Annotation of rpl/lapack/lapack/zlanhe.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER NORM, UPLO
! 10: INTEGER LDA, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION WORK( * )
! 14: COMPLEX*16 A( LDA, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLANHE returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of a
! 22: * complex hermitian matrix A.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANHE returns the value
! 28: *
! 29: * ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 30: * (
! 31: * ( norm1(A), NORM = '1', 'O' or 'o'
! 32: * (
! 33: * ( normI(A), NORM = 'I' or 'i'
! 34: * (
! 35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 36: *
! 37: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 38: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 39: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 41: *
! 42: * Arguments
! 43: * =========
! 44: *
! 45: * NORM (input) CHARACTER*1
! 46: * Specifies the value to be returned in ZLANHE as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the upper or lower triangular part of the
! 51: * hermitian matrix A is to be referenced.
! 52: * = 'U': Upper triangular part of A is referenced
! 53: * = 'L': Lower triangular part of A is referenced
! 54: *
! 55: * N (input) INTEGER
! 56: * The order of the matrix A. N >= 0. When N = 0, ZLANHE is
! 57: * set to zero.
! 58: *
! 59: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 60: * The hermitian matrix A. If UPLO = 'U', the leading n by n
! 61: * upper triangular part of A contains the upper triangular part
! 62: * of the matrix A, and the strictly lower triangular part of A
! 63: * is not referenced. If UPLO = 'L', the leading n by n lower
! 64: * triangular part of A contains the lower triangular part of
! 65: * the matrix A, and the strictly upper triangular part of A is
! 66: * not referenced. Note that the imaginary parts of the diagonal
! 67: * elements need not be set and are assumed to be zero.
! 68: *
! 69: * LDA (input) INTEGER
! 70: * The leading dimension of the array A. LDA >= max(N,1).
! 71: *
! 72: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 73: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 74: * WORK is not referenced.
! 75: *
! 76: * =====================================================================
! 77: *
! 78: * .. Parameters ..
! 79: DOUBLE PRECISION ONE, ZERO
! 80: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 81: * ..
! 82: * .. Local Scalars ..
! 83: INTEGER I, J
! 84: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 85: * ..
! 86: * .. External Functions ..
! 87: LOGICAL LSAME
! 88: EXTERNAL LSAME
! 89: * ..
! 90: * .. External Subroutines ..
! 91: EXTERNAL ZLASSQ
! 92: * ..
! 93: * .. Intrinsic Functions ..
! 94: INTRINSIC ABS, DBLE, MAX, SQRT
! 95: * ..
! 96: * .. Executable Statements ..
! 97: *
! 98: IF( N.EQ.0 ) THEN
! 99: VALUE = ZERO
! 100: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 101: *
! 102: * Find max(abs(A(i,j))).
! 103: *
! 104: VALUE = ZERO
! 105: IF( LSAME( UPLO, 'U' ) ) THEN
! 106: DO 20 J = 1, N
! 107: DO 10 I = 1, J - 1
! 108: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 109: 10 CONTINUE
! 110: VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
! 111: 20 CONTINUE
! 112: ELSE
! 113: DO 40 J = 1, N
! 114: VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
! 115: DO 30 I = J + 1, N
! 116: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 117: 30 CONTINUE
! 118: 40 CONTINUE
! 119: END IF
! 120: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 121: $ ( NORM.EQ.'1' ) ) THEN
! 122: *
! 123: * Find normI(A) ( = norm1(A), since A is hermitian).
! 124: *
! 125: VALUE = ZERO
! 126: IF( LSAME( UPLO, 'U' ) ) THEN
! 127: DO 60 J = 1, N
! 128: SUM = ZERO
! 129: DO 50 I = 1, J - 1
! 130: ABSA = ABS( A( I, J ) )
! 131: SUM = SUM + ABSA
! 132: WORK( I ) = WORK( I ) + ABSA
! 133: 50 CONTINUE
! 134: WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) )
! 135: 60 CONTINUE
! 136: DO 70 I = 1, N
! 137: VALUE = MAX( VALUE, WORK( I ) )
! 138: 70 CONTINUE
! 139: ELSE
! 140: DO 80 I = 1, N
! 141: WORK( I ) = ZERO
! 142: 80 CONTINUE
! 143: DO 100 J = 1, N
! 144: SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) )
! 145: DO 90 I = J + 1, N
! 146: ABSA = ABS( A( I, J ) )
! 147: SUM = SUM + ABSA
! 148: WORK( I ) = WORK( I ) + ABSA
! 149: 90 CONTINUE
! 150: VALUE = MAX( VALUE, SUM )
! 151: 100 CONTINUE
! 152: END IF
! 153: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 154: *
! 155: * Find normF(A).
! 156: *
! 157: SCALE = ZERO
! 158: SUM = ONE
! 159: IF( LSAME( UPLO, 'U' ) ) THEN
! 160: DO 110 J = 2, N
! 161: CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
! 162: 110 CONTINUE
! 163: ELSE
! 164: DO 120 J = 1, N - 1
! 165: CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
! 166: 120 CONTINUE
! 167: END IF
! 168: SUM = 2*SUM
! 169: DO 130 I = 1, N
! 170: IF( DBLE( A( I, I ) ).NE.ZERO ) THEN
! 171: ABSA = ABS( DBLE( A( I, I ) ) )
! 172: IF( SCALE.LT.ABSA ) THEN
! 173: SUM = ONE + SUM*( SCALE / ABSA )**2
! 174: SCALE = ABSA
! 175: ELSE
! 176: SUM = SUM + ( ABSA / SCALE )**2
! 177: END IF
! 178: END IF
! 179: 130 CONTINUE
! 180: VALUE = SCALE*SQRT( SUM )
! 181: END IF
! 182: *
! 183: ZLANHE = VALUE
! 184: RETURN
! 185: *
! 186: * End of ZLANHE
! 187: *
! 188: END
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