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- DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
- $ 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 LDA, M, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DLANTR returns the value of the one norm, or the Frobenius norm, or
-* the infinity norm, or the element of largest absolute value of a
-* trapezoidal or triangular matrix A.
-*
-* Description
-* ===========
-*
-* DLANTR returns the value
-*
-* DLANTR = ( 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 DLANTR as described
-* above.
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the matrix A is upper or lower trapezoidal.
-* = 'U': Upper trapezoidal
-* = 'L': Lower trapezoidal
-* Note that A is triangular instead of trapezoidal if M = N.
-*
-* DIAG (input) CHARACTER*1
-* Specifies whether or not the matrix A has unit diagonal.
-* = 'N': Non-unit diagonal
-* = 'U': Unit diagonal
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0, and if
-* UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero.
-*
-* N (input) INTEGER
-* The number of columns of the matrix A. N >= 0, and if
-* UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero.
-*
-* A (input) DOUBLE PRECISION array, dimension (LDA,N)
-* The trapezoidal matrix A (A is triangular if M = N).
-* If UPLO = 'U', the leading m by n upper trapezoidal part of
-* the array A contains the upper trapezoidal matrix, and the
-* strictly lower triangular part of A is not referenced.
-* If UPLO = 'L', the leading m by n lower trapezoidal part of
-* the array A contains the lower trapezoidal matrix, and the
-* strictly upper triangular part of A is not referenced. Note
-* that when DIAG = 'U', the diagonal elements of A are not
-* referenced and are assumed to be one.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(M,1).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
-* where LWORK >= M 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
- DOUBLE PRECISION SCALE, SUM, VALUE
-* ..
-* .. External Subroutines ..
- EXTERNAL DLASSQ
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, MIN, SQRT
-* ..
-* .. Executable Statements ..
-*
- IF( MIN( M, 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 = 1, MIN( M, J-1 )
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
- 10 CONTINUE
- 20 CONTINUE
- ELSE
- DO 40 J = 1, N
- DO 30 I = J + 1, M
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
- 30 CONTINUE
- 40 CONTINUE
- END IF
- ELSE
- VALUE = ZERO
- IF( LSAME( UPLO, 'U' ) ) THEN
- DO 60 J = 1, N
- DO 50 I = 1, MIN( M, J )
- VALUE = MAX( VALUE, ABS( A( I, J ) ) )
- 50 CONTINUE
- 60 CONTINUE
- ELSE
- DO 80 J = 1, N
- DO 70 I = J, M
- VALUE = MAX( VALUE, ABS( A( 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 ) .AND. ( J.LE.M ) ) THEN
- SUM = ONE
- DO 90 I = 1, J - 1
- SUM = SUM + ABS( A( I, J ) )
- 90 CONTINUE
- ELSE
- SUM = ZERO
- DO 100 I = 1, MIN( M, J )
- SUM = SUM + ABS( A( 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 = J + 1, M
- SUM = SUM + ABS( A( I, J ) )
- 120 CONTINUE
- ELSE
- SUM = ZERO
- DO 130 I = J, M
- SUM = SUM + ABS( A( I, J ) )
- 130 CONTINUE
- END IF
- VALUE = MAX( VALUE, SUM )
- 140 CONTINUE
- END IF
- ELSE IF( LSAME( NORM, 'I' ) ) THEN
-*
-* Find normI(A).
-*
- IF( LSAME( UPLO, 'U' ) ) THEN
- IF( LSAME( DIAG, 'U' ) ) THEN
- DO 150 I = 1, M
- WORK( I ) = ONE
- 150 CONTINUE
- DO 170 J = 1, N
- DO 160 I = 1, MIN( M, J-1 )
- WORK( I ) = WORK( I ) + ABS( A( I, J ) )
- 160 CONTINUE
- 170 CONTINUE
- ELSE
- DO 180 I = 1, M
- WORK( I ) = ZERO
- 180 CONTINUE
- DO 200 J = 1, N
- DO 190 I = 1, MIN( M, J )
- WORK( I ) = WORK( I ) + ABS( A( 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 220 I = N + 1, M
- WORK( I ) = ZERO
- 220 CONTINUE
- DO 240 J = 1, N
- DO 230 I = J + 1, M
- WORK( I ) = WORK( I ) + ABS( A( I, J ) )
- 230 CONTINUE
- 240 CONTINUE
- ELSE
- DO 250 I = 1, M
- WORK( I ) = ZERO
- 250 CONTINUE
- DO 270 J = 1, N
- DO 260 I = J, M
- WORK( I ) = WORK( I ) + ABS( A( I, J ) )
- 260 CONTINUE
- 270 CONTINUE
- END IF
- END IF
- VALUE = ZERO
- DO 280 I = 1, M
- VALUE = MAX( VALUE, WORK( I ) )
- 280 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 = MIN( M, N )
- DO 290 J = 2, N
- CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
- 290 CONTINUE
- ELSE
- SCALE = ZERO
- SUM = ONE
- DO 300 J = 1, N
- CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
- 300 CONTINUE
- END IF
- ELSE
- IF( LSAME( DIAG, 'U' ) ) THEN
- SCALE = ONE
- SUM = MIN( M, N )
- DO 310 J = 1, N
- CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
- $ SUM )
- 310 CONTINUE
- ELSE
- SCALE = ZERO
- SUM = ONE
- DO 320 J = 1, N
- CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
- 320 CONTINUE
- END IF
- END IF
- VALUE = SCALE*SQRT( SUM )
- END IF
-*
- DLANTR = VALUE
- RETURN
-*
-* End of DLANTR
-*
- END
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