/* ztrsv.f -- translated by f2c (version 20061008). 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 "f2c.h" #include "blaswrap.h" /* Subroutine */ int ztrsv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *a, integer *lda, doublecomplex *x, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); logical noconj, nounit; /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZTRSV solves one of the systems of equations */ /* A*x = b, or A'*x = b, or conjg( A' )*x = b, */ /* where b and x are n element vectors and A is an n by n unit, or */ /* non-unit, upper or lower triangular matrix. */ /* No test for singularity or near-singularity is included in this */ /* routine. Such tests must be performed before calling this routine. */ /* 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 equations to be solved as */ /* follows: */ /* TRANS = 'N' or 'n' A*x = b. */ /* TRANS = 'T' or 't' A'*x = b. */ /* TRANS = 'C' or 'c' conjg( A' )*x = b. */ /* 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. */ /* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */ /* Before entry with UPLO = 'U' or 'u', the leading n by n */ /* upper triangular part of the array A must contain the upper */ /* triangular matrix and the strictly lower triangular part of */ /* A is not referenced. */ /* Before entry with UPLO = 'L' or 'l', the leading n by n */ /* lower triangular part of the array A must contain the lower */ /* triangular matrix and the strictly upper triangular part of */ /* A is not referenced. */ /* Note that when DIAG = 'U' or 'u', the diagonal elements of */ /* A are not referenced either, 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 */ /* max( 1, n ). */ /* Unchanged on exit. */ /* X - COMPLEX*16 array of dimension at least */ /* ( 1 + ( n - 1 )*abs( INCX ) ). */ /* Before entry, the incremented array X must contain the n */ /* element right-hand side vector b. On exit, X is overwritten */ /* with the solution 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. */ /* .. 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") && ! 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 (*lda < max(1,*n)) { info = 6; } else if (*incx == 0) { info = 8; } if (info != 0) { xerbla_("ZTRSV ", &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 A are */ /* accessed sequentially with one pass through A. */ if (lsame_(trans, "N")) { /* Form x := inv( A )*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = j; z_div(&z__1, &x[j], &a[j + j * a_dim1]); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; for (i__ = j - 1; i__ >= 1; --i__) { i__1 = i__; i__2 = i__; i__3 = i__ + j * a_dim1; z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, z__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - z__2.i; x[i__1].r = z__1.r, x[i__1].i = z__1.i; /* L10: */ } } /* L20: */ } } else { jx = kx + (*n - 1) * *incx; for (j = *n; j >= 1; --j) { i__1 = jx; if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = jx; z_div(&z__1, &x[jx], &a[j + j * a_dim1]); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = jx; for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; i__1 = ix; i__2 = ix; i__3 = i__ + j * a_dim1; z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, z__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - z__2.i; x[i__1].r = z__1.r, x[i__1].i = z__1.i; /* L30: */ } } jx -= *incx; /* L40: */ } } } else { 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.) { if (nounit) { i__2 = j; z_div(&z__1, &x[j], &a[j + j * a_dim1]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__ + j * a_dim1; z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ 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; /* L50: */ } } /* L60: */ } } 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.) { if (nounit) { i__2 = jx; z_div(&z__1, &x[jx], &a[j + j * a_dim1]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = jx; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; i__3 = ix; i__4 = ix; i__5 = i__ + j * a_dim1; z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ 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; /* L70: */ } } jx += *incx; /* L80: */ } } } } else { /* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. */ if (lsame_(uplo, "U")) { 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; if (noconj) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[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; /* L90: */ } if (nounit) { z_div(&z__1, &temp, &a[j + j * a_dim1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a[i__ + j * a_dim1]); 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; /* L100: */ } if (nounit) { d_cnjg(&z__2, &a[j + j * a_dim1]); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; /* L110: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { ix = kx; i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; if (noconj) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = ix; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[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; ix += *incx; /* L120: */ } if (nounit) { z_div(&z__1, &temp, &a[j + j * a_dim1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a[i__ + j * a_dim1]); 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; ix += *incx; /* L130: */ } if (nounit) { d_cnjg(&z__2, &a[j + j * a_dim1]); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; /* L140: */ } } } else { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; if (noconj) { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = i__ + j * a_dim1; i__3 = i__; z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, z__2.i = a[i__2].r * x[i__3].i + a[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; /* L150: */ } if (nounit) { z_div(&z__1, &temp, &a[j + j * a_dim1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { d_cnjg(&z__3, &a[i__ + j * a_dim1]); i__2 = i__; 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; /* L160: */ } if (nounit) { d_cnjg(&z__2, &a[j + j * a_dim1]); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; /* L170: */ } } else { kx += (*n - 1) * *incx; jx = kx; for (j = *n; j >= 1; --j) { ix = kx; i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; if (noconj) { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = i__ + j * a_dim1; i__3 = ix; z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, z__2.i = a[i__2].r * x[i__3].i + a[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; ix -= *incx; /* L180: */ } if (nounit) { z_div(&z__1, &temp, &a[j + j * a_dim1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { d_cnjg(&z__3, &a[i__ + j * a_dim1]); 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; ix -= *incx; /* L190: */ } if (nounit) { d_cnjg(&z__2, &a[j + j * a_dim1]); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; /* L200: */ } } } } return 0; /* End of ZTRSV . */ } /* ztrsv_ */