429 lines
11 KiB
C
429 lines
11 KiB
C
|
/* dtbmv.f -- translated by f2c (version 20100827).
|
||
|
|
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 "datatypes.h"
|
||
|
|
|
||
|
|
/* Subroutine */ int dtbmv_(char *uplo, char *trans, char *diag, integer *n,
|
||
|
|
integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx,
|
||
|
|
ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)
|
||
|
|
{
|
||
|
|
/* System generated locals */
|
||
|
|
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
|
||
|
|
|
||
|
|
/* Local variables */
|
||
|
|
integer i__, j, l, ix, jx, kx, info;
|
||
|
|
doublereal temp;
|
||
|
|
extern logical lsame_(char *, char *, ftnlen, ftnlen);
|
||
|
|
integer kplus1;
|
||
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
||
|
|
logical nounit;
|
||
|
|
|
||
|
|
/* .. Scalar Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Array Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
|
||
|
|
/* Purpose */
|
||
|
|
/* ======= */
|
||
|
|
|
||
|
|
/* DTBMV performs one of the matrix-vector operations */
|
||
|
|
|
||
|
|
/* x := A*x, or x := A'*x, */
|
||
|
|
|
||
|
|
/* where x is an n element vector and A is an n by n unit, or non-unit, */
|
||
|
|
/* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */
|
||
|
|
|
||
|
|
/* 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 operation to be performed as */
|
||
|
|
/* follows: */
|
||
|
|
|
||
|
|
/* TRANS = 'N' or 'n' x := A*x. */
|
||
|
|
|
||
|
|
/* TRANS = 'T' or 't' x := A'*x. */
|
||
|
|
|
||
|
|
/* TRANS = 'C' or 'c' x := A'*x. */
|
||
|
|
|
||
|
|
/* 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION array of dimension at least */
|
||
|
|
/* ( 1 + ( n - 1 )*abs( INCX ) ). */
|
||
|
|
/* Before entry, the incremented array X must contain the n */
|
||
|
|
/* element vector x. On exit, X is overwritten with the */
|
||
|
|
/* transformed vector x. */
|
||
|
|
|
||
|
|
/* INCX - INTEGER. */
|
||
|
|
/* On entry, INCX specifies the increment for the elements of */
|
||
|
|
/* X. INCX must not be zero. */
|
||
|
|
/* Unchanged on exit. */
|
||
|
|
|
||
|
|
/* Further Details */
|
||
|
|
/* =============== */
|
||
|
|
|
||
|
|
/* 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", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
|
||
|
|
ftnlen)1, (ftnlen)1)) {
|
||
|
|
info = 1;
|
||
|
|
} else if (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
|
||
|
|
"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
|
||
|
|
ftnlen)1)) {
|
||
|
|
info = 2;
|
||
|
|
} else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
|
||
|
|
"N", (ftnlen)1, (ftnlen)1)) {
|
||
|
|
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_("DTBMV ", &info, (ftnlen)6);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Quick return if possible. */
|
||
|
|
|
||
|
|
if (*n == 0) {
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
|
||
|
|
|
||
|
|
/* 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 sequentially with one pass through A. */
|
||
|
|
|
||
|
|
if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
|
||
|
|
|
||
|
|
/* Form x := A*x. */
|
||
|
|
|
||
|
|
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
|
||
|
|
kplus1 = *k + 1;
|
||
|
|
if (*incx == 1) {
|
||
|
|
i__1 = *n;
|
||
|
|
for (j = 1; j <= i__1; ++j) {
|
||
|
|
if (x[j] != 0.) {
|
||
|
|
temp = x[j];
|
||
|
|
l = kplus1 - j;
|
||
|
|
/* Computing MAX */
|
||
|
|
i__2 = 1, i__3 = j - *k;
|
||
|
|
i__4 = j - 1;
|
||
|
|
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
|
||
|
|
x[i__] += temp * a[l + i__ + j * a_dim1];
|
||
|
|
/* L10: */
|
||
|
|
}
|
||
|
|
if (nounit) {
|
||
|
|
x[j] *= a[kplus1 + j * a_dim1];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L20: */
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
jx = kx;
|
||
|
|
i__1 = *n;
|
||
|
|
for (j = 1; j <= i__1; ++j) {
|
||
|
|
if (x[jx] != 0.) {
|
||
|
|
temp = x[jx];
|
||
|
|
ix = kx;
|
||
|
|
l = kplus1 - j;
|
||
|
|
/* Computing MAX */
|
||
|
|
i__4 = 1, i__2 = j - *k;
|
||
|
|
i__3 = j - 1;
|
||
|
|
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
|
||
|
|
x[ix] += temp * a[l + i__ + j * a_dim1];
|
||
|
|
ix += *incx;
|
||
|
|
/* L30: */
|
||
|
|
}
|
||
|
|
if (nounit) {
|
||
|
|
x[jx] *= a[kplus1 + j * a_dim1];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
jx += *incx;
|
||
|
|
if (j > *k) {
|
||
|
|
kx += *incx;
|
||
|
|
}
|
||
|
|
/* L40: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
if (*incx == 1) {
|
||
|
|
for (j = *n; j >= 1; --j) {
|
||
|
|
if (x[j] != 0.) {
|
||
|
|
temp = x[j];
|
||
|
|
l = 1 - j;
|
||
|
|
/* Computing MIN */
|
||
|
|
i__1 = *n, i__3 = j + *k;
|
||
|
|
i__4 = j + 1;
|
||
|
|
for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
|
||
|
|
x[i__] += temp * a[l + i__ + j * a_dim1];
|
||
|
|
/* L50: */
|
||
|
|
}
|
||
|
|
if (nounit) {
|
||
|
|
x[j] *= a[j * a_dim1 + 1];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L60: */
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
kx += (*n - 1) * *incx;
|
||
|
|
jx = kx;
|
||
|
|
for (j = *n; j >= 1; --j) {
|
||
|
|
if (x[jx] != 0.) {
|
||
|
|
temp = x[jx];
|
||
|
|
ix = kx;
|
||
|
|
l = 1 - j;
|
||
|
|
/* Computing MIN */
|
||
|
|
i__4 = *n, i__1 = j + *k;
|
||
|
|
i__3 = j + 1;
|
||
|
|
for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
|
||
|
|
x[ix] += temp * a[l + i__ + j * a_dim1];
|
||
|
|
ix -= *incx;
|
||
|
|
/* L70: */
|
||
|
|
}
|
||
|
|
if (nounit) {
|
||
|
|
x[jx] *= a[j * a_dim1 + 1];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
jx -= *incx;
|
||
|
|
if (*n - j >= *k) {
|
||
|
|
kx -= *incx;
|
||
|
|
}
|
||
|
|
/* L80: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
|
||
|
|
/* Form x := A'*x. */
|
||
|
|
|
||
|
|
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
|
||
|
|
kplus1 = *k + 1;
|
||
|
|
if (*incx == 1) {
|
||
|
|
for (j = *n; j >= 1; --j) {
|
||
|
|
temp = x[j];
|
||
|
|
l = kplus1 - j;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[kplus1 + j * a_dim1];
|
||
|
|
}
|
||
|
|
/* Computing MAX */
|
||
|
|
i__4 = 1, i__1 = j - *k;
|
||
|
|
i__3 = max(i__4,i__1);
|
||
|
|
for (i__ = j - 1; i__ >= i__3; --i__) {
|
||
|
|
temp += a[l + i__ + j * a_dim1] * x[i__];
|
||
|
|
/* L90: */
|
||
|
|
}
|
||
|
|
x[j] = temp;
|
||
|
|
/* L100: */
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
kx += (*n - 1) * *incx;
|
||
|
|
jx = kx;
|
||
|
|
for (j = *n; j >= 1; --j) {
|
||
|
|
temp = x[jx];
|
||
|
|
kx -= *incx;
|
||
|
|
ix = kx;
|
||
|
|
l = kplus1 - j;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[kplus1 + j * a_dim1];
|
||
|
|
}
|
||
|
|
/* Computing MAX */
|
||
|
|
i__4 = 1, i__1 = j - *k;
|
||
|
|
i__3 = max(i__4,i__1);
|
||
|
|
for (i__ = j - 1; i__ >= i__3; --i__) {
|
||
|
|
temp += a[l + i__ + j * a_dim1] * x[ix];
|
||
|
|
ix -= *incx;
|
||
|
|
/* L110: */
|
||
|
|
}
|
||
|
|
x[jx] = temp;
|
||
|
|
jx -= *incx;
|
||
|
|
/* L120: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
if (*incx == 1) {
|
||
|
|
i__3 = *n;
|
||
|
|
for (j = 1; j <= i__3; ++j) {
|
||
|
|
temp = x[j];
|
||
|
|
l = 1 - j;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[j * a_dim1 + 1];
|
||
|
|
}
|
||
|
|
/* Computing MIN */
|
||
|
|
i__1 = *n, i__2 = j + *k;
|
||
|
|
i__4 = min(i__1,i__2);
|
||
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
||
|
|
temp += a[l + i__ + j * a_dim1] * x[i__];
|
||
|
|
/* L130: */
|
||
|
|
}
|
||
|
|
x[j] = temp;
|
||
|
|
/* L140: */
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
jx = kx;
|
||
|
|
i__3 = *n;
|
||
|
|
for (j = 1; j <= i__3; ++j) {
|
||
|
|
temp = x[jx];
|
||
|
|
kx += *incx;
|
||
|
|
ix = kx;
|
||
|
|
l = 1 - j;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[j * a_dim1 + 1];
|
||
|
|
}
|
||
|
|
/* Computing MIN */
|
||
|
|
i__1 = *n, i__2 = j + *k;
|
||
|
|
i__4 = min(i__1,i__2);
|
||
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
||
|
|
temp += a[l + i__ + j * a_dim1] * x[ix];
|
||
|
|
ix += *incx;
|
||
|
|
/* L150: */
|
||
|
|
}
|
||
|
|
x[jx] = temp;
|
||
|
|
jx += *incx;
|
||
|
|
/* L160: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of DTBMV . */
|
||
|
|
|
||
|
|
} /* dtbmv_ */
|
||
|
|
|