, or A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by CGTTRF.
Arguments
=========
ITRANS (input) INTEGER
Specifies the form of the system of equations.
= 0: A * X = B (No transpose)
= 1: A**T * X = B (Transpose)
= 2: A**H * X = B (Conjugate transpose)
N (input) INTEGER
The order of the matrix A.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
DL (input) COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.
D (input) COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DU (input) COMPLEX array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.
DU2 (input) COMPLEX array, dimension (N-2)
The (n-2) elements of the second super-diagonal of U.
IPIV (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.
B (input/output) COMPLEX array, dimension (LDB,NRHS)
On entry, the matrix of right hand side vectors B.
On exit, B is overwritten by the solution vectors X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
=====================================================================
Quick return if possible
Parameter adjustments */
/* System generated locals */
integer b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8;
complex q__1, q__2, q__3, q__4, q__5, q__6, q__7, q__8;
/* Builtin functions */
void c_div(complex *, complex *, complex *), r_cnjg(complex *, complex *);
/* Local variables */
static integer i__, j;
static complex temp;
--dl;
--d__;
--du;
--du2;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
if (*n == 0 || *nrhs == 0) {
return 0;
}
if (*itrans == 0) {
/* Solve A*X = B using the LU factorization of A,
overwriting each right hand side vector with its solution. */
if (*nrhs <= 1) {
j = 1;
L10:
/* Solve L*x = b. */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (ipiv[i__] == i__) {
i__2 = i__ + 1 + j * b_dim1;
i__3 = i__ + 1 + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__2.r = dl[i__4].r * b[i__5].r - dl[i__4].i * b[i__5].i,
q__2.i = dl[i__4].r * b[i__5].i + dl[i__4].i * b[
i__5].r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i - q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
} else {
i__2 = i__ + j * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
i__2 = i__ + j * b_dim1;
i__3 = i__ + 1 + j * b_dim1;
b[i__2].r = b[i__3].r, b[i__2].i = b[i__3].i;
i__2 = i__ + 1 + j * b_dim1;
i__3 = i__;
i__4 = i__ + j * b_dim1;
q__2.r = dl[i__3].r * b[i__4].r - dl[i__3].i * b[i__4].i,
q__2.i = dl[i__3].r * b[i__4].i + dl[i__3].i * b[
i__4].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
/* L20: */
}
/* Solve U*x = b. */
i__1 = *n + j * b_dim1;
c_div(&q__1, &b[*n + j * b_dim1], &d__[*n]);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
if (*n > 1) {
i__1 = *n - 1 + j * b_dim1;
i__2 = *n - 1 + j * b_dim1;
i__3 = *n - 1;
i__4 = *n + j * b_dim1;
q__3.r = du[i__3].r * b[i__4].r - du[i__3].i * b[i__4].i,
q__3.i = du[i__3].r * b[i__4].i + du[i__3].i * b[i__4]
.r;
q__2.r = b[i__2].r - q__3.r, q__2.i = b[i__2].i - q__3.i;
c_div(&q__1, &q__2, &d__[*n - 1]);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
}
for (i__ = *n - 2; i__ >= 1; --i__) {
i__1 = i__ + j * b_dim1;
i__2 = i__ + j * b_dim1;
i__3 = i__;
i__4 = i__ + 1 + j * b_dim1;
q__4.r = du[i__3].r * b[i__4].r - du[i__3].i * b[i__4].i,
q__4.i = du[i__3].r * b[i__4].i + du[i__3].i * b[i__4]
.r;
q__3.r = b[i__2].r - q__4.r, q__3.i = b[i__2].i - q__4.i;
i__5 = i__;
i__6 = i__ + 2 + j * b_dim1;
q__5.r = du2[i__5].r * b[i__6].r - du2[i__5].i * b[i__6].i,
q__5.i = du2[i__5].r * b[i__6].i + du2[i__5].i * b[
i__6].r;
q__2.r = q__3.r - q__5.r, q__2.i = q__3.i - q__5.i;
c_div(&q__1, &q__2, &d__[i__]);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
/* L30: */
}
if (j < *nrhs) {
++j;
goto L10;
}
} else {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Solve L*x = b. */
i__2 = *n - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
if (ipiv[i__] == i__) {
i__3 = i__ + 1 + j * b_dim1;
i__4 = i__ + 1 + j * b_dim1;
i__5 = i__;
i__6 = i__ + j * b_dim1;
q__2.r = dl[i__5].r * b[i__6].r - dl[i__5].i * b[i__6]
.i, q__2.i = dl[i__5].r * b[i__6].i + dl[i__5]
.i * b[i__6].r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4].i -
q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
} else {
i__3 = i__ + j * b_dim1;
temp.r = b[i__3].r, temp.i = b[i__3].i;
i__3 = i__ + j * b_dim1;
i__4 = i__ + 1 + j * b_dim1;
b[i__3].r = b[i__4].r, b[i__3].i = b[i__4].i;
i__3 = i__ + 1 + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__2.r = dl[i__4].r * b[i__5].r - dl[i__4].i * b[i__5]
.i, q__2.i = dl[i__4].r * b[i__5].i + dl[i__4]
.i * b[i__5].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
}
/* L40: */
}
/* Solve U*x = b. */
i__2 = *n + j * b_dim1;
c_div(&q__1, &b[*n + j * b_dim1], &d__[*n]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
if (*n > 1) {
i__2 = *n - 1 + j * b_dim1;
i__3 = *n - 1 + j * b_dim1;
i__4 = *n - 1;
i__5 = *n + j * b_dim1;
q__3.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i,
q__3.i = du[i__4].r * b[i__5].i + du[i__4].i * b[
i__5].r;
q__2.r = b[i__3].r - q__3.r, q__2.i = b[i__3].i - q__3.i;
c_div(&q__1, &q__2, &d__[*n - 1]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
for (i__ = *n - 2; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + 1 + j * b_dim1;
q__4.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i,
q__4.i = du[i__4].r * b[i__5].i + du[i__4].i * b[
i__5].r;
q__3.r = b[i__3].r - q__4.r, q__3.i = b[i__3].i - q__4.i;
i__6 = i__;
i__7 = i__ + 2 + j * b_dim1;
q__5.r = du2[i__6].r * b[i__7].r - du2[i__6].i * b[i__7]
.i, q__5.i = du2[i__6].r * b[i__7].i + du2[i__6]
.i * b[i__7].r;
q__2.r = q__3.r - q__5.r, q__2.i = q__3.i - q__5.i;
c_div(&q__1, &q__2, &d__[i__]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L50: */
}
/* L60: */
}
}
} else if (*itrans == 1) {
/* Solve A**T * X = B. */
if (*nrhs <= 1) {
j = 1;
L70:
/* Solve U**T * x = b. */
i__1 = j * b_dim1 + 1;
c_div(&q__1, &b[j * b_dim1 + 1], &d__[1]);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
if (*n > 1) {
i__1 = j * b_dim1 + 2;
i__2 = j * b_dim1 + 2;
i__3 = j * b_dim1 + 1;
q__3.r = du[1].r * b[i__3].r - du[1].i * b[i__3].i, q__3.i =
du[1].r * b[i__3].i + du[1].i * b[i__3].r;
q__2.r = b[i__2].r - q__3.r, q__2.i = b[i__2].i - q__3.i;
c_div(&q__1, &q__2, &d__[2]);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
}
i__1 = *n;
for (i__ = 3; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
i__4 = i__ - 1;
i__5 = i__ - 1 + j * b_dim1;
q__4.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i,
q__4.i = du[i__4].r * b[i__5].i + du[i__4].i * b[i__5]
.r;
q__3.r = b[i__3].r - q__4.r, q__3.i = b[i__3].i - q__4.i;
i__6 = i__ - 2;
i__7 = i__ - 2 + j * b_dim1;
q__5.r = du2[i__6].r * b[i__7].r - du2[i__6].i * b[i__7].i,
q__5.i = du2[i__6].r * b[i__7].i + du2[i__6].i * b[
i__7].r;
q__2.r = q__3.r - q__5.r, q__2.i = q__3.i - q__5.i;
c_div(&q__1, &q__2, &d__[i__]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L80: */
}
/* Solve L**T * x = b. */
for (i__ = *n - 1; i__ >= 1; --i__) {
if (ipiv[i__] == i__) {
i__1 = i__ + j * b_dim1;
i__2 = i__ + j * b_dim1;
i__3 = i__;
i__4 = i__ + 1 + j * b_dim1;
q__2.r = dl[i__3].r * b[i__4].r - dl[i__3].i * b[i__4].i,
q__2.i = dl[i__3].r * b[i__4].i + dl[i__3].i * b[
i__4].r;
q__1.r = b[i__2].r - q__2.r, q__1.i = b[i__2].i - q__2.i;
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
} else {
i__1 = i__ + 1 + j * b_dim1;
temp.r = b[i__1].r, temp.i = b[i__1].i;
i__1 = i__ + 1 + j * b_dim1;
i__2 = i__ + j * b_dim1;
i__3 = i__;
q__2.r = dl[i__3].r * temp.r - dl[i__3].i * temp.i,
q__2.i = dl[i__3].r * temp.i + dl[i__3].i *
temp.r;
q__1.r = b[i__2].r - q__2.r, q__1.i = b[i__2].i - q__2.i;
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
i__1 = i__ + j * b_dim1;
b[i__1].r = temp.r, b[i__1].i = temp.i;
}
/* L90: */
}
if (j < *nrhs) {
++j;
goto L70;
}
} else {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Solve U**T * x = b. */
i__2 = j * b_dim1 + 1;
c_div(&q__1, &b[j * b_dim1 + 1], &d__[1]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
if (*n > 1) {
i__2 = j * b_dim1 + 2;
i__3 = j * b_dim1 + 2;
i__4 = j * b_dim1 + 1;
q__3.r = du[1].r * b[i__4].r - du[1].i * b[i__4].i,
q__3.i = du[1].r * b[i__4].i + du[1].i * b[i__4]
.r;
q__2.r = b[i__3].r - q__3.r, q__2.i = b[i__3].i - q__3.i;
c_div(&q__1, &q__2, &d__[2]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
i__2 = *n;
for (i__ = 3; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ - 1;
i__6 = i__ - 1 + j * b_dim1;
q__4.r = du[i__5].r * b[i__6].r - du[i__5].i * b[i__6].i,
q__4.i = du[i__5].r * b[i__6].i + du[i__5].i * b[
i__6].r;
q__3.r = b[i__4].r - q__4.r, q__3.i = b[i__4].i - q__4.i;
i__7 = i__ - 2;
i__8 = i__ - 2 + j * b_dim1;
q__5.r = du2[i__7].r * b[i__8].r - du2[i__7].i * b[i__8]
.i, q__5.i = du2[i__7].r * b[i__8].i + du2[i__7]
.i * b[i__8].r;
q__2.r = q__3.r - q__5.r, q__2.i = q__3.i - q__5.i;
c_div(&q__1, &q__2, &d__[i__]);
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L100: */
}
/* Solve L**T * x = b. */
for (i__ = *n - 1; i__ >= 1; --i__) {
if (ipiv[i__] == i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + 1 + j * b_dim1;
q__2.r = dl[i__4].r * b[i__5].r - dl[i__4].i * b[i__5]
.i, q__2.i = dl[i__4].r * b[i__5].i + dl[i__4]
.i * b[i__5].r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i -
q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
} else {
i__2 = i__ + 1 + j * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
i__2 = i__ + 1 + j * b_dim1;
i__3 = i__ + j * b_dim1;
i__4 = i__;
q__2.r = dl[i__4].r * temp.r - dl[i__4].i * temp.i,
q__2.i = dl[i__4].r * temp.i + dl[i__4].i *
temp.r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i -
q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
}
/* L110: */
}
/* L120: */
}
}
} else {
/* Solve A**H * X = B. */
if (*nrhs <= 1) {
j = 1;
L130:
/* Solve U**H * x = b. */
i__1 = j * b_dim1 + 1;
r_cnjg(&q__2, &d__[1]);
c_div(&q__1, &b[j * b_dim1 + 1], &q__2);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
if (*n > 1) {
i__1 = j * b_dim1 + 2;
i__2 = j * b_dim1 + 2;
r_cnjg(&q__4, &du[1]);
i__3 = j * b_dim1 + 1;
q__3.r = q__4.r * b[i__3].r - q__4.i * b[i__3].i, q__3.i =
q__4.r * b[i__3].i + q__4.i * b[i__3].r;
q__2.r = b[i__2].r - q__3.r, q__2.i = b[i__2].i - q__3.i;
r_cnjg(&q__5, &d__[2]);
c_div(&q__1, &q__2, &q__5);
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
}
i__1 = *n;
for (i__ = 3; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
r_cnjg(&q__5, &du[i__ - 1]);
i__4 = i__ - 1 + j * b_dim1;
q__4.r = q__5.r * b[i__4].r - q__5.i * b[i__4].i, q__4.i =
q__5.r * b[i__4].i + q__5.i * b[i__4].r;
q__3.r = b[i__3].r - q__4.r, q__3.i = b[i__3].i - q__4.i;
r_cnjg(&q__7, &du2[i__ - 2]);
i__5 = i__ - 2 + j * b_dim1;
q__6.r = q__7.r * b[i__5].r - q__7.i * b[i__5].i, q__6.i =
q__7.r * b[i__5].i + q__7.i * b[i__5].r;
q__2.r = q__3.r - q__6.r, q__2.i = q__3.i - q__6.i;
r_cnjg(&q__8, &d__[i__]);
c_div(&q__1, &q__2, &q__8);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L140: */
}
/* Solve L**H * x = b. */
for (i__ = *n - 1; i__ >= 1; --i__) {
if (ipiv[i__] == i__) {
i__1 = i__ + j * b_dim1;
i__2 = i__ + j * b_dim1;
r_cnjg(&q__3, &dl[i__]);
i__3 = i__ + 1 + j * b_dim1;
q__2.r = q__3.r * b[i__3].r - q__3.i * b[i__3].i, q__2.i =
q__3.r * b[i__3].i + q__3.i * b[i__3].r;
q__1.r = b[i__2].r - q__2.r, q__1.i = b[i__2].i - q__2.i;
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
} else {
i__1 = i__ + 1 + j * b_dim1;
temp.r = b[i__1].r, temp.i = b[i__1].i;
i__1 = i__ + 1 + j * b_dim1;
i__2 = i__ + j * b_dim1;
r_cnjg(&q__3, &dl[i__]);
q__2.r = q__3.r * temp.r - q__3.i * temp.i, q__2.i =
q__3.r * temp.i + q__3.i * temp.r;
q__1.r = b[i__2].r - q__2.r, q__1.i = b[i__2].i - q__2.i;
b[i__1].r = q__1.r, b[i__1].i = q__1.i;
i__1 = i__ + j * b_dim1;
b[i__1].r = temp.r, b[i__1].i = temp.i;
}
/* L150: */
}
if (j < *nrhs) {
++j;
goto L130;
}
} else {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Solve U**H * x = b. */
i__2 = j * b_dim1 + 1;
r_cnjg(&q__2, &d__[1]);
c_div(&q__1, &b[j * b_dim1 + 1], &q__2);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
if (*n > 1) {
i__2 = j * b_dim1 + 2;
i__3 = j * b_dim1 + 2;
r_cnjg(&q__4, &du[1]);
i__4 = j * b_dim1 + 1;
q__3.r = q__4.r * b[i__4].r - q__4.i * b[i__4].i, q__3.i =
q__4.r * b[i__4].i + q__4.i * b[i__4].r;
q__2.r = b[i__3].r - q__3.r, q__2.i = b[i__3].i - q__3.i;
r_cnjg(&q__5, &d__[2]);
c_div(&q__1, &q__2, &q__5);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
i__2 = *n;
for (i__ = 3; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
r_cnjg(&q__5, &du[i__ - 1]);
i__5 = i__ - 1 + j * b_dim1;
q__4.r = q__5.r * b[i__5].r - q__5.i * b[i__5].i, q__4.i =
q__5.r * b[i__5].i + q__5.i * b[i__5].r;
q__3.r = b[i__4].r - q__4.r, q__3.i = b[i__4].i - q__4.i;
r_cnjg(&q__7, &du2[i__ - 2]);
i__6 = i__ - 2 + j * b_dim1;
q__6.r = q__7.r * b[i__6].r - q__7.i * b[i__6].i, q__6.i =
q__7.r * b[i__6].i + q__7.i * b[i__6].r;
q__2.r = q__3.r - q__6.r, q__2.i = q__3.i - q__6.i;
r_cnjg(&q__8, &d__[i__]);
c_div(&q__1, &q__2, &q__8);
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L160: */
}
/* Solve L**H * x = b. */
for (i__ = *n - 1; i__ >= 1; --i__) {
if (ipiv[i__] == i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
r_cnjg(&q__3, &dl[i__]);
i__4 = i__ + 1 + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
.r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i -
q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
} else {
i__2 = i__ + 1 + j * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
i__2 = i__ + 1 + j * b_dim1;
i__3 = i__ + j * b_dim1;
r_cnjg(&q__3, &dl[i__]);
q__2.r = q__3.r * temp.r - q__3.i * temp.i, q__2.i =
q__3.r * temp.i + q__3.i * temp.r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i -
q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
}
/* L170: */
}
/* L180: */
}
}
}
/* End of CGTTS2 */
return 0;
} /* cgtts2_ */