Annotation of rpl/lapack/lapack/zlangb.f, revision 1.18

1.11      bertrand    1: *> \brief \b ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
1.8       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.15      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.8       bertrand    7: *
                      8: *> \htmlonly
1.15      bertrand    9: *> Download ZLANGB + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f">
1.8       bertrand   15: *> [TXT]</a>
1.15      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
                     22: *                        WORK )
1.15      bertrand   23: *
1.8       bertrand   24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          NORM
                     26: *       INTEGER            KL, KU, LDAB, N
                     27: *       ..
                     28: *       .. Array Arguments ..
                     29: *       DOUBLE PRECISION   WORK( * )
                     30: *       COMPLEX*16         AB( LDAB, * )
                     31: *       ..
1.15      bertrand   32: *
1.8       bertrand   33: *
                     34: *> \par Purpose:
                     35: *  =============
                     36: *>
                     37: *> \verbatim
                     38: *>
                     39: *> ZLANGB  returns the value of the one norm,  or the Frobenius norm, or
                     40: *> the  infinity norm,  or the element of  largest absolute value  of an
                     41: *> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
                     42: *> \endverbatim
                     43: *>
                     44: *> \return ZLANGB
                     45: *> \verbatim
                     46: *>
                     47: *>    ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                     48: *>             (
                     49: *>             ( norm1(A),         NORM = '1', 'O' or 'o'
                     50: *>             (
                     51: *>             ( normI(A),         NORM = 'I' or 'i'
                     52: *>             (
                     53: *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
                     54: *>
                     55: *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
                     56: *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
                     57: *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
                     58: *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
                     59: *> \endverbatim
                     60: *
                     61: *  Arguments:
                     62: *  ==========
                     63: *
                     64: *> \param[in] NORM
                     65: *> \verbatim
                     66: *>          NORM is CHARACTER*1
                     67: *>          Specifies the value to be returned in ZLANGB as described
                     68: *>          above.
                     69: *> \endverbatim
                     70: *>
                     71: *> \param[in] N
                     72: *> \verbatim
                     73: *>          N is INTEGER
                     74: *>          The order of the matrix A.  N >= 0.  When N = 0, ZLANGB is
                     75: *>          set to zero.
                     76: *> \endverbatim
                     77: *>
                     78: *> \param[in] KL
                     79: *> \verbatim
                     80: *>          KL is INTEGER
                     81: *>          The number of sub-diagonals of the matrix A.  KL >= 0.
                     82: *> \endverbatim
                     83: *>
                     84: *> \param[in] KU
                     85: *> \verbatim
                     86: *>          KU is INTEGER
                     87: *>          The number of super-diagonals of the matrix A.  KU >= 0.
                     88: *> \endverbatim
                     89: *>
                     90: *> \param[in] AB
                     91: *> \verbatim
                     92: *>          AB is COMPLEX*16 array, dimension (LDAB,N)
                     93: *>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
                     94: *>          column of A is stored in the j-th column of the array AB as
                     95: *>          follows:
                     96: *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
                     97: *> \endverbatim
                     98: *>
                     99: *> \param[in] LDAB
                    100: *> \verbatim
                    101: *>          LDAB is INTEGER
                    102: *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
                    103: *> \endverbatim
                    104: *>
                    105: *> \param[out] WORK
                    106: *> \verbatim
                    107: *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
                    108: *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
                    109: *>          referenced.
                    110: *> \endverbatim
                    111: *
                    112: *  Authors:
                    113: *  ========
                    114: *
1.15      bertrand  115: *> \author Univ. of Tennessee
                    116: *> \author Univ. of California Berkeley
                    117: *> \author Univ. of Colorado Denver
                    118: *> \author NAG Ltd.
1.8       bertrand  119: *
1.15      bertrand  120: *> \date December 2016
1.8       bertrand  121: *
                    122: *> \ingroup complex16GBauxiliary
                    123: *
                    124: *  =====================================================================
1.1       bertrand  125:       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
                    126:      $                 WORK )
                    127: *
1.15      bertrand  128: *  -- LAPACK auxiliary routine (version 3.7.0) --
1.1       bertrand  129: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    130: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15      bertrand  131: *     December 2016
1.1       bertrand  132: *
1.18    ! bertrand  133:       IMPLICIT NONE
1.1       bertrand  134: *     .. Scalar Arguments ..
                    135:       CHARACTER          NORM
                    136:       INTEGER            KL, KU, LDAB, N
                    137: *     ..
                    138: *     .. Array Arguments ..
                    139:       DOUBLE PRECISION   WORK( * )
                    140:       COMPLEX*16         AB( LDAB, * )
                    141: *     ..
                    142: *
                    143: * =====================================================================
                    144: *
                    145: *     .. Parameters ..
                    146:       DOUBLE PRECISION   ONE, ZERO
                    147:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
                    148: *     ..
                    149: *     .. Local Scalars ..
                    150:       INTEGER            I, J, K, L
1.18    ! bertrand  151:       DOUBLE PRECISION   SUM, VALUE, TEMP
        !           152: *     ..
        !           153: *     .. Local Arrays ..
        !           154:       DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
1.1       bertrand  155: *     ..
                    156: *     .. External Functions ..
1.11      bertrand  157:       LOGICAL            LSAME, DISNAN
                    158:       EXTERNAL           LSAME, DISNAN
1.1       bertrand  159: *     ..
                    160: *     .. External Subroutines ..
1.18    ! bertrand  161:       EXTERNAL           ZLASSQ, DCOMBSSQ
1.1       bertrand  162: *     ..
                    163: *     .. Intrinsic Functions ..
                    164:       INTRINSIC          ABS, MAX, MIN, SQRT
                    165: *     ..
                    166: *     .. Executable Statements ..
                    167: *
                    168:       IF( N.EQ.0 ) THEN
                    169:          VALUE = ZERO
                    170:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
                    171: *
                    172: *        Find max(abs(A(i,j))).
                    173: *
                    174:          VALUE = ZERO
                    175:          DO 20 J = 1, N
                    176:             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
1.11      bertrand  177:                TEMP = ABS( AB( I, J ) )
                    178:                IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
1.1       bertrand  179:    10       CONTINUE
                    180:    20    CONTINUE
                    181:       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
                    182: *
                    183: *        Find norm1(A).
                    184: *
                    185:          VALUE = ZERO
                    186:          DO 40 J = 1, N
                    187:             SUM = ZERO
                    188:             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
                    189:                SUM = SUM + ABS( AB( I, J ) )
                    190:    30       CONTINUE
1.11      bertrand  191:             IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1       bertrand  192:    40    CONTINUE
                    193:       ELSE IF( LSAME( NORM, 'I' ) ) THEN
                    194: *
                    195: *        Find normI(A).
                    196: *
                    197:          DO 50 I = 1, N
                    198:             WORK( I ) = ZERO
                    199:    50    CONTINUE
                    200:          DO 70 J = 1, N
                    201:             K = KU + 1 - J
                    202:             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
                    203:                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
                    204:    60       CONTINUE
                    205:    70    CONTINUE
                    206:          VALUE = ZERO
                    207:          DO 80 I = 1, N
1.11      bertrand  208:             TEMP = WORK( I )
                    209:             IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
1.1       bertrand  210:    80    CONTINUE
                    211:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
                    212: *
                    213: *        Find normF(A).
1.18    ! bertrand  214: *        SSQ(1) is scale
        !           215: *        SSQ(2) is sum-of-squares
        !           216: *        For better accuracy, sum each column separately.
1.1       bertrand  217: *
1.18    ! bertrand  218:          SSQ( 1 ) = ZERO
        !           219:          SSQ( 2 ) = ONE
1.1       bertrand  220:          DO 90 J = 1, N
                    221:             L = MAX( 1, J-KU )
                    222:             K = KU + 1 - J + L
1.18    ! bertrand  223:             COLSSQ( 1 ) = ZERO
        !           224:             COLSSQ( 2 ) = ONE
        !           225:             CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
        !           226:      $                   COLSSQ( 1 ), COLSSQ( 2 ) )
        !           227:             CALL DCOMBSSQ( SSQ, COLSSQ )
1.1       bertrand  228:    90    CONTINUE
1.18    ! bertrand  229:          VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
1.1       bertrand  230:       END IF
                    231: *
                    232:       ZLANGB = VALUE
                    233:       RETURN
                    234: *
                    235: *     End of ZLANGB
                    236: *
                    237:       END

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