Move LAPACK trunk into position.

1 files changed, 277 insertions, 0 deletions

diff --git a/SRC/zlantr.f b/SRC/zlantr.f
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+      DOUBLE PRECISION FUNCTION ZLANTR( 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   WORK( * )
+      COMPLEX*16         A( LDA, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  ZLANTR  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
+*  ===========
+*
+*  ZLANTR returns the value
+*
+*     ZLANTR = ( 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 ZLANTR 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, ZLANTR 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, ZLANTR is set to zero.
+*
+*  A       (input) COMPLEX*16 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 Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           ZLASSQ
+*     ..
+*     .. 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 ZLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
+  290          CONTINUE
+            ELSE
+               SCALE = ZERO
+               SUM = ONE
+               DO 300 J = 1, N
+                  CALL ZLASSQ( 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 ZLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
+     $                         SUM )
+  310          CONTINUE
+            ELSE
+               SCALE = ZERO
+               SUM = ONE
+               DO 320 J = 1, N
+                  CALL ZLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
+  320          CONTINUE
+            END IF
+         END IF
+         VALUE = SCALE*SQRT( SUM )
+      END IF
+*
+      ZLANTR = VALUE
+      RETURN
+*
+*     End of ZLANTR
+*
+      END