Annotation of rpl/lapack/lapack/zlansy.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANSY( 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: * ZLANSY 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 symmetric matrix A.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANSY returns the value
! 28: *
! 29: * ZLANSY = ( 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 ZLANSY as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the upper or lower triangular part of the
! 51: * symmetric 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, ZLANSY is
! 57: * set to zero.
! 58: *
! 59: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 60: * The symmetric 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.
! 67: *
! 68: * LDA (input) INTEGER
! 69: * The leading dimension of the array A. LDA >= max(N,1).
! 70: *
! 71: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 72: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 73: * WORK is not referenced.
! 74: *
! 75: * =====================================================================
! 76: *
! 77: * .. Parameters ..
! 78: DOUBLE PRECISION ONE, ZERO
! 79: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 80: * ..
! 81: * .. Local Scalars ..
! 82: INTEGER I, J
! 83: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 84: * ..
! 85: * .. External Functions ..
! 86: LOGICAL LSAME
! 87: EXTERNAL LSAME
! 88: * ..
! 89: * .. External Subroutines ..
! 90: EXTERNAL ZLASSQ
! 91: * ..
! 92: * .. Intrinsic Functions ..
! 93: INTRINSIC ABS, MAX, SQRT
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: IF( N.EQ.0 ) THEN
! 98: VALUE = ZERO
! 99: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 100: *
! 101: * Find max(abs(A(i,j))).
! 102: *
! 103: VALUE = ZERO
! 104: IF( LSAME( UPLO, 'U' ) ) THEN
! 105: DO 20 J = 1, N
! 106: DO 10 I = 1, J
! 107: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 108: 10 CONTINUE
! 109: 20 CONTINUE
! 110: ELSE
! 111: DO 40 J = 1, N
! 112: DO 30 I = J, N
! 113: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
! 114: 30 CONTINUE
! 115: 40 CONTINUE
! 116: END IF
! 117: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 118: $ ( NORM.EQ.'1' ) ) THEN
! 119: *
! 120: * Find normI(A) ( = norm1(A), since A is symmetric).
! 121: *
! 122: VALUE = ZERO
! 123: IF( LSAME( UPLO, 'U' ) ) THEN
! 124: DO 60 J = 1, N
! 125: SUM = ZERO
! 126: DO 50 I = 1, J - 1
! 127: ABSA = ABS( A( I, J ) )
! 128: SUM = SUM + ABSA
! 129: WORK( I ) = WORK( I ) + ABSA
! 130: 50 CONTINUE
! 131: WORK( J ) = SUM + ABS( A( J, J ) )
! 132: 60 CONTINUE
! 133: DO 70 I = 1, N
! 134: VALUE = MAX( VALUE, WORK( I ) )
! 135: 70 CONTINUE
! 136: ELSE
! 137: DO 80 I = 1, N
! 138: WORK( I ) = ZERO
! 139: 80 CONTINUE
! 140: DO 100 J = 1, N
! 141: SUM = WORK( J ) + ABS( A( J, J ) )
! 142: DO 90 I = J + 1, N
! 143: ABSA = ABS( A( I, J ) )
! 144: SUM = SUM + ABSA
! 145: WORK( I ) = WORK( I ) + ABSA
! 146: 90 CONTINUE
! 147: VALUE = MAX( VALUE, SUM )
! 148: 100 CONTINUE
! 149: END IF
! 150: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 151: *
! 152: * Find normF(A).
! 153: *
! 154: SCALE = ZERO
! 155: SUM = ONE
! 156: IF( LSAME( UPLO, 'U' ) ) THEN
! 157: DO 110 J = 2, N
! 158: CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
! 159: 110 CONTINUE
! 160: ELSE
! 161: DO 120 J = 1, N - 1
! 162: CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
! 163: 120 CONTINUE
! 164: END IF
! 165: SUM = 2*SUM
! 166: CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
! 167: VALUE = SCALE*SQRT( SUM )
! 168: END IF
! 169: *
! 170: ZLANSY = VALUE
! 171: RETURN
! 172: *
! 173: * End of ZLANSY
! 174: *
! 175: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlansy.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack