/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Subroutine */ int zgbmv_(char *trans, integer *m, integer *n, integer *kl, integer *ku, 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, i__6; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer lenx, leny, i, j, k; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj; static integer kup1; /* Purpose ======= ZGBMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals. Parameters ========== TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A'*x + beta*y. TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. KL - INTEGER. On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. Unchanged on exit. KU - INTEGER. On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. 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, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE 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 ( kl + ku + 1 ). Unchanged on exit. X - COMPLEX*16 array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. 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. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. Y - COMPLEX*16 array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. 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. 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 Function Body */ #define X(I) x[(I)-1] #define Y(I) y[(I)-1] #define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)] info = 0; if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 1; } else if (*m < 0) { info = 2; } else if (*n < 0) { info = 3; } else if (*kl < 0) { info = 4; } else if (*ku < 0) { info = 5; } else if (*lda < *kl + *ku + 1) { info = 8; } else if (*incx == 0) { info = 10; } else if (*incy == 0) { info = 13; } if (info != 0) { xerbla_("ZGBMV ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.)) { return 0; } noconj = lsame_(trans, "T"); /* Set LENX and LENY, the lengths of the vectors x and y, and set up the start points in X and Y. */ if (lsame_(trans, "N")) { lenx = *n; leny = *m; } else { lenx = *m; leny = *n; } if (*incx > 0) { kx = 1; } else { kx = 1 - (lenx - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (leny - 1) * *incy; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through the band part of 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 = leny; for (i = 1; i <= leny; ++i) { i__2 = i; Y(i).r = 0., Y(i).i = 0.; /* L10: */ } } else { i__1 = leny; for (i = 1; i <= leny; ++i) { i__2 = i; i__3 = i; z__1.r = beta->r * Y(i).r - beta->i * Y(i).i, z__1.i = beta->r * Y(i).i + beta->i * Y(i) .r; Y(i).r = z__1.r, Y(i).i = z__1.i; /* L20: */ } } } else { iy = ky; if (beta->r == 0. && beta->i == 0.) { i__1 = leny; for (i = 1; i <= leny; ++i) { i__2 = iy; Y(iy).r = 0., Y(iy).i = 0.; iy += *incy; /* L30: */ } } else { i__1 = leny; for (i = 1; i <= leny; ++i) { i__2 = iy; i__3 = iy; z__1.r = beta->r * Y(iy).r - beta->i * Y(iy).i, z__1.i = beta->r * Y(iy).i + beta->i * Y(iy) .r; Y(iy).r = z__1.r, Y(iy).i = z__1.i; iy += *incy; /* L40: */ } } } } if (alpha->r == 0. && alpha->i == 0.) { return 0; } kup1 = *ku + 1; if (lsame_(trans, "N")) { /* Form y := alpha*A*x + y. */ jx = kx; if (*incy == 1) { i__1 = *n; for (j = 1; j <= *n; ++j) { i__2 = jx; if (X(jx).r != 0. || X(jx).i != 0.) { i__2 = jx; z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i = alpha->r * X(jx).i + alpha->i * X(jx) .r; temp.r = z__1.r, temp.i = z__1.i; k = kup1 - j; /* Computing MAX */ i__2 = 1, i__3 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__4 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { i__2 = i; i__3 = i; i__5 = k + i + j * a_dim1; z__2.r = temp.r * A(k+i,j).r - temp.i * A(k+i,j).i, z__2.i = temp.r * A(k+i,j).i + temp.i * A(k+i,j) .r; z__1.r = Y(i).r + z__2.r, z__1.i = Y(i).i + z__2.i; Y(i).r = z__1.r, Y(i).i = z__1.i; /* L50: */ } } jx += *incx; /* L60: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { i__4 = jx; if (X(jx).r != 0. || X(jx).i != 0.) { i__4 = jx; z__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, z__1.i = alpha->r * X(jx).i + alpha->i * X(jx) .r; temp.r = z__1.r, temp.i = z__1.i; iy = ky; k = kup1 - j; /* Computing MAX */ i__4 = 1, i__2 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__3 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { i__4 = iy; i__2 = iy; i__5 = k + i + j * a_dim1; z__2.r = temp.r * A(k+i,j).r - temp.i * A(k+i,j).i, z__2.i = temp.r * A(k+i,j).i + temp.i * A(k+i,j) .r; z__1.r = Y(iy).r + z__2.r, z__1.i = Y(iy).i + z__2.i; Y(iy).r = z__1.r, Y(iy).i = z__1.i; iy += *incy; /* L70: */ } } jx += *incx; if (j > *ku) { ky += *incy; } /* L80: */ } } } else { /* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */ jy = ky; if (*incx == 1) { i__1 = *n; for (j = 1; j <= *n; ++j) { temp.r = 0., temp.i = 0.; k = kup1 - j; if (noconj) { /* Computing MAX */ i__3 = 1, i__4 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__2 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { i__3 = k + i + j * a_dim1; i__4 = i; z__2.r = A(k+i,j).r * X(i).r - A(k+i,j).i * X(i) .i, z__2.i = A(k+i,j).r * X(i).i + A(k+i,j) .i * X(i).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: */ } } else { /* Computing MAX */ i__2 = 1, i__3 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__4 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { d_cnjg(&z__3, &A(k+i,j)); i__2 = i; z__2.r = z__3.r * X(i).r - z__3.i * X(i).i, z__2.i = z__3.r * X(i).i + z__3.i * X(i) .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: */ } } i__4 = jy; i__2 = jy; z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = Y(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i; Y(jy).r = z__1.r, Y(jy).i = z__1.i; jy += *incy; /* L110: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { temp.r = 0., temp.i = 0.; ix = kx; k = kup1 - j; if (noconj) { /* Computing MAX */ i__4 = 1, i__2 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__3 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { i__4 = k + i + j * a_dim1; i__2 = ix; z__2.r = A(k+i,j).r * X(ix).r - A(k+i,j).i * X(ix) .i, z__2.i = A(k+i,j).r * X(ix).i + A(k+i,j) .i * X(ix).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: */ } } else { /* Computing MAX */ i__3 = 1, i__4 = j - *ku; /* Computing MIN */ i__5 = *m, i__6 = j + *kl; i__2 = min(i__5,i__6); for (i = max(1,j-*ku); i <= min(*m,j+*kl); ++i) { d_cnjg(&z__3, &A(k+i,j)); i__3 = ix; z__2.r = z__3.r * X(ix).r - z__3.i * X(ix).i, z__2.i = z__3.r * X(ix).i + z__3.i * X(ix) .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: */ } } i__2 = jy; i__3 = jy; z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = Y(jy).r + z__2.r, z__1.i = Y(jy).i + z__2.i; Y(jy).r = z__1.r, Y(jy).i = z__1.i; jy += *incy; if (j > *ku) { kx += *incx; } /* L140: */ } } } return 0; /* End of ZGBMV . */ } /* zgbmv_ */