Annotation of rpl/lapack/lapack/dlansb.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
! 2: $ WORK )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER NORM, UPLO
! 11: INTEGER K, LDAB, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DLANSB returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of an
! 22: * n by n symmetric band matrix A, with k super-diagonals.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * DLANSB returns the value
! 28: *
! 29: * DLANSB = ( 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 DLANSB as described
! 47: * above.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * Specifies whether the upper or lower triangular part of the
! 51: * band matrix A is supplied.
! 52: * = 'U': Upper triangular part is supplied
! 53: * = 'L': Lower triangular part is supplied
! 54: *
! 55: * N (input) INTEGER
! 56: * The order of the matrix A. N >= 0. When N = 0, DLANSB is
! 57: * set to zero.
! 58: *
! 59: * K (input) INTEGER
! 60: * The number of super-diagonals or sub-diagonals of the
! 61: * band matrix A. K >= 0.
! 62: *
! 63: * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
! 64: * The upper or lower triangle of the symmetric band matrix A,
! 65: * stored in the first K+1 rows of AB. The j-th column of A is
! 66: * stored in the j-th column of the array AB as follows:
! 67: * if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
! 68: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
! 69: *
! 70: * LDAB (input) INTEGER
! 71: * The leading dimension of the array AB. LDAB >= K+1.
! 72: *
! 73: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 74: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 75: * WORK is not referenced.
! 76: *
! 77: * =====================================================================
! 78: *
! 79: * .. Parameters ..
! 80: DOUBLE PRECISION ONE, ZERO
! 81: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 82: * ..
! 83: * .. Local Scalars ..
! 84: INTEGER I, J, L
! 85: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
! 86: * ..
! 87: * .. External Subroutines ..
! 88: EXTERNAL DLASSQ
! 89: * ..
! 90: * .. External Functions ..
! 91: LOGICAL LSAME
! 92: EXTERNAL LSAME
! 93: * ..
! 94: * .. Intrinsic Functions ..
! 95: INTRINSIC ABS, MAX, MIN, SQRT
! 96: * ..
! 97: * .. Executable Statements ..
! 98: *
! 99: IF( N.EQ.0 ) THEN
! 100: VALUE = ZERO
! 101: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 102: *
! 103: * Find max(abs(A(i,j))).
! 104: *
! 105: VALUE = ZERO
! 106: IF( LSAME( UPLO, 'U' ) ) THEN
! 107: DO 20 J = 1, N
! 108: DO 10 I = MAX( K+2-J, 1 ), K + 1
! 109: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 110: 10 CONTINUE
! 111: 20 CONTINUE
! 112: ELSE
! 113: DO 40 J = 1, N
! 114: DO 30 I = 1, MIN( N+1-J, K+1 )
! 115: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 116: 30 CONTINUE
! 117: 40 CONTINUE
! 118: END IF
! 119: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 120: $ ( NORM.EQ.'1' ) ) THEN
! 121: *
! 122: * Find normI(A) ( = norm1(A), since A is symmetric).
! 123: *
! 124: VALUE = ZERO
! 125: IF( LSAME( UPLO, 'U' ) ) THEN
! 126: DO 60 J = 1, N
! 127: SUM = ZERO
! 128: L = K + 1 - J
! 129: DO 50 I = MAX( 1, J-K ), J - 1
! 130: ABSA = ABS( AB( L+I, J ) )
! 131: SUM = SUM + ABSA
! 132: WORK( I ) = WORK( I ) + ABSA
! 133: 50 CONTINUE
! 134: WORK( J ) = SUM + ABS( AB( K+1, 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( AB( 1, J ) )
! 145: L = 1 - J
! 146: DO 90 I = J + 1, MIN( N, J+K )
! 147: ABSA = ABS( AB( L+I, J ) )
! 148: SUM = SUM + ABSA
! 149: WORK( I ) = WORK( I ) + ABSA
! 150: 90 CONTINUE
! 151: VALUE = MAX( VALUE, SUM )
! 152: 100 CONTINUE
! 153: END IF
! 154: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 155: *
! 156: * Find normF(A).
! 157: *
! 158: SCALE = ZERO
! 159: SUM = ONE
! 160: IF( K.GT.0 ) THEN
! 161: IF( LSAME( UPLO, 'U' ) ) THEN
! 162: DO 110 J = 2, N
! 163: CALL DLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
! 164: $ 1, SCALE, SUM )
! 165: 110 CONTINUE
! 166: L = K + 1
! 167: ELSE
! 168: DO 120 J = 1, N - 1
! 169: CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
! 170: $ SUM )
! 171: 120 CONTINUE
! 172: L = 1
! 173: END IF
! 174: SUM = 2*SUM
! 175: ELSE
! 176: L = 1
! 177: END IF
! 178: CALL DLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
! 179: VALUE = SCALE*SQRT( SUM )
! 180: END IF
! 181: *
! 182: DLANSB = VALUE
! 183: RETURN
! 184: *
! 185: * End of DLANSB
! 186: *
! 187: END
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