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