Squashed 'third_party/eigen/' changes from 61d72f6..cf794d3
Change-Id: I9b814151b01f49af6337a8605d0c42a3a1ed4c72
git-subtree-dir: third_party/eigen
git-subtree-split: cf794d3b741a6278df169e58461f8529f43bce5d
diff --git a/blas/f2c/chbmv.c b/blas/f2c/chbmv.c
new file mode 100644
index 0000000..f218fe3
--- /dev/null
+++ b/blas/f2c/chbmv.c
@@ -0,0 +1,487 @@
+/* chbmv.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 chbmv_(char *uplo, integer *n, integer *k, complex *
+ alpha, complex *a, integer *lda, complex *x, integer *incx, complex *
+ beta, complex *y, integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+ real r__1;
+ complex q__1, q__2, q__3, q__4;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
+ complex temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CHBMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n hermitian band matrix, with k super-diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the band matrix A is being supplied as */
+/* follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* being supplied. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* being supplied. */
+
+/* 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, K specifies the number of super-diagonals of the */
+/* matrix A. K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* ALPHA - COMPLEX . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* A - COMPLEX 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 hermitian matrix, 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 the upper */
+/* triangular part of a hermitian 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 hermitian matrix, 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 the lower */
+/* triangular part of a hermitian 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 the imaginary parts of the diagonal elements need */
+/* not be set and are assumed to be zero. */
+/* 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 array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* 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. */
+/* Unchanged on exit. */
+
+/* Y - COMPLEX array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* 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. */
+
+/* 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;
+ --y;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*k < 0) {
+ info = 3;
+ } else if (*lda < *k + 1) {
+ info = 6;
+ } else if (*incx == 0) {
+ info = 8;
+ } else if (*incy == 0) {
+ info = 11;
+ }
+ if (info != 0) {
+ xerbla_("CHBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f &&
+ beta->i == 0.f))) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array A */
+/* are accessed sequentially with one pass through 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 = *n;
+ 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 = *n;
+ 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 = *n;
+ 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 = *n;
+ 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;
+ }
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when upper triangle of A is stored. */
+
+ kplus1 = *k + 1;
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ 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;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ 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__) {
+ i__2 = i__;
+ i__3 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.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;
+ r_cnjg(&q__3, &a[l + 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 = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L50: */
+ }
+ i__4 = j;
+ i__2 = j;
+ i__3 = kplus1 + j * a_dim1;
+ r__1 = a[i__3].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__2].r + q__3.r, q__2.i = y[i__2].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__4].r = q__1.r, y[i__4].i = q__1.i;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ 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;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ ix = kx;
+ iy = ky;
+ 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__) {
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.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;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = kplus1 + j * a_dim1;
+ r__1 = a[i__2].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__4].r + q__3.r, q__2.i = y[i__4].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+ if (j > *k) {
+ kx += *incx;
+ ky += *incy;
+ }
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when lower triangle of A is stored. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = j;
+ q__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__3 = j;
+ i__4 = j;
+ i__2 = j * a_dim1 + 1;
+ r__1 = a[i__2].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ i__4 = i__;
+ i__2 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.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;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = i__;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L90: */
+ }
+ i__3 = j;
+ i__4 = j;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = jx;
+ q__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = j * a_dim1 + 1;
+ r__1 = a[i__2].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ l = 1 - j;
+ ix = jx;
+ iy = jy;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ ix += *incx;
+ iy += *incy;
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.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;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L110: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of CHBMV . */
+
+} /* chbmv_ */
+