/* ztbsv.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int ztbsv_(char *uplo, char *trans, char *diag, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *x, integer
*incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg(
doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, l, ix, jx, kx, info;
doublecomplex temp;
extern logical lsame_(char *, char *);
integer kplus1;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical noconj, nounit;
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTBSV solves one of the systems of equations */
/* A*x = b, or A'*x = b, or conjg( A' )*x = b, */
/* where b and x are n element vectors and A is an n by n unit, or */
/* non-unit, upper or lower triangular band matrix, with ( k + 1 ) */
/* diagonals. */
/* No test for singularity or near-singularity is included in this */
/* routine. Such tests must be performed before calling this routine. */
/* Arguments */
/* ========== */
/* UPLO - CHARACTER*1. */
/* 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 - CHARACTER*1. */
/* 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' conjg( A' )*x = b. */
/* Unchanged on exit. */
/* DIAG - CHARACTER*1. */
/* 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 - INTEGER. */
/* On entry, N specifies the order of the matrix A. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* K - INTEGER. */
/* On entry with UPLO = 'U' or 'u', K specifies the number of */
/* super-diagonals of the matrix A. */
/* On entry with UPLO = 'L' or 'l', K specifies the number of */
/* sub-diagonals of the matrix A. */
/* K must satisfy 0 .le. K. */
/* Unchanged on exit. */
/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
/* by n part of the array A must contain the upper triangular */
/* band part of the matrix of coefficients, supplied column by */
/* column, with the leading diagonal of the matrix in row */
/* ( k + 1 ) of the array, the first super-diagonal starting at */
/* position 2 in row k, and so on. The top left k by k triangle */
/* of the array A is not referenced. */
/* The following program segment will transfer an upper */
/* triangular band matrix from conventional full matrix storage */
/* to band storage: */
/* DO 20, J = 1, N */
/* M = K + 1 - J */
/* DO 10, I = MAX( 1, J - K ), J */
/* A( M + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
/* by n part of the array A must contain the lower triangular */
/* band part of the matrix of coefficients, supplied column by */
/* column, with the leading diagonal of the matrix in row 1 of */
/* the array, the first sub-diagonal starting at position 1 in */
/* row 2, and so on. The bottom right k by k triangle of the */
/* array A is not referenced. */
/* The following program segment will transfer a lower */
/* triangular band matrix from conventional full matrix storage */
/* to band storage: */
/* DO 20, J = 1, N */
/* M = 1 - J */
/* DO 10, I = J, MIN( N, J + K ) */
/* A( M + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* Note that when DIAG = 'U' or 'u' the elements of the array A */
/* corresponding to the diagonal elements of the matrix are not */
/* referenced, but are assumed to be unity. */
/* Unchanged on exit. */
/* LDA - INTEGER. */
/* On entry, LDA specifies the first dimension of A as declared */
/* in the calling (sub) program. LDA must be at least */
/* ( k + 1 ). */
/* Unchanged on exit. */
/* X - COMPLEX*16 array of dimension at least */
/* ( 1 + ( n - 1 )*abs( INCX ) ). */
/* Before entry, the incremented array X must contain the n */
/* element right-hand side vector b. On exit, X is overwritten */
/* with the solution vector x. */
/* INCX - INTEGER. */
/* On entry, INCX specifies the increment for the elements of */
/* X. INCX must not be zero. */
/* Unchanged on exit. */
/* Level 2 Blas routine. */
/* -- Written on 22-October-1986. */
/* Jack Dongarra, Argonne National Lab. */
/* Jeremy Du Croz, Nag Central Office. */
/* Sven Hammarling, Nag Central Office. */
/* Richard Hanson, Sandia National Labs. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < *k + 1) {
info = 7;
} else if (*incx == 0) {
info = 9;
}
if (info != 0) {
xerbla_("ZTBSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
noconj = lsame_(trans, "T");
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This */
/* will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are */
/* accessed by sequentially with one pass through A. */
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
l = kplus1 - j;
if (nounit) {
i__1 = j;
z_div(&z__1, &x[j], &a[kplus1 + j * a_dim1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__1 = max(i__2,i__3);
for (i__ = j - 1; i__ >= i__1; --i__) {
i__2 = i__;
i__3 = i__;
i__4 = l + i__ + j * a_dim1;
z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
z__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i -
z__2.i;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/* L10: */
}
}
/* L20: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
kx -= *incx;
i__1 = jx;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
ix = kx;
l = kplus1 - j;
if (nounit) {
i__1 = jx;
z_div(&z__1, &x[jx], &a[kplus1 + j * a_dim1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__1 = max(i__2,i__3);
for (i__ = j - 1; i__ >= i__1; --i__) {
i__2 = ix;
i__3 = ix;
i__4 = l + i__ + j * a_dim1;
z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
z__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i -
z__2.i;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
ix -= *incx;
/* L30: */
}
}
jx -= *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
l = 1 - j;
if (nounit) {
i__2 = j;
z_div(&z__1, &x[j], &a[j * a_dim1 + 1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
/* Computing MIN */
i__3 = *n, i__4 = j + *k;
i__2 = min(i__3,i__4);
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = l + i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i -
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
kx += *incx;
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
ix = kx;
l = 1 - j;
if (nounit) {
i__2 = jx;
z_div(&z__1, &x[jx], &a[j * a_dim1 + 1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
/* Computing MIN */
i__3 = *n, i__4 = j + *k;
i__2 = min(i__3,i__4);
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = ix;
i__4 = ix;
i__5 = l + i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i -
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
ix += *incx;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
} else {
/* Form x := inv( A' )*x or x := inv( conjg( A') )*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
l = kplus1 - j;
if (noconj) {
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
i__2 = l + i__ + j * a_dim1;
i__3 = i__;
z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[
i__3].i, z__2.i = a[i__2].r * x[i__3].i +
a[i__2].i * x[i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
if (nounit) {
z_div(&z__1, &temp, &a[kplus1 + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j - 1;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__4 = i__;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i,
z__2.i = z__3.r * x[i__4].i + z__3.i * x[
i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
if (nounit) {
d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__3 = j;
x[i__3].r = temp.r, x[i__3].i = temp.i;
/* L110: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__3 = jx;
temp.r = x[i__3].r, temp.i = x[i__3].i;
ix = kx;
l = kplus1 - j;
if (noconj) {
/* Computing MAX */
i__3 = 1, i__4 = j - *k;
i__2 = j - 1;
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
i__3 = l + i__ + j * a_dim1;
i__4 = ix;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, z__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L120: */
}
if (nounit) {
z_div(&z__1, &temp, &a[kplus1 + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__2 = ix;
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
z__2.i = z__3.r * x[i__2].i + z__3.i * x[
i__2].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L130: */
}
if (nounit) {
d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__4 = jx;
x[i__4].r = temp.r, x[i__4].i = temp.i;
jx += *incx;
if (j > *k) {
kx += *incx;
}
/* L140: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
l = 1 - j;
if (noconj) {
/* Computing MIN */
i__1 = *n, i__4 = j + *k;
i__2 = j + 1;
for (i__ = min(i__1,i__4); i__ >= i__2; --i__) {
i__1 = l + i__ + j * a_dim1;
i__4 = i__;
z__2.r = a[i__1].r * x[i__4].r - a[i__1].i * x[
i__4].i, z__2.i = a[i__1].r * x[i__4].i +
a[i__1].i * x[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L150: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j * a_dim1 + 1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
/* Computing MIN */
i__2 = *n, i__1 = j + *k;
i__4 = j + 1;
for (i__ = min(i__2,i__1); i__ >= i__4; --i__) {
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__2 = i__;
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
z__2.i = z__3.r * x[i__2].i + z__3.i * x[
i__2].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L160: */
}
if (nounit) {
d_cnjg(&z__2, &a[j * a_dim1 + 1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__4 = j;
x[i__4].r = temp.r, x[i__4].i = temp.i;
/* L170: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
i__4 = jx;
temp.r = x[i__4].r, temp.i = x[i__4].i;
ix = kx;
l = 1 - j;
if (noconj) {
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__1 = j + 1;
for (i__ = min(i__4,i__2); i__ >= i__1; --i__) {
i__4 = l + i__ + j * a_dim1;
i__2 = ix;
z__2.r = a[i__4].r * x[i__2].r - a[i__4].i * x[
i__2].i, z__2.i = a[i__4].r * x[i__2].i +
a[i__4].i * x[i__2].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix -= *incx;
/* L180: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j * a_dim1 + 1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
/* Computing MIN */
i__1 = *n, i__4 = j + *k;
i__2 = j + 1;
for (i__ = min(i__1,i__4); i__ >= i__2; --i__) {
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__1 = ix;
z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
z__2.i = z__3.r * x[i__1].i + z__3.i * x[
i__1].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix -= *incx;
/* L190: */
}
if (nounit) {
d_cnjg(&z__2, &a[j * a_dim1 + 1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__2 = jx;
x[i__2].r = temp.r, x[i__2].i = temp.i;
jx -= *incx;
if (*n - j >= *k) {
kx -= *incx;
}
/* L200: */
}
}
}
}
return 0;
/* End of ZTBSV . */
} /* ztbsv_ */