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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 REAL FUNCTION CLANSP( NORM, UPLO, N, AP, 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 N 00011 * .. 00012 * .. Array Arguments .. 00013 REAL WORK( * ) 00014 COMPLEX AP( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CLANSP 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 symmetric matrix A, supplied in packed form. 00023 * 00024 * Description 00025 * =========== 00026 * 00027 * CLANSP returns the value 00028 * 00029 * CLANSP = ( 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 CLANSP as described 00047 * above. 00048 * 00049 * UPLO (input) CHARACTER*1 00050 * Specifies whether the upper or lower triangular part of the 00051 * symmetric matrix A is supplied. 00052 * = 'U': Upper triangular part of A is supplied 00053 * = 'L': Lower triangular part of A is supplied 00054 * 00055 * N (input) INTEGER 00056 * The order of the matrix A. N >= 0. When N = 0, CLANSP is 00057 * set to zero. 00058 * 00059 * AP (input) COMPLEX array, dimension (N*(N+1)/2) 00060 * The upper or lower triangle of the symmetric matrix A, packed 00061 * columnwise in a linear array. The j-th column of A is stored 00062 * in the array AP as follows: 00063 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00064 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00065 * 00066 * WORK (workspace) REAL array, dimension (MAX(1,LWORK)), 00067 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00068 * WORK is not referenced. 00069 * 00070 * ===================================================================== 00071 * 00072 * .. Parameters .. 00073 REAL ONE, ZERO 00074 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00075 * .. 00076 * .. Local Scalars .. 00077 INTEGER I, J, K 00078 REAL ABSA, SCALE, SUM, VALUE 00079 * .. 00080 * .. External Functions .. 00081 LOGICAL LSAME 00082 EXTERNAL LSAME 00083 * .. 00084 * .. External Subroutines .. 00085 EXTERNAL CLASSQ 00086 * .. 00087 * .. Intrinsic Functions .. 00088 INTRINSIC ABS, AIMAG, MAX, REAL, SQRT 00089 * .. 00090 * .. Executable Statements .. 00091 * 00092 IF( N.EQ.0 ) THEN 00093 VALUE = ZERO 00094 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00095 * 00096 * Find max(abs(A(i,j))). 00097 * 00098 VALUE = ZERO 00099 IF( LSAME( UPLO, 'U' ) ) THEN 00100 K = 1 00101 DO 20 J = 1, N 00102 DO 10 I = K, K + J - 1 00103 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00104 10 CONTINUE 00105 K = K + J 00106 20 CONTINUE 00107 ELSE 00108 K = 1 00109 DO 40 J = 1, N 00110 DO 30 I = K, K + N - J 00111 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00112 30 CONTINUE 00113 K = K + N - J + 1 00114 40 CONTINUE 00115 END IF 00116 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00117 $ ( NORM.EQ.'1' ) ) THEN 00118 * 00119 * Find normI(A) ( = norm1(A), since A is symmetric). 00120 * 00121 VALUE = ZERO 00122 K = 1 00123 IF( LSAME( UPLO, 'U' ) ) THEN 00124 DO 60 J = 1, N 00125 SUM = ZERO 00126 DO 50 I = 1, J - 1 00127 ABSA = ABS( AP( K ) ) 00128 SUM = SUM + ABSA 00129 WORK( I ) = WORK( I ) + ABSA 00130 K = K + 1 00131 50 CONTINUE 00132 WORK( J ) = SUM + ABS( AP( K ) ) 00133 K = K + 1 00134 60 CONTINUE 00135 DO 70 I = 1, N 00136 VALUE = MAX( VALUE, WORK( I ) ) 00137 70 CONTINUE 00138 ELSE 00139 DO 80 I = 1, N 00140 WORK( I ) = ZERO 00141 80 CONTINUE 00142 DO 100 J = 1, N 00143 SUM = WORK( J ) + ABS( AP( K ) ) 00144 K = K + 1 00145 DO 90 I = J + 1, N 00146 ABSA = ABS( AP( K ) ) 00147 SUM = SUM + ABSA 00148 WORK( I ) = WORK( I ) + ABSA 00149 K = K + 1 00150 90 CONTINUE 00151 VALUE = MAX( VALUE, SUM ) 00152 100 CONTINUE 00153 END IF 00154 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00155 * 00156 * Find normF(A). 00157 * 00158 SCALE = ZERO 00159 SUM = ONE 00160 K = 2 00161 IF( LSAME( UPLO, 'U' ) ) THEN 00162 DO 110 J = 2, N 00163 CALL CLASSQ( J-1, AP( K ), 1, SCALE, SUM ) 00164 K = K + J 00165 110 CONTINUE 00166 ELSE 00167 DO 120 J = 1, N - 1 00168 CALL CLASSQ( N-J, AP( K ), 1, SCALE, SUM ) 00169 K = K + N - J + 1 00170 120 CONTINUE 00171 END IF 00172 SUM = 2*SUM 00173 K = 1 00174 DO 130 I = 1, N 00175 IF( REAL( AP( K ) ).NE.ZERO ) THEN 00176 ABSA = ABS( REAL( AP( K ) ) ) 00177 IF( SCALE.LT.ABSA ) THEN 00178 SUM = ONE + SUM*( SCALE / ABSA )**2 00179 SCALE = ABSA 00180 ELSE 00181 SUM = SUM + ( ABSA / SCALE )**2 00182 END IF 00183 END IF 00184 IF( AIMAG( AP( K ) ).NE.ZERO ) THEN 00185 ABSA = ABS( AIMAG( AP( K ) ) ) 00186 IF( SCALE.LT.ABSA ) THEN 00187 SUM = ONE + SUM*( SCALE / ABSA )**2 00188 SCALE = ABSA 00189 ELSE 00190 SUM = SUM + ( ABSA / SCALE )**2 00191 END IF 00192 END IF 00193 IF( LSAME( UPLO, 'U' ) ) THEN 00194 K = K + I + 1 00195 ELSE 00196 K = K + N - I + 1 00197 END IF 00198 130 CONTINUE 00199 VALUE = SCALE*SQRT( SUM ) 00200 END IF 00201 * 00202 CLANSP = VALUE 00203 RETURN 00204 * 00205 * End of CLANSP 00206 * 00207 END
1.7.3 
