#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cspmv_(char *uplo, integer *n, complex *alpha, complex * ap, complex *x, integer *incx, complex *beta, complex *y, integer * incy) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CSPMV 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 symmetric matrix, supplied in packed form. Arguments ========== UPLO (input) CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. Unchanged on exit. N (input) INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA (input) COMPLEX On entry, ALPHA specifies the scalar alpha. Unchanged on exit. AP (input) COMPLEX array, dimension at least ( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry, with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Unchanged on exit. X (input) COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N- element vector x. Unchanged on exit. INCX (input) INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA (input) 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 (input/output) COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. INCY (input) INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. ===================================================================== Test the input parameters. Parameter adjustments */ /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; complex q__1, q__2, q__3, q__4; /* Local variables */ static integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info; static complex temp1, temp2; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); --y; --x; --ap; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 6; } else if (*incy == 0) { info = 9; } if (info != 0) { xerbla_("CSPMV ", &info); 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 AP are accessed sequentially with one pass through AP. 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; } kk = 1; if (lsame_(uplo, "U")) { /* Form y when AP contains the upper triangle. */ 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; k = kk; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = k; q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; i__3 = k; i__4 = i__; q__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, q__2.i = ap[i__3].r * x[i__4].i + ap[i__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; ++k; /* L50: */ } i__2 = j; i__3 = j; i__4 = kk + j - 1; q__3.r = temp1.r * ap[i__4].r - temp1.i * ap[i__4].i, q__3.i = temp1.r * ap[i__4].i + temp1.i * ap[i__4].r; q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].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__2].r = q__1.r, y[i__2].i = q__1.i; kk += j; /* L60: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { 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; temp1.r = q__1.r, temp1.i = q__1.i; temp2.r = 0.f, temp2.i = 0.f; ix = kx; iy = ky; i__2 = kk + j - 2; for (k = kk; k <= i__2; ++k) { i__3 = iy; i__4 = iy; i__5 = k; q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; i__3 = k; i__4 = ix; q__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, q__2.i = ap[i__3].r * x[i__4].i + ap[i__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__2 = jy; i__3 = jy; i__4 = kk + j - 1; q__3.r = temp1.r * ap[i__4].r - temp1.i * ap[i__4].i, q__3.i = temp1.r * ap[i__4].i + temp1.i * ap[i__4].r; q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].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__2].r = q__1.r, y[i__2].i = q__1.i; jx += *incx; jy += *incy; kk += j; /* L80: */ } } } else { /* Form y when AP contains the lower triangle. */ 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; i__2 = j; i__3 = j; i__4 = kk; q__2.r = temp1.r * ap[i__4].r - temp1.i * ap[i__4].i, q__2.i = temp1.r * ap[i__4].i + temp1.i * ap[i__4].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; k = kk + 1; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = k; q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; i__3 = k; i__4 = i__; q__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, q__2.i = ap[i__3].r * x[i__4].i + ap[i__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; ++k; /* L90: */ } i__2 = j; i__3 = 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__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; kk += *n - j + 1; /* L100: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { 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; temp1.r = q__1.r, temp1.i = q__1.i; temp2.r = 0.f, temp2.i = 0.f; i__2 = jy; i__3 = jy; i__4 = kk; q__2.r = temp1.r * ap[i__4].r - temp1.i * ap[i__4].i, q__2.i = temp1.r * ap[i__4].i + temp1.i * ap[i__4].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; ix = jx; iy = jy; i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; iy += *incy; i__3 = iy; i__4 = iy; i__5 = k; q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5] .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; i__3 = k; i__4 = ix; q__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, q__2.i = ap[i__3].r * x[i__4].i + ap[i__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__2 = jy; i__3 = 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__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; jx += *incx; jy += *incy; kk += *n - j + 1; /* L120: */ } } } return 0; /* End of CSPMV */ } /* cspmv_ */