| /* zhbmv.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" |
| |
| static inline void d_cnjg(doublecomplex *r, doublecomplex *z) { |
| r->r = z->r; |
| r->i = -(z->i); |
| } |
| |
| /* Subroutine */ void zhbmv_(char *uplo, integer *n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, |
| doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *y, integer *incy) { |
| /* System generated locals */ |
| integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; |
| doublereal d__1; |
| doublecomplex z__1, z__2, z__3, z__4; |
| |
| /* Local variables */ |
| integer i__, j, l, ix, iy, jx, jy, kx, ky, info; |
| doublecomplex temp1, temp2; |
| extern logical lsame_(char *, char *); |
| integer kplus1; |
| extern /* Subroutine */ void xerbla_(const char *, integer *); |
| |
| /* .. Scalar Arguments .. */ |
| /* .. */ |
| /* .. Array Arguments .. */ |
| /* .. */ |
| |
| /* Purpose */ |
| /* ======= */ |
| |
| /* ZHBMV 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*16 . */ |
| /* On entry, ALPHA specifies the scalar alpha. */ |
| /* Unchanged on exit. */ |
| |
| /* A - COMPLEX*16 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*16 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*16 . */ |
| /* On entry, BETA specifies the scalar beta. */ |
| /* Unchanged on exit. */ |
| |
| /* Y - COMPLEX*16 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") && !lsame_(uplo, "L")) { |
| 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_("ZHBMV ", &info); |
| return; |
| } |
| |
| /* Quick return if possible. */ |
| |
| if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.))) { |
| return; |
| } |
| |
| /* 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. || beta->i != 0.) { |
| if (*incy == 1) { |
| if (beta->r == 0. && beta->i == 0.) { |
| i__1 = *n; |
| for (i__ = 1; i__ <= i__1; ++i__) { |
| i__2 = i__; |
| y[i__2].r = 0., y[i__2].i = 0.; |
| /* L10: */ |
| } |
| } else { |
| i__1 = *n; |
| for (i__ = 1; i__ <= i__1; ++i__) { |
| i__2 = i__; |
| i__3 = i__; |
| z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; |
| y[i__2].r = z__1.r, y[i__2].i = z__1.i; |
| /* L20: */ |
| } |
| } |
| } else { |
| iy = ky; |
| if (beta->r == 0. && beta->i == 0.) { |
| i__1 = *n; |
| for (i__ = 1; i__ <= i__1; ++i__) { |
| i__2 = iy; |
| y[i__2].r = 0., y[i__2].i = 0.; |
| iy += *incy; |
| /* L30: */ |
| } |
| } else { |
| i__1 = *n; |
| for (i__ = 1; i__ <= i__1; ++i__) { |
| i__2 = iy; |
| i__3 = iy; |
| z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; |
| y[i__2].r = z__1.r, y[i__2].i = z__1.i; |
| iy += *incy; |
| /* L40: */ |
| } |
| } |
| } |
| } |
| if (alpha->r == 0. && alpha->i == 0.) { |
| return; |
| } |
| if (lsame_(uplo, "U")) { |
| /* 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; |
| z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; |
| temp1.r = z__1.r, temp1.i = z__1.i; |
| temp2.r = 0., temp2.i = 0.; |
| 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; |
| z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; |
| z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; |
| y[i__2].r = z__1.r, y[i__2].i = z__1.i; |
| d_cnjg(&z__3, &a[l + 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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; |
| temp2.r = z__1.r, temp2.i = z__1.i; |
| /* L50: */ |
| } |
| i__4 = j; |
| i__2 = j; |
| i__3 = kplus1 + j * a_dim1; |
| d__1 = a[i__3].r; |
| z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; |
| z__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].i + z__3.i; |
| z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; |
| z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; |
| y[i__4].r = z__1.r, y[i__4].i = z__1.i; |
| /* L60: */ |
| } |
| } else { |
| jx = kx; |
| jy = ky; |
| i__1 = *n; |
| for (j = 1; j <= i__1; ++j) { |
| i__4 = jx; |
| z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, z__1.i = alpha->r * x[i__4].i + alpha->i * x[i__4].r; |
| temp1.r = z__1.r, temp1.i = z__1.i; |
| temp2.r = 0., temp2.i = 0.; |
| 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; |
| z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; |
| z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i; |
| y[i__4].r = z__1.r, y[i__4].i = z__1.i; |
| d_cnjg(&z__3, &a[l + i__ + j * a_dim1]); |
| i__4 = ix; |
| z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i = z__3.r * x[i__4].i + z__3.i * x[i__4].r; |
| z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; |
| temp2.r = z__1.r, temp2.i = z__1.i; |
| ix += *incx; |
| iy += *incy; |
| /* L70: */ |
| } |
| i__3 = jy; |
| i__4 = jy; |
| i__2 = kplus1 + j * a_dim1; |
| d__1 = a[i__2].r; |
| z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; |
| z__2.r = y[i__4].r + z__3.r, z__2.i = y[i__4].i + z__3.i; |
| z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; |
| z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; |
| y[i__3].r = z__1.r, y[i__3].i = z__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; |
| z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i = alpha->r * x[i__3].i + alpha->i * x[i__3].r; |
| temp1.r = z__1.r, temp1.i = z__1.i; |
| temp2.r = 0., temp2.i = 0.; |
| i__3 = j; |
| i__4 = j; |
| i__2 = j * a_dim1 + 1; |
| d__1 = a[i__2].r; |
| z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; |
| z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; |
| y[i__3].r = z__1.r, y[i__3].i = z__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; |
| z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; |
| z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i; |
| y[i__4].r = z__1.r, y[i__4].i = z__1.i; |
| d_cnjg(&z__3, &a[l + i__ + j * a_dim1]); |
| i__4 = i__; |
| z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i = z__3.r * x[i__4].i + z__3.i * x[i__4].r; |
| z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; |
| temp2.r = z__1.r, temp2.i = z__1.i; |
| /* L90: */ |
| } |
| i__3 = j; |
| i__4 = j; |
| z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; |
| z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; |
| y[i__3].r = z__1.r, y[i__3].i = z__1.i; |
| /* L100: */ |
| } |
| } else { |
| jx = kx; |
| jy = ky; |
| i__1 = *n; |
| for (j = 1; j <= i__1; ++j) { |
| i__3 = jx; |
| z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i = alpha->r * x[i__3].i + alpha->i * x[i__3].r; |
| temp1.r = z__1.r, temp1.i = z__1.i; |
| temp2.r = 0., temp2.i = 0.; |
| i__3 = jy; |
| i__4 = jy; |
| i__2 = j * a_dim1 + 1; |
| d__1 = a[i__2].r; |
| z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; |
| z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; |
| y[i__3].r = z__1.r, y[i__3].i = z__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; |
| z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; |
| z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i; |
| y[i__4].r = z__1.r, y[i__4].i = z__1.i; |
| d_cnjg(&z__3, &a[l + i__ + j * a_dim1]); |
| i__4 = ix; |
| z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i = z__3.r * x[i__4].i + z__3.i * x[i__4].r; |
| z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; |
| temp2.r = z__1.r, temp2.i = z__1.i; |
| /* L110: */ |
| } |
| i__3 = jy; |
| i__4 = jy; |
| z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; |
| z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; |
| y[i__3].r = z__1.r, y[i__3].i = z__1.i; |
| jx += *incx; |
| jy += *incy; |
| /* L120: */ |
| } |
| } |
| } |
| |
| /* End of ZHBMV . */ |
| |
| } /* zhbmv_ */ |
