dlantb.c

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/* dlantb.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"

/* Table of constant values */

static integer c__1 = 1;

doublereal dlantb_(char *norm, char *uplo, char *diag, integer *n, integer *k, 
         doublereal *ab, integer *ldab, doublereal *work)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal ret_val, d__1, d__2, d__3;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__, j, l;
    doublereal sum, scale;
    logical udiag;
    extern logical lsame_(char *, char *);
    doublereal value;
    extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, 
            doublereal *, doublereal *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DLANTB  returns the value of the one norm,  or the Frobenius norm, or */
/*  the  infinity norm,  or the element of  largest absolute value  of an */
/*  n by n triangular band matrix A,  with ( k + 1 ) diagonals. */

/*  Description */
/*  =========== */

/*  DLANTB returns the value */

/*     DLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
/*              ( */
/*              ( norm1(A),         NORM = '1', 'O' or 'o' */
/*              ( */
/*              ( normI(A),         NORM = 'I' or 'i' */
/*              ( */
/*              ( normF(A),         NORM = 'F', 'f', 'E' or 'e' */

/*  where  norm1  denotes the  one norm of a matrix (maximum column sum), */
/*  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and */
/*  normF  denotes the  Frobenius norm of a matrix (square root of sum of */
/*  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm. */

/*  Arguments */
/*  ========= */

/*  NORM    (input) CHARACTER*1 */
/*          Specifies the value to be returned in DLANTB as described */
/*          above. */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the matrix A is upper or lower triangular. */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  DIAG    (input) CHARACTER*1 */
/*          Specifies whether or not the matrix A is unit triangular. */
/*          = 'N':  Non-unit triangular */
/*          = 'U':  Unit triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0.  When N = 0, DLANTB is */
/*          set to zero. */

/*  K       (input) INTEGER */
/*          The number of super-diagonals of the matrix A if UPLO = 'U', */
/*          or the number of sub-diagonals of the matrix A if UPLO = 'L'. */
/*          K >= 0. */

/*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          The upper or lower triangular band matrix A, stored in the */
/*          first k+1 rows of AB.  The j-th column of A is stored */
/*          in the j-th column of the array AB as follows: */
/*          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k). */
/*          Note that when DIAG = 'U', the elements of the array AB */
/*          corresponding to the diagonal elements of the matrix A are */
/*          not referenced, but are assumed to be one. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= K+1. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/*          where LWORK >= N when NORM = 'I'; otherwise, WORK is not */
/*          referenced. */

/* ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --work;

    /* Function Body */
    if (*n == 0) {
        value = 0.;
    } else if (lsame_(norm, "M")) {

/*        Find max(abs(A(i,j))). */

        if (lsame_(diag, "U")) {
            value = 1.;
            if (lsame_(uplo, "U")) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
                    i__2 = *k + 2 - j;
                    i__3 = *k;
                    for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
                        d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1], 
                                abs(d__1));
                        value = max(d__2,d__3);
/* L10: */
                    }
/* L20: */
                }
            } else {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__2 = *n + 1 - j, i__4 = *k + 1;
                    i__3 = min(i__2,i__4);
                    for (i__ = 2; i__ <= i__3; ++i__) {
/* Computing MAX */
                        d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1], 
                                abs(d__1));
                        value = max(d__2,d__3);
/* L30: */
                    }
/* L40: */
                }
            }
        } else {
            value = 0.;
            if (lsame_(uplo, "U")) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
                    i__3 = *k + 2 - j;
                    i__2 = *k + 1;
                    for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
/* Computing MAX */
                        d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1], 
                                abs(d__1));
                        value = max(d__2,d__3);
/* L50: */
                    }
/* L60: */
                }
            } else {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__3 = *n + 1 - j, i__4 = *k + 1;
                    i__2 = min(i__3,i__4);
                    for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
                        d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1], 
                                abs(d__1));
                        value = max(d__2,d__3);
/* L70: */
                    }
/* L80: */
                }
            }
        }
    } else if (lsame_(norm, "O") || *(unsigned char *)
            norm == '1') {

/*        Find norm1(A). */

        value = 0.;
        udiag = lsame_(diag, "U");
        if (lsame_(uplo, "U")) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (udiag) {
                    sum = 1.;
/* Computing MAX */
                    i__2 = *k + 2 - j;
                    i__3 = *k;
                    for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
                        sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L90: */
                    }
                } else {
                    sum = 0.;
/* Computing MAX */
                    i__3 = *k + 2 - j;
                    i__2 = *k + 1;
                    for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
                        sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L100: */
                    }
                }
                value = max(value,sum);
/* L110: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (udiag) {
                    sum = 1.;
/* Computing MIN */
                    i__3 = *n + 1 - j, i__4 = *k + 1;
                    i__2 = min(i__3,i__4);
                    for (i__ = 2; i__ <= i__2; ++i__) {
                        sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L120: */
                    }
                } else {
                    sum = 0.;
/* Computing MIN */
                    i__3 = *n + 1 - j, i__4 = *k + 1;
                    i__2 = min(i__3,i__4);
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L130: */
                    }
                }
                value = max(value,sum);
/* L140: */
            }
        }
    } else if (lsame_(norm, "I")) {

/*        Find normI(A). */

        value = 0.;
        if (lsame_(uplo, "U")) {
            if (lsame_(diag, "U")) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 1.;
/* L150: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    l = *k + 1 - 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__) {
                        work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
                                d__1));
/* L160: */
                    }
/* L170: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 0.;
/* L180: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    l = *k + 1 - j;
/* Computing MAX */
                    i__4 = 1, i__2 = j - *k;
                    i__3 = j;
                    for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
                        work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
                                d__1));
/* L190: */
                    }
/* L200: */
                }
            }
        } else {
            if (lsame_(diag, "U")) {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 1.;
/* L210: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    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__) {
                        work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
                                d__1));
/* L220: */
                    }
/* L230: */
                }
            } else {
                i__1 = *n;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    work[i__] = 0.;
/* L240: */
                }
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    l = 1 - j;
/* Computing MIN */
                    i__4 = *n, i__2 = j + *k;
                    i__3 = min(i__4,i__2);
                    for (i__ = j; i__ <= i__3; ++i__) {
                        work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
                                d__1));
/* L250: */
                    }
/* L260: */
                }
            }
        }
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
            d__1 = value, d__2 = work[i__];
            value = max(d__1,d__2);
/* L270: */
        }
    } else if (lsame_(norm, "F") || lsame_(norm, "E")) {

/*        Find normF(A). */

        if (lsame_(uplo, "U")) {
            if (lsame_(diag, "U")) {
                scale = 1.;
                sum = (doublereal) (*n);
                if (*k > 0) {
                    i__1 = *n;
                    for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
                        i__4 = j - 1;
                        i__3 = min(i__4,*k);
/* Computing MAX */
                        i__2 = *k + 2 - j;
                        dlassq_(&i__3, &ab[max(i__2, 1)+ j * ab_dim1], &c__1, 
                                &scale, &sum);
/* L280: */
                    }
                }
            } else {
                scale = 0.;
                sum = 1.;
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__4 = j, i__2 = *k + 1;
                    i__3 = min(i__4,i__2);
/* Computing MAX */
                    i__5 = *k + 2 - j;
                    dlassq_(&i__3, &ab[max(i__5, 1)+ j * ab_dim1], &c__1, &
                            scale, &sum);
/* L290: */
                }
            }
        } else {
            if (lsame_(diag, "U")) {
                scale = 1.;
                sum = (doublereal) (*n);
                if (*k > 0) {
                    i__1 = *n - 1;
                    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                        i__4 = *n - j;
                        i__3 = min(i__4,*k);
                        dlassq_(&i__3, &ab[j * ab_dim1 + 2], &c__1, &scale, &
                                sum);
/* L300: */
                    }
                }
            } else {
                scale = 0.;
                sum = 1.;
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__4 = *n - j + 1, i__2 = *k + 1;
                    i__3 = min(i__4,i__2);
                    dlassq_(&i__3, &ab[j * ab_dim1 + 1], &c__1, &scale, &sum);
/* L310: */
                }
            }
        }
        value = scale * sqrt(sum);
    }

    ret_val = value;
    return ret_val;

/*     End of DLANTB */

} /* dlantb_ */