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Diffstat (limited to '2.3-1/src/fortran/lapack/zlanhe.f')
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diff --git a/2.3-1/src/fortran/lapack/zlanhe.f b/2.3-1/src/fortran/lapack/zlanhe.f new file mode 100644 index 00000000..86e57fcd --- /dev/null +++ b/2.3-1/src/fortran/lapack/zlanhe.f @@ -0,0 +1,187 @@ + DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER NORM, UPLO + INTEGER LDA, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION WORK( * ) + COMPLEX*16 A( LDA, * ) +* .. +* +* Purpose +* ======= +* +* ZLANHE returns the value of the one norm, or the Frobenius norm, or +* the infinity norm, or the element of largest absolute value of a +* complex hermitian matrix A. +* +* Description +* =========== +* +* ZLANHE returns the value +* +* ZLANHE = ( 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 ZLANHE as described +* above. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* hermitian matrix A is to be referenced. +* = 'U': Upper triangular part of A is referenced +* = 'L': Lower triangular part of A is referenced +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. When N = 0, ZLANHE is +* set to zero. +* +* A (input) COMPLEX*16 array, dimension (LDA,N) +* The hermitian matrix A. If UPLO = 'U', the leading n by n +* upper triangular part of A contains the upper triangular part +* of the matrix A, and the strictly lower triangular part of A +* is not referenced. If UPLO = 'L', the leading n by n lower +* triangular part of A contains the lower triangular part of +* the matrix A, and the strictly upper triangular part of A is +* not referenced. Note that the imaginary parts of the diagonal +* elements need not be set and are assumed to be zero. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(N,1). +* +* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), +* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, +* WORK is not referenced. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J + DOUBLE PRECISION ABSA, SCALE, SUM, VALUE +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL ZLASSQ +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, MAX, SQRT +* .. +* .. Executable Statements .. +* + IF( N.EQ.0 ) THEN + VALUE = ZERO + ELSE IF( LSAME( NORM, 'M' ) ) THEN +* +* Find max(abs(A(i,j))). +* + VALUE = ZERO + IF( LSAME( UPLO, 'U' ) ) THEN + DO 20 J = 1, N + DO 10 I = 1, J - 1 + VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + 10 CONTINUE + VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) ) + 20 CONTINUE + ELSE + DO 40 J = 1, N + VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) ) + DO 30 I = J + 1, N + VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + 30 CONTINUE + 40 CONTINUE + END IF + ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. + $ ( NORM.EQ.'1' ) ) THEN +* +* Find normI(A) ( = norm1(A), since A is hermitian). +* + VALUE = ZERO + IF( LSAME( UPLO, 'U' ) ) THEN + DO 60 J = 1, N + SUM = ZERO + DO 50 I = 1, J - 1 + ABSA = ABS( A( I, J ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + 50 CONTINUE + WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) ) + 60 CONTINUE + DO 70 I = 1, N + VALUE = MAX( VALUE, WORK( I ) ) + 70 CONTINUE + ELSE + DO 80 I = 1, N + WORK( I ) = ZERO + 80 CONTINUE + DO 100 J = 1, N + SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) ) + DO 90 I = J + 1, N + ABSA = ABS( A( I, J ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + 90 CONTINUE + VALUE = MAX( VALUE, SUM ) + 100 CONTINUE + END IF + ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN +* +* Find normF(A). +* + SCALE = ZERO + SUM = ONE + IF( LSAME( UPLO, 'U' ) ) THEN + DO 110 J = 2, N + CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) + 110 CONTINUE + ELSE + DO 120 J = 1, N - 1 + CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) + 120 CONTINUE + END IF + SUM = 2*SUM + DO 130 I = 1, N + IF( DBLE( A( I, I ) ).NE.ZERO ) THEN + ABSA = ABS( DBLE( A( I, I ) ) ) + IF( SCALE.LT.ABSA ) THEN + SUM = ONE + SUM*( SCALE / ABSA )**2 + SCALE = ABSA + ELSE + SUM = SUM + ( ABSA / SCALE )**2 + END IF + END IF + 130 CONTINUE + VALUE = SCALE*SQRT( SUM ) + END IF +* + ZLANHE = VALUE + RETURN +* +* End of ZLANHE +* + END |