#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctpmv_(char *uplo, char *trans, char *diag, integer *n, complex *ap, complex *x, integer *incx) { /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; complex q__1, q__2, q__3; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ static integer i__, j, k, kk, ix, jx, kx, info; static complex temp; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; /* Purpose ======= CTPMV performs one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. 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 := conjg( 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. AP - COMPLEX array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular 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 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. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. Unchanged on exit. X - COMPLEX 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. 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. Test the input parameters. Parameter adjustments */ --x; --ap; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 3; } else if (*n < 0) { info = 4; } else if (*incx == 0) { info = 7; } if (info != 0) { xerbla_("CTPMV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } noconj = lsame_(trans, "T"); nounit = lsame_(diag, "N"); /* 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 AP are accessed sequentially with one pass through AP. */ if (lsame_(trans, "N")) { /* Form x:= A*x. */ if (lsame_(uplo, "U")) { kk = 1; if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0.f || x[i__2].i != 0.f) { i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; 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 = temp.r * ap[i__5].r - temp.i * ap[i__5] .i, q__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; q__1.r = x[i__4].r + q__2.r, q__1.i = x[i__4].i + q__2.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; ++k; /* L10: */ } if (nounit) { i__2 = j; i__3 = j; i__4 = kk + j - 1; q__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ i__4].i, q__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = q__1.r, x[i__2].i = q__1.i; } } kk += j; /* L20: */ } } else { jx = kx; 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; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = kx; i__2 = kk + j - 2; for (k = kk; k <= i__2; ++k) { i__3 = ix; i__4 = ix; i__5 = k; q__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] .i, q__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; q__1.r = x[i__4].r + q__2.r, q__1.i = x[i__4].i + q__2.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; ix += *incx; /* L30: */ } if (nounit) { i__2 = jx; i__3 = jx; i__4 = kk + j - 1; q__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ i__4].i, q__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = q__1.r, x[i__2].i = q__1.i; } } jx += *incx; kk += j; /* L40: */ } } } else { kk = *n * (*n + 1) / 2; if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; if (x[i__1].r != 0.f || x[i__1].i != 0.f) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; k = kk; i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = i__; i__3 = i__; i__4 = k; q__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] .i, q__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i + q__2.i; x[i__2].r = q__1.r, x[i__2].i = q__1.i; --k; /* L50: */ } if (nounit) { i__1 = j; i__2 = j; i__3 = kk - *n + j; q__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ i__3].i, q__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = q__1.r, x[i__1].i = q__1.i; } } kk -= *n - j + 1; /* L60: */ } } else { kx += (*n - 1) * *incx; jx = kx; for (j = *n; j >= 1; --j) { i__1 = jx; if (x[i__1].r != 0.f || x[i__1].i != 0.f) { i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = kx; i__1 = kk - (*n - (j + 1)); for (k = kk; k >= i__1; --k) { i__2 = ix; i__3 = ix; i__4 = k; q__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] .i, q__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i + q__2.i; x[i__2].r = q__1.r, x[i__2].i = q__1.i; ix -= *incx; /* L70: */ } if (nounit) { i__1 = jx; i__2 = jx; i__3 = kk - *n + j; q__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ i__3].i, q__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = q__1.r, x[i__1].i = q__1.i; } } jx -= *incx; kk -= *n - j + 1; /* L80: */ } } } } else { /* Form x := A'*x or x := conjg( A' )*x. */ if (lsame_(uplo, "U")) { kk = *n * (*n + 1) / 2; if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; k = kk - 1; if (noconj) { if (nounit) { i__1 = kk; q__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] .i, q__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = q__1.r, temp.i = q__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { i__1 = k; i__2 = i__; q__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ i__2].i, q__2.i = ap[i__1].r * x[i__2].i + ap[i__1].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; --k; /* L90: */ } } else { if (nounit) { r_cnjg(&q__2, &ap[kk]); q__1.r = temp.r * q__2.r - temp.i * q__2.i, q__1.i = temp.r * q__2.i + temp.i * q__2.r; temp.r = q__1.r, temp.i = q__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { r_cnjg(&q__3, &ap[k]); i__1 = i__; q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i, q__2.i = q__3.r * x[i__1].i + q__3.i * x[ i__1].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; --k; /* L100: */ } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; kk -= j; /* L110: */ } } else { jx = kx + (*n - 1) * *incx; for (j = *n; j >= 1; --j) { i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = jx; if (noconj) { if (nounit) { i__1 = kk; q__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] .i, q__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = q__1.r, temp.i = q__1.i; } i__1 = kk - j + 1; for (k = kk - 1; k >= i__1; --k) { ix -= *incx; i__2 = k; i__3 = ix; q__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ i__3].i, q__2.i = ap[i__2].r * x[i__3].i + ap[i__2].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; /* L120: */ } } else { if (nounit) { r_cnjg(&q__2, &ap[kk]); q__1.r = temp.r * q__2.r - temp.i * q__2.i, q__1.i = temp.r * q__2.i + temp.i * q__2.r; temp.r = q__1.r, temp.i = q__1.i; } i__1 = kk - j + 1; for (k = kk - 1; k >= i__1; --k) { ix -= *incx; r_cnjg(&q__3, &ap[k]); i__2 = ix; 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; /* L130: */ } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; kk -= j; /* L140: */ } } } else { kk = 1; if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; k = kk + 1; if (noconj) { if (nounit) { i__2 = kk; q__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] .i, q__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = q__1.r, temp.i = q__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++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 = temp.r + q__2.r, q__1.i = temp.i + q__2.i; temp.r = q__1.r, temp.i = q__1.i; ++k; /* L150: */ } } else { if (nounit) { r_cnjg(&q__2, &ap[kk]); q__1.r = temp.r * q__2.r - temp.i * q__2.i, q__1.i = temp.r * q__2.i + temp.i * q__2.r; temp.r = q__1.r, temp.i = q__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { r_cnjg(&q__3, &ap[k]); i__3 = i__; 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; ++k; /* L160: */ } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; kk += *n - j + 1; /* L170: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = jx; if (noconj) { if (nounit) { i__2 = kk; q__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] .i, q__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = q__1.r, temp.i = q__1.i; } i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; 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 = temp.r + q__2.r, q__1.i = temp.i + q__2.i; temp.r = q__1.r, temp.i = q__1.i; /* L180: */ } } else { if (nounit) { r_cnjg(&q__2, &ap[kk]); q__1.r = temp.r * q__2.r - temp.i * q__2.i, q__1.i = temp.r * q__2.i + temp.i * q__2.r; temp.r = q__1.r, temp.i = q__1.i; } i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; r_cnjg(&q__3, &ap[k]); 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; /* L190: */ } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; kk += *n - j + 1; /* L200: */ } } } } return 0; /* End of CTPMV . */ } /* ctpmv_ */