zlantb.f

          DOUBLE PRECISION FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB,
         $                 LDAB, WORK )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, NORM, UPLO
          INTEGER            K, LDAB, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   WORK( * )
          COMPLEX*16         AB( LDAB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZLANTB  returns the value of the one norm,  or the Frobenius norm, or
    *  the  infinity norm,  or the element of  largest absolute value  of an
    *  n by n triangular band matrix A,  with ( k + 1 ) diagonals.
    *
    *  Description
    *  ===========
    *
    *  ZLANTB returns the value
    *
    *     ZLANTB = ( 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 ZLANTB as described
    *          above.
    *
    *  UPLO    (input) CHARACTER*1
    *          Specifies whether the matrix A is upper or lower triangular.
    *          = 'U':  Upper triangular
    *          = 'L':  Lower triangular
    *
    *  DIAG    (input) CHARACTER*1
    *          Specifies whether or not the matrix A is unit triangular.
    *          = 'N':  Non-unit triangular
    *          = 'U':  Unit triangular
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.  When N = 0, ZLANTB is
    *          set to zero.
    *
    *  K       (input) INTEGER
    *          The number of super-diagonals of the matrix A if UPLO = 'U',
    *          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
    *          K >= 0.
    *
    *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
    *          The upper or lower triangular band matrix A, stored in the
    *          first k+1 rows of AB.  The j-th column of A is stored
    *          in the j-th column of the array AB as follows:
    *          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
    *          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
    *          Note that when DIAG = 'U', the elements of the array AB
    *          corresponding to the diagonal elements of the matrix A are
    *          not referenced, but are assumed to be one.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= K+1.
    *
    *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
    *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
    *          referenced.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UDIAG
          INTEGER            I, J, L
          DOUBLE PRECISION   SCALE, SUM, VALUE
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           ZLASSQ
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, MAX, MIN, SQRT
    *     ..
    *     .. Executable Statements ..
    *
          IF( N.EQ.0 ) THEN
             VALUE = ZERO
          ELSE IF( LSAME( NORM, 'M' ) ) THEN
    *
    *        Find max(abs(A(i,j))).
    *
             IF( LSAME( DIAG, 'U' ) ) THEN
                VALUE = ONE
                IF( LSAME( UPLO, 'U' ) ) THEN
                   DO 20 J = 1, N
                      DO 10 I = MAX( K+2-J, 1 ), K
                         VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
       10             CONTINUE
       20          CONTINUE
                ELSE
                   DO 40 J = 1, N
                      DO 30 I = 2, MIN( N+1-J, K+1 )
                         VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
       30             CONTINUE
       40          CONTINUE
                END IF
             ELSE
                VALUE = ZERO
                IF( LSAME( UPLO, 'U' ) ) THEN
                   DO 60 J = 1, N
                      DO 50 I = MAX( K+2-J, 1 ), K + 1
                         VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
       50             CONTINUE
       60          CONTINUE
                ELSE
                   DO 80 J = 1, N
                      DO 70 I = 1, MIN( N+1-J, K+1 )
                         VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
       70             CONTINUE
       80          CONTINUE
                END IF
             END IF
          ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
    *
    *        Find norm1(A).
    *
             VALUE = ZERO
             UDIAG = LSAME( DIAG, 'U' )
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 110 J = 1, N
                   IF( UDIAG ) THEN
                      SUM = ONE
                      DO 90 I = MAX( K+2-J, 1 ), K
                         SUM = SUM + ABS( AB( I, J ) )
       90             CONTINUE
                   ELSE
                      SUM = ZERO
                      DO 100 I = MAX( K+2-J, 1 ), K + 1
                         SUM = SUM + ABS( AB( I, J ) )
      100             CONTINUE
                   END IF
                   VALUE = MAX( VALUE, SUM )
      110       CONTINUE
             ELSE
                DO 140 J = 1, N
                   IF( UDIAG ) THEN
                      SUM = ONE
                      DO 120 I = 2, MIN( N+1-J, K+1 )
                         SUM = SUM + ABS( AB( I, J ) )
      120             CONTINUE
                   ELSE
                      SUM = ZERO
                      DO 130 I = 1, MIN( N+1-J, K+1 )
                         SUM = SUM + ABS( AB( I, J ) )
      130             CONTINUE
                   END IF
                   VALUE = MAX( VALUE, SUM )
      140       CONTINUE
             END IF
          ELSE IF( LSAME( NORM, 'I' ) ) THEN
    *
    *        Find normI(A).
    *
             VALUE = ZERO
             IF( LSAME( UPLO, 'U' ) ) THEN
                IF( LSAME( DIAG, 'U' ) ) THEN
                   DO 150 I = 1, N
                      WORK( I ) = ONE
      150          CONTINUE
                   DO 170 J = 1, N
                      L = K + 1 - J
                      DO 160 I = MAX( 1, J-K ), J - 1
                         WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
      160             CONTINUE
      170          CONTINUE
                ELSE
                   DO 180 I = 1, N
                      WORK( I ) = ZERO
      180          CONTINUE
                   DO 200 J = 1, N
                      L = K + 1 - J
                      DO 190 I = MAX( 1, J-K ), J
                         WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
      190             CONTINUE
      200          CONTINUE
                END IF
             ELSE
                IF( LSAME( DIAG, 'U' ) ) THEN
                   DO 210 I = 1, N
                      WORK( I ) = ONE
      210          CONTINUE
                   DO 230 J = 1, N
                      L = 1 - J
                      DO 220 I = J + 1, MIN( N, J+K )
                         WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
      220             CONTINUE
      230          CONTINUE
                ELSE
                   DO 240 I = 1, N
                      WORK( I ) = ZERO
      240          CONTINUE
                   DO 260 J = 1, N
                      L = 1 - J
                      DO 250 I = J, MIN( N, J+K )
                         WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
      250             CONTINUE
      260          CONTINUE
                END IF
             END IF
             DO 270 I = 1, N
                VALUE = MAX( VALUE, WORK( I ) )
      270    CONTINUE
          ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
    *
    *        Find normF(A).
    *
             IF( LSAME( UPLO, 'U' ) ) THEN
                IF( LSAME( DIAG, 'U' ) ) THEN
                   SCALE = ONE
                   SUM = N
                   IF( K.GT.0 ) THEN
                      DO 280 J = 2, N
                         CALL ZLASSQ( MIN( J-1, K ),
         $                            AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
         $                            SUM )
      280             CONTINUE
                   END IF
                ELSE
                   SCALE = ZERO
                   SUM = ONE
                   DO 290 J = 1, N
                      CALL ZLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
         $                         1, SCALE, SUM )
      290          CONTINUE
                END IF
             ELSE
                IF( LSAME( DIAG, 'U' ) ) THEN
                   SCALE = ONE
                   SUM = N
                   IF( K.GT.0 ) THEN
                      DO 300 J = 1, N - 1
                         CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
         $                            SUM )
      300             CONTINUE
                   END IF
                ELSE
                   SCALE = ZERO
                   SUM = ONE
                   DO 310 J = 1, N
                      CALL ZLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
         $                         SUM )
      310          CONTINUE
                END IF
             END IF
             VALUE = SCALE*SQRT( SUM )
          END IF
    *
          ZLANTB = VALUE
          RETURN
    *
    *     End of ZLANTB
    *
          END