| /* dtbmv.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" |
| |
| /* Subroutine */ void dtbmv_(char *uplo, char *trans, char *diag, integer *n, integer *k, doublereal *a, integer *lda, |
| doublereal *x, integer *incx) { |
| /* System generated locals */ |
| integer a_dim1, a_offset, i__1, i__2, i__3, i__4; |
| |
| /* Local variables */ |
| integer i__, j, l, ix, jx, kx, info; |
| doublereal temp; |
| extern logical lsame_(char *, char *); |
| integer kplus1; |
| extern /* Subroutine */ void xerbla_(const char *, integer *); |
| logical nounit; |
| |
| /* .. Scalar Arguments .. */ |
| /* .. */ |
| /* .. Array Arguments .. */ |
| /* .. */ |
| |
| /* Purpose */ |
| /* ======= */ |
| |
| /* DTBMV performs one of the matrix-vector operations */ |
| |
| /* x := A*x, or x := A'*x, */ |
| |
| /* where x is an n element vector and A is an n by n unit, or non-unit, */ |
| /* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */ |
| |
| /* 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 := 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. */ |
| |
| /* K - INTEGER. */ |
| /* On entry with UPLO = 'U' or 'u', K specifies the number of */ |
| /* super-diagonals of the matrix A. */ |
| /* On entry with UPLO = 'L' or 'l', K specifies the number of */ |
| /* sub-diagonals of the matrix A. */ |
| /* K must satisfy 0 .le. K. */ |
| /* Unchanged on exit. */ |
| |
| /* A - DOUBLE PRECISION 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 matrix of coefficients, 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 an upper */ |
| /* triangular 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 matrix of coefficients, 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 a lower */ |
| /* triangular 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 when DIAG = 'U' or 'u' the elements of the array A */ |
| /* corresponding to the diagonal elements of the matrix are not */ |
| /* referenced, 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 */ |
| /* ( k + 1 ). */ |
| /* Unchanged on exit. */ |
| |
| /* X - DOUBLE PRECISION 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 */ |
| /* transformed vector x. */ |
| |
| /* INCX - INTEGER. */ |
| /* On entry, INCX specifies the increment for the elements of */ |
| /* X. INCX 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; |
| |
| /* 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 (*k < 0) { |
| info = 5; |
| } else if (*lda < *k + 1) { |
| info = 7; |
| } else if (*incx == 0) { |
| info = 9; |
| } |
| if (info != 0) { |
| xerbla_("DTBMV ", &info); |
| return; |
| } |
| |
| /* Quick return if possible. */ |
| |
| if (*n == 0) { |
| return; |
| } |
| |
| 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 := A*x. */ |
| |
| if (lsame_(uplo, "U")) { |
| kplus1 = *k + 1; |
| if (*incx == 1) { |
| i__1 = *n; |
| for (j = 1; j <= i__1; ++j) { |
| if (x[j] != 0.) { |
| temp = x[j]; |
| 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__) { |
| x[i__] += temp * a[l + i__ + j * a_dim1]; |
| /* L10: */ |
| } |
| if (nounit) { |
| x[j] *= a[kplus1 + j * a_dim1]; |
| } |
| } |
| /* L20: */ |
| } |
| } else { |
| jx = kx; |
| i__1 = *n; |
| for (j = 1; j <= i__1; ++j) { |
| if (x[jx] != 0.) { |
| temp = x[jx]; |
| ix = kx; |
| 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__) { |
| x[ix] += temp * a[l + i__ + j * a_dim1]; |
| ix += *incx; |
| /* L30: */ |
| } |
| if (nounit) { |
| x[jx] *= a[kplus1 + j * a_dim1]; |
| } |
| } |
| jx += *incx; |
| if (j > *k) { |
| kx += *incx; |
| } |
| /* L40: */ |
| } |
| } |
| } else { |
| if (*incx == 1) { |
| for (j = *n; j >= 1; --j) { |
| if (x[j] != 0.) { |
| temp = x[j]; |
| l = 1 - j; |
| /* Computing MIN */ |
| i__1 = *n, i__3 = j + *k; |
| i__4 = j + 1; |
| for (i__ = min(i__1, i__3); i__ >= i__4; --i__) { |
| x[i__] += temp * a[l + i__ + j * a_dim1]; |
| /* L50: */ |
| } |
| if (nounit) { |
| x[j] *= a[j * a_dim1 + 1]; |
| } |
| } |
| /* L60: */ |
| } |
| } else { |
| kx += (*n - 1) * *incx; |
| jx = kx; |
| for (j = *n; j >= 1; --j) { |
| if (x[jx] != 0.) { |
| temp = x[jx]; |
| ix = kx; |
| l = 1 - j; |
| /* Computing MIN */ |
| i__4 = *n, i__1 = j + *k; |
| i__3 = j + 1; |
| for (i__ = min(i__4, i__1); i__ >= i__3; --i__) { |
| x[ix] += temp * a[l + i__ + j * a_dim1]; |
| ix -= *incx; |
| /* L70: */ |
| } |
| if (nounit) { |
| x[jx] *= a[j * a_dim1 + 1]; |
| } |
| } |
| jx -= *incx; |
| if (*n - j >= *k) { |
| kx -= *incx; |
| } |
| /* L80: */ |
| } |
| } |
| } |
| } else { |
| /* Form x := A'*x. */ |
| |
| if (lsame_(uplo, "U")) { |
| kplus1 = *k + 1; |
| if (*incx == 1) { |
| for (j = *n; j >= 1; --j) { |
| temp = x[j]; |
| l = kplus1 - j; |
| if (nounit) { |
| temp *= a[kplus1 + j * a_dim1]; |
| } |
| /* Computing MAX */ |
| i__4 = 1, i__1 = j - *k; |
| i__3 = max(i__4, i__1); |
| for (i__ = j - 1; i__ >= i__3; --i__) { |
| temp += a[l + i__ + j * a_dim1] * x[i__]; |
| /* L90: */ |
| } |
| x[j] = temp; |
| /* L100: */ |
| } |
| } else { |
| kx += (*n - 1) * *incx; |
| jx = kx; |
| for (j = *n; j >= 1; --j) { |
| temp = x[jx]; |
| kx -= *incx; |
| ix = kx; |
| l = kplus1 - j; |
| if (nounit) { |
| temp *= a[kplus1 + j * a_dim1]; |
| } |
| /* Computing MAX */ |
| i__4 = 1, i__1 = j - *k; |
| i__3 = max(i__4, i__1); |
| for (i__ = j - 1; i__ >= i__3; --i__) { |
| temp += a[l + i__ + j * a_dim1] * x[ix]; |
| ix -= *incx; |
| /* L110: */ |
| } |
| x[jx] = temp; |
| jx -= *incx; |
| /* L120: */ |
| } |
| } |
| } else { |
| if (*incx == 1) { |
| i__3 = *n; |
| for (j = 1; j <= i__3; ++j) { |
| temp = x[j]; |
| l = 1 - j; |
| if (nounit) { |
| temp *= a[j * a_dim1 + 1]; |
| } |
| /* Computing MIN */ |
| i__1 = *n, i__2 = j + *k; |
| i__4 = min(i__1, i__2); |
| for (i__ = j + 1; i__ <= i__4; ++i__) { |
| temp += a[l + i__ + j * a_dim1] * x[i__]; |
| /* L130: */ |
| } |
| x[j] = temp; |
| /* L140: */ |
| } |
| } else { |
| jx = kx; |
| i__3 = *n; |
| for (j = 1; j <= i__3; ++j) { |
| temp = x[jx]; |
| kx += *incx; |
| ix = kx; |
| l = 1 - j; |
| if (nounit) { |
| temp *= a[j * a_dim1 + 1]; |
| } |
| /* Computing MIN */ |
| i__1 = *n, i__2 = j + *k; |
| i__4 = min(i__1, i__2); |
| for (i__ = j + 1; i__ <= i__4; ++i__) { |
| temp += a[l + i__ + j * a_dim1] * x[ix]; |
| ix += *incx; |
| /* L150: */ |
| } |
| x[jx] = temp; |
| jx += *incx; |
| /* L160: */ |
| } |
| } |
| } |
| } |
| |
| /* End of DTBMV . */ |
| |
| } /* dtbmv_ */ |
