#include "blaswrap.h" #include "f2c.h" doublereal clanhb_(char *norm, char *uplo, integer *n, integer *k, complex * ab, integer *ldab, real *work) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CLANHB 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 hermitian band matrix A, with k super-diagonals. Description =========== CLANHB returns the value CLANHB = ( 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 CLANHB as described above. UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHB is set to zero. K (input) INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB (input) COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need not be set and are assumed to be zero. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK (workspace) REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. ===================================================================== Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4; real ret_val, r__1, r__2, r__3; /* Builtin functions */ double c_abs(complex *), sqrt(doublereal); /* Local variables */ static integer i__, j, l; static real sum, absa, scale; extern logical lsame_(char *, char *); static real value; extern /* Subroutine */ int classq_(integer *, complex *, integer *, real *, real *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --work; /* Function Body */ if (*n == 0) { value = 0.f; } else if (lsame_(norm, "M")) { /* Find max(abs(A(i,j))). */ value = 0.f; 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 */ r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]); value = dmax(r__1,r__2); /* L10: */ } /* Computing MAX */ i__3 = *k + 1 + j * ab_dim1; r__2 = value, r__3 = (r__1 = ab[i__3].r, dabs(r__1)); value = dmax(r__2,r__3); /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__3 = j * ab_dim1 + 1; r__2 = value, r__3 = (r__1 = ab[i__3].r, dabs(r__1)); value = dmax(r__2,r__3); /* 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 */ r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]); value = dmax(r__1,r__2); /* L30: */ } /* L40: */ } } } else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') { /* Find normI(A) ( = norm1(A), since A is hermitian). */ value = 0.f; if (lsame_(uplo, "U")) { i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = 0.f; l = *k + 1 - j; /* Computing MAX */ i__3 = 1, i__2 = j - *k; i__4 = j - 1; for (i__ = max(i__3,i__2); i__ <= i__4; ++i__) { absa = c_abs(&ab[l + i__ + j * ab_dim1]); sum += absa; work[i__] += absa; /* L50: */ } i__4 = *k + 1 + j * ab_dim1; work[j] = sum + (r__1 = ab[i__4].r, dabs(r__1)); /* L60: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ r__1 = value, r__2 = work[i__]; value = dmax(r__1,r__2); /* L70: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.f; /* L80: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { i__4 = j * ab_dim1 + 1; sum = work[j] + (r__1 = ab[i__4].r, dabs(r__1)); l = 1 - j; /* Computing MIN */ i__3 = *n, i__2 = j + *k; i__4 = min(i__3,i__2); for (i__ = j + 1; i__ <= i__4; ++i__) { absa = c_abs(&ab[l + i__ + j * ab_dim1]); sum += absa; work[i__] += absa; /* L90: */ } value = dmax(value,sum); /* L100: */ } } } else if (lsame_(norm, "F") || lsame_(norm, "E")) { /* Find normF(A). */ scale = 0.f; sum = 1.f; if (*k > 0) { if (lsame_(uplo, "U")) { i__1 = *n; for (j = 2; j <= i__1; ++j) { /* Computing MIN */ i__3 = j - 1; i__4 = min(i__3,*k); /* Computing MAX */ i__2 = *k + 2 - j; classq_(&i__4, &ab[max(i__2,1) + j * ab_dim1], &c__1, & scale, &sum); /* L110: */ } l = *k + 1; } else { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__3 = *n - j; i__4 = min(i__3,*k); classq_(&i__4, &ab[j * ab_dim1 + 2], &c__1, &scale, &sum); /* L120: */ } l = 1; } sum *= 2; } else { l = 1; } i__1 = *n; for (j = 1; j <= i__1; ++j) { i__4 = l + j * ab_dim1; if (ab[i__4].r != 0.f) { i__4 = l + j * ab_dim1; absa = (r__1 = ab[i__4].r, dabs(r__1)); if (scale < absa) { /* Computing 2nd power */ r__1 = scale / absa; sum = sum * (r__1 * r__1) + 1.f; scale = absa; } else { /* Computing 2nd power */ r__1 = absa / scale; sum += r__1 * r__1; } } /* L130: */ } value = scale * sqrt(sum); } ret_val = value; return ret_val; /* End of CLANHB */ } /* clanhb_ */