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+/* 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 */
+/* tranformed 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_ */
+
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