|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER NORM, UPLO 00010 INTEGER LDA, N 00011 * .. 00012 * .. Array Arguments .. 00013 REAL WORK( * ) 00014 COMPLEX A( LDA, * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CLANHE returns the value of the one norm, or the Frobenius norm, or 00021 * the infinity norm, or the element of largest absolute value of a 00022 * complex hermitian matrix A. 00023 * 00024 * Description 00025 * =========== 00026 * 00027 * CLANHE returns the value 00028 * 00029 * CLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00030 * ( 00031 * ( norm1(A), NORM = '1', 'O' or 'o' 00032 * ( 00033 * ( normI(A), NORM = 'I' or 'i' 00034 * ( 00035 * ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00036 * 00037 * where norm1 denotes the one norm of a matrix (maximum column sum), 00038 * normI denotes the infinity norm of a matrix (maximum row sum) and 00039 * normF denotes the Frobenius norm of a matrix (square root of sum of 00040 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. 00041 * 00042 * Arguments 00043 * ========= 00044 * 00045 * NORM (input) CHARACTER*1 00046 * Specifies the value to be returned in CLANHE as described 00047 * above. 00048 * 00049 * UPLO (input) CHARACTER*1 00050 * Specifies whether the upper or lower triangular part of the 00051 * hermitian matrix A is to be referenced. 00052 * = 'U': Upper triangular part of A is referenced 00053 * = 'L': Lower triangular part of A is referenced 00054 * 00055 * N (input) INTEGER 00056 * The order of the matrix A. N >= 0. When N = 0, CLANHE is 00057 * set to zero. 00058 * 00059 * A (input) COMPLEX array, dimension (LDA,N) 00060 * The hermitian matrix A. If UPLO = 'U', the leading n by n 00061 * upper triangular part of A contains the upper triangular part 00062 * of the matrix A, and the strictly lower triangular part of A 00063 * is not referenced. If UPLO = 'L', the leading n by n lower 00064 * triangular part of A contains the lower triangular part of 00065 * the matrix A, and the strictly upper triangular part of A is 00066 * not referenced. Note that the imaginary parts of the diagonal 00067 * elements need not be set and are assumed to be zero. 00068 * 00069 * LDA (input) INTEGER 00070 * The leading dimension of the array A. LDA >= max(N,1). 00071 * 00072 * WORK (workspace) REAL array, dimension (MAX(1,LWORK)), 00073 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00074 * WORK is not referenced. 00075 * 00076 * ===================================================================== 00077 * 00078 * .. Parameters .. 00079 REAL ONE, ZERO 00080 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00081 * .. 00082 * .. Local Scalars .. 00083 INTEGER I, J 00084 REAL ABSA, SCALE, SUM, VALUE 00085 * .. 00086 * .. External Functions .. 00087 LOGICAL LSAME 00088 EXTERNAL LSAME 00089 * .. 00090 * .. External Subroutines .. 00091 EXTERNAL CLASSQ 00092 * .. 00093 * .. Intrinsic Functions .. 00094 INTRINSIC ABS, MAX, REAL, SQRT 00095 * .. 00096 * .. Executable Statements .. 00097 * 00098 IF( N.EQ.0 ) THEN 00099 VALUE = ZERO 00100 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00101 * 00102 * Find max(abs(A(i,j))). 00103 * 00104 VALUE = ZERO 00105 IF( LSAME( UPLO, 'U' ) ) THEN 00106 DO 20 J = 1, N 00107 DO 10 I = 1, J - 1 00108 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00109 10 CONTINUE 00110 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) ) 00111 20 CONTINUE 00112 ELSE 00113 DO 40 J = 1, N 00114 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) ) 00115 DO 30 I = J + 1, N 00116 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00117 30 CONTINUE 00118 40 CONTINUE 00119 END IF 00120 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00121 $ ( NORM.EQ.'1' ) ) THEN 00122 * 00123 * Find normI(A) ( = norm1(A), since A is hermitian). 00124 * 00125 VALUE = ZERO 00126 IF( LSAME( UPLO, 'U' ) ) THEN 00127 DO 60 J = 1, N 00128 SUM = ZERO 00129 DO 50 I = 1, J - 1 00130 ABSA = ABS( A( I, J ) ) 00131 SUM = SUM + ABSA 00132 WORK( I ) = WORK( I ) + ABSA 00133 50 CONTINUE 00134 WORK( J ) = SUM + ABS( REAL( A( J, J ) ) ) 00135 60 CONTINUE 00136 DO 70 I = 1, N 00137 VALUE = MAX( VALUE, WORK( I ) ) 00138 70 CONTINUE 00139 ELSE 00140 DO 80 I = 1, N 00141 WORK( I ) = ZERO 00142 80 CONTINUE 00143 DO 100 J = 1, N 00144 SUM = WORK( J ) + ABS( REAL( A( J, J ) ) ) 00145 DO 90 I = J + 1, N 00146 ABSA = ABS( A( I, J ) ) 00147 SUM = SUM + ABSA 00148 WORK( I ) = WORK( I ) + ABSA 00149 90 CONTINUE 00150 VALUE = MAX( VALUE, SUM ) 00151 100 CONTINUE 00152 END IF 00153 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00154 * 00155 * Find normF(A). 00156 * 00157 SCALE = ZERO 00158 SUM = ONE 00159 IF( LSAME( UPLO, 'U' ) ) THEN 00160 DO 110 J = 2, N 00161 CALL CLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) 00162 110 CONTINUE 00163 ELSE 00164 DO 120 J = 1, N - 1 00165 CALL CLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) 00166 120 CONTINUE 00167 END IF 00168 SUM = 2*SUM 00169 DO 130 I = 1, N 00170 IF( REAL( A( I, I ) ).NE.ZERO ) THEN 00171 ABSA = ABS( REAL( A( I, I ) ) ) 00172 IF( SCALE.LT.ABSA ) THEN 00173 SUM = ONE + SUM*( SCALE / ABSA )**2 00174 SCALE = ABSA 00175 ELSE 00176 SUM = SUM + ( ABSA / SCALE )**2 00177 END IF 00178 END IF 00179 130 CONTINUE 00180 VALUE = SCALE*SQRT( SUM ) 00181 END IF 00182 * 00183 CLANHE = VALUE 00184 RETURN 00185 * 00186 * End of CLANHE 00187 * 00188 END
1.7.3 
