/* fortran/ztpmv.f -- translated by f2c (version 20200916). 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 */ #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" /* > \brief \b ZTPMV */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) */ /* .. Scalar Arguments .. */ /* INTEGER INCX,N */ /* CHARACTER DIAG,TRANS,UPLO */ /* .. */ /* .. Array Arguments .. */ /* COMPLEX*16 AP(*),X(*) */ /* .. */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTPMV performs one of the matrix-vector operations */ /* > */ /* > x := A*x, or x := A**T*x, or x := A**H*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. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is 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. */ /* > \endverbatim */ /* > */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is 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**T*x. */ /* > */ /* > TRANS = 'C' or 'c' x := A**H*x. */ /* > \endverbatim */ /* > */ /* > \param[in] DIAG */ /* > \verbatim */ /* > DIAG is 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. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > On entry, N specifies the order of the matrix A. */ /* > N must be at least zero. */ /* > \endverbatim */ /* > */ /* > \param[in] AP */ /* > \verbatim */ /* > AP is COMPLEX*16 array, 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. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X */ /* > \verbatim */ /* > X is COMPLEX*16 array, 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. */ /* > \endverbatim */ /* > */ /* > \param[in] INCX */ /* > \verbatim */ /* > INCX is INTEGER */ /* > On entry, INCX specifies the increment for the elements of */ /* > X. INCX must not be zero. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \ingroup complex16_blas_level2 */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Level 2 Blas routine. */ /* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ /* > */ /* > -- 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. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical noconj, nounit; /* -- Reference BLAS level2 routine -- */ /* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* Test the input parameters. */ /* Parameter adjustments */ --x; --ap; /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( ftnlen)1, (ftnlen)1)) { info = 1; } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( ftnlen)1)) { info = 2; } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; } else if (*incx == 0) { info = 7; } if (info != 0) { xerbla_((char *)"ZTPMV ", &info, (ftnlen)6); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"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 AP are */ /* accessed sequentially with one pass through AP. */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form x:= A*x. */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { kk = 1; if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0. || x[i__2].i != 0.) { 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; z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] .i, z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ++k; /* L10: */ } if (nounit) { i__2 = j; i__3 = j; i__4 = kk + j - 1; z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ i__4].i, z__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__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. || x[i__2].i != 0.) { 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; z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] .i, z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ix += *incx; /* L30: */ } if (nounit) { i__2 = jx; i__3 = jx; i__4 = kk + j - 1; z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ i__4].i, z__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__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. || x[i__1].i != 0.) { 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; z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] .i, z__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; --k; /* L50: */ } if (nounit) { i__1 = j; i__2 = j; i__3 = kk - *n + j; z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ i__3].i, z__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__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. || x[i__1].i != 0.) { 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; z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] .i, z__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; ix -= *incx; /* L70: */ } if (nounit) { i__1 = jx; i__2 = jx; i__3 = kk - *n + j; z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ i__3].i, z__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } jx -= *incx; kk -= *n - j + 1; /* L80: */ } } } } else { /* Form x := A**T*x or x := A**H*x. */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { 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; z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] .i, z__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { i__1 = k; i__2 = i__; z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ i__2].i, z__2.i = ap[i__1].r * x[i__2].i + ap[i__1].i * x[i__2].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; --k; /* L90: */ } } else { if (nounit) { d_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { d_cnjg(&z__3, &ap[k]); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ i__1].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__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; z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] .i, z__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = kk - j + 1; for (k = kk - 1; k >= i__1; --k) { ix -= *incx; i__2 = k; i__3 = ix; z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ i__3].i, z__2.i = ap[i__2].r * x[i__3].i + ap[i__2].i * x[i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L120: */ } } else { if (nounit) { d_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = kk - j + 1; for (k = kk - 1; k >= i__1; --k) { ix -= *incx; d_cnjg(&z__3, &ap[k]); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ i__2].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__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; z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] .i, z__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = k; i__4 = i__; z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ i__4].i, z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ++k; /* L150: */ } } else { if (nounit) { d_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &ap[k]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__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; z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] .i, z__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; i__3 = k; i__4 = ix; z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ i__4].i, z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L180: */ } } else { if (nounit) { d_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; d_cnjg(&z__3, &ap[k]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__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 ZTPMV */ } /* ztpmv_ */ #ifdef __cplusplus } #endif