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/* cgbmv.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 cgbmv_(char *trans, integer *m, integer *n, integer *kl,
integer *ku, complex *alpha, complex *a, integer *lda, complex *x,
integer *incx, complex *beta, complex *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
complex q__1, q__2, q__3;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j, k, ix, iy, jx, jy, kx, ky, kup1, info;
complex temp;
integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
logical noconj;
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGBMV performs one of the matrix-vector operations */
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or */
/* y := alpha*conjg( A' )*x + beta*y, */
/* where alpha and beta are scalars, x and y are vectors and A is an */
/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
/* Arguments */
/* ========== */
/* TRANS - CHARACTER*1. */
/* On entry, TRANS specifies the operation to be performed as */
/* follows: */
/* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */
/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
/* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. */
/* Unchanged on exit. */
/* M - INTEGER. */
/* On entry, M specifies the number of rows of the matrix A. */
/* M must be at least zero. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the number of columns of the matrix A. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* KL - INTEGER. */
/* On entry, KL specifies the number of sub-diagonals of the */
/* matrix A. KL must satisfy 0 .le. KL. */
/* Unchanged on exit. */
/* KU - INTEGER. */
/* On entry, KU specifies the number of super-diagonals of the */
/* matrix A. KU must satisfy 0 .le. KU. */
/* Unchanged on exit. */
/* ALPHA - COMPLEX . */
/* On entry, ALPHA specifies the scalar alpha. */
/* Unchanged on exit. */
/* A - COMPLEX array of DIMENSION ( LDA, n ). */
/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
/* array A must contain the matrix of coefficients, supplied */
/* column by column, with the leading diagonal of the matrix in */
/* row ( ku + 1 ) of the array, the first super-diagonal */
/* starting at position 2 in row ku, the first sub-diagonal */
/* starting at position 1 in row ( ku + 2 ), and so on. */
/* Elements in the array A that do not correspond to elements */
/* in the band matrix (such as the top left ku by ku triangle) */
/* are not referenced. */
/* The following program segment will transfer a band matrix */
/* from conventional full matrix storage to band storage: */
/* DO 20, J = 1, N */
/* K = KU + 1 - J */
/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
/* A( K + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* 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 */
/* ( kl + ku + 1 ). */
/* Unchanged on exit. */
/* X - COMPLEX array of DIMENSION at least */
/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
/* Before entry, the incremented array X must contain the */
/* vector x. */
/* Unchanged on exit. */
/* INCX - INTEGER. */
/* On entry, INCX specifies the increment for the elements of */
/* X. INCX must not be zero. */
/* Unchanged on exit. */
/* BETA - COMPLEX . */
/* On entry, BETA specifies the scalar beta. When BETA is */
/* supplied as zero then Y need not be set on input. */
/* Unchanged on exit. */
/* Y - COMPLEX array of DIMENSION at least */
/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
/* Before entry, the incremented array Y must contain the */
/* vector y. On exit, Y is overwritten by the updated vector y. */
/* INCY - INTEGER. */
/* On entry, INCY specifies the increment for the elements of */
/* Y. INCY 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;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*kl < 0) {
info = 4;
} else if (*ku < 0) {
info = 5;
} else if (*lda < *kl + *ku + 1) {
info = 8;
} else if (*incx == 0) {
info = 10;
} else if (*incy == 0) {
info = 13;
}
if (info != 0) {
xerbla_("CGBMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0.f && alpha->i == 0.f && (beta->r
== 1.f && beta->i == 0.f)) {
return 0;
}
noconj = lsame_(trans, "T");
/* Set LENX and LENY, the lengths of the vectors x and y, and set */
/* up the start points in X and Y. */
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/* Start the operations. In this version the elements of A are */
/* accessed sequentially with one pass through the band part of A. */
/* First form y := beta*y. */
if (beta->r != 1.f || beta->i != 0.f) {
if (*incy == 1) {
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0.f, y[i__2].i = 0.f;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0.f, y[i__2].i = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
kup1 = *ku + 1;
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
i__2 = jx;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = q__1.r, temp.i = q__1.i;
k = kup1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
i__2 = i__;
i__3 = i__;
i__5 = k + i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i +
q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__4 = jx;
if (x[i__4].r != 0.f || x[i__4].i != 0.f) {
i__4 = jx;
q__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i,
q__1.i = alpha->r * x[i__4].i + alpha->i * x[i__4]
.r;
temp.r = q__1.r, temp.i = q__1.i;
iy = ky;
k = kup1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = iy;
i__2 = iy;
i__5 = k + i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i +
q__2.i;
y[i__4].r = q__1.r, y[i__4].i = q__1.i;
iy += *incy;
/* L70: */
}
}
jx += *incx;
if (j > *ku) {
ky += *incy;
}
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0.f, temp.i = 0.f;
k = kup1 - j;
if (noconj) {
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
i__3 = k + i__ + j * a_dim1;
i__4 = i__;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, q__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L90: */
}
} else {
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
i__2 = i__;
q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i,
q__2.i = q__3.r * x[i__2].i + q__3.i * x[i__2]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
}
i__4 = jy;
i__2 = jy;
q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i =
alpha->r * temp.i + alpha->i * temp.r;
q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;
y[i__4].r = q__1.r, y[i__4].i = q__1.i;
jy += *incy;
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0.f, temp.i = 0.f;
ix = kx;
k = kup1 - j;
if (noconj) {
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = k + i__ + j * a_dim1;
i__2 = ix;
q__2.r = a[i__4].r * x[i__2].r - a[i__4].i * x[i__2]
.i, q__2.i = a[i__4].r * x[i__2].i + a[i__4]
.i * x[i__2].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L120: */
}
} else {
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[i__3]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L130: */
}
}
i__2 = jy;
i__3 = jy;
q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i =
alpha->r * temp.i + alpha->i * temp.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
jy += *incy;
if (j > *ku) {
kx += *incx;
}
/* L140: */
}
}
}
return 0;
/* End of CGBMV . */
} /* cgbmv_ */
|
